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<h1>修正されたアダム (RaDAM) オプティマイザー</h1>
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<p>この実装は<a href="https://github.com/LiyuanLucasLiu/RAdam">、「<a href="https://papers.labml.ai/paper/1908.03265">適応学習率とその後の差異に関する論文」の公式実装に基づいています</a></a>。</p>
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<p><a href="https://pytorch.org">amsGrad実装の拡張としてPyTorchに実装したので</a><a href="amsgrad.html">、実装する必要があるのは変更だけです</a>。</p>
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<p>アダムオプティマイザーは、トレーニングの初期段階、特にトランスフォーマーをトレーニングしているときに、不適切な局所最適値に収束することがあります。研究者はこれに対抗するためにウォームアップを使います。最初のトレーニングステップ（ウォームアップ段階）では低い学習率を使います。本稿では、トレーニングの初期段階における適応学習率のばらつきが大きいという問題を特定し、分散を減らすための新しい修正項を用いてその問題に対処しています</p>。
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<p>この論文では、2つの分散削減メカニズムについても評価しています。<em><strong>Adam-2k</strong>：パラメータを変更したり、運動量を計算したりせずに、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcg" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>最初の2kステップでは（<a href="adam.html">Adamで</a>）適応学習率のみを計算します</em>（）。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqce" style=""><span class="mord" style=""><span class="mord mathnormal" style="">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span><strong>Adam-EPS</strong>: アダム・ウィズ・ラージ・ウィズ・ラージ</p>. <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.48312em;vertical-align:0em;"></span><span class="mord coloredeq eqbv" style=""><span class="mord mathnormal" style="">ϵ</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span></span></span></span>
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<h2>正義のアダム</h2>
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<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbf" style=""><span class="mord mathnormal" style="margin-right:0.03588em">ψ</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">...</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqcd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span>運動量と適応学習率を計算する関数としましょう<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">...</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqcd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span>。アダムにとって、彼らは</p>
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<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:6.225502em;vertical-align:-2.862751em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.362751em;"><span style="top:-5.5893250000000005em;"><span class="pstrut" style="height:3.84974em;"></span><span class="mord"><span class="mord coloredeq eqbd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">...</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqcd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-2.4772490000000005em;"><span class="pstrut" style="height:3.84974em;"></span><span class="mord"><span class="mord coloredeq eqbf" style=""><span class="mord mathnormal" style="margin-right:0.03588em">ψ</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">...</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqcd" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.862751em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.362751em;"><span style="top:-5.5893250000000005em;"><span class="pstrut" style="height:3.84974em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231659999999999em;"><span style="top:-2.2321040000000005em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbk" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqbw" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.6897100000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqbw" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.933456em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqbw" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9090039999999999em;"><span style="top:-3.14734em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">i</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9623359999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.4772490000000005em;"><span class="pstrut" style="height:3.84974em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8497400000000002em;"><span class="svg-align" style="top:-5em;"><span class="pstrut" style="height:5em;"></span><span class="mord" style="padding-left:1em;"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5548959999999998em;"><span style="top:-2.1765440000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.933456em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9090039999999999em;"><span style="top:-3.14734em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">i</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7959080000000001em;"><span style="top:-2.4231360000000004em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbl" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqbr" style=""><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.1231659999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span style="top:-3.80974em;"><span class="pstrut" style="height:5em;"></span><span class="hide-tail" style="min-width:1.02em;height:3.08em;"><svg height="3.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 3240" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M473,2793
|
||
c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0
|
||
c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7
|
||
s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9
|
||
c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200
|
||
c0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26
|
||
s76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,
|
||
606zM1001 80h400000v40H1017.7z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.1902599999999999em;"><span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.862751em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><h3>単純移動平均としての指数移動平均</h3>
|
||
<p>指数移動平均の分布は、単純な移動平均として近似できます。</p>
|
||
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.30003em;vertical-align:-1.400015em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.900015em;"><span style="top:-3.9000150000000002em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord coloredeq eqch" style=""><span class="mord mathnormal" style="">p</span></span><span class="mord"><span class="delimsizing size4">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231659999999999em;"><span style="top:-2.2321040000000005em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbl" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqbr" style=""><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.6897100000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.933456em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9090039999999999em;"><span style="top:-3.14734em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">i</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9623359999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="delimsizing size4">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqch" style=""><span class="mord mathnormal" style="">p</span></span><span class="mord"><span class="delimsizing size4">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7348949999999999em;"><span style="top:-2.3419em;"><span class="pstrut" style="height:3.0279em;"></span><span class="mord"><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqcj" style="">t</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-3.2579em;"><span class="pstrut" style="height:3.0279em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.734895em;"><span class="pstrut" style="height:3.0279em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0278999999999998em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqbo" style=""><span class="mord mathnormal mtight" style="margin-right:0.10764em">f</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbx" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="mclose mtight" style="">)</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.316995em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="delimsizing size4">)</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.400015em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>ここでは、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqcj" style="">t</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span>最後の勾配の単純移動平均を取っています。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqcj" style="">t</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span>以下を満たし、</p>
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<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.979946em;vertical-align:-1.239973em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.739973em;"><span style="top:-3.739973em;"><span class="pstrut" style="height:3.71761em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231659999999999em;"><span style="top:-2.2321040000000005em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbl" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqbr" style=""><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.6897100000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.933456em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9090039999999999em;"><span style="top:-3.14734em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">i</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9623359999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.71761em;"><span style="top:-2.3419em;"><span class="pstrut" style="height:3.0279em;"></span><span class="mord"><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqcj" style="">t</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-3.2579em;"><span class="pstrut" style="height:3.0279em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.71761em;"><span class="pstrut" style="height:3.0279em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0278999999999998em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqbo" style=""><span class="mord mathnormal mtight" style="margin-right:0.10764em">f</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbx" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="mclose mtight" style="">)</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqcj" style=""><span class="mord mathnormal" style="">t</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal">i</span><span class="mclose">)</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.239973em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>これにより、<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqcj" style="">t</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.20188em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.517232em;vertical-align:-0.9623359999999999em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5548959999999998em;"><span style="top:-2.2321040000000005em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbl" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqbr" style=""><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mord coloredeq eqcj" style=""><span class="mord mathnormal" style="">t</span></span><span class="mord coloredeq eqbr" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9623359999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></p>
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<h3>スケーリングされた逆カイ二乗</h3>
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<p>上から見ると、<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></span><span class="mord coloredeq eqch" style=""><span class="mord mathnormal" style="">p</span></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">...</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqcd" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord"><span class="delimsizing size2">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em;"></span><span class="mord coloredeq eqch" style=""><span class="mord mathnormal" style="">p</span></span><span class="mord"><span class="delimsizing size4">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7348949999999999em;"><span style="top:-2.3419em;"><span class="pstrut" style="height:3.0279em;"></span><span class="mord"><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqcj" style="">t</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-3.2579em;"><span class="pstrut" style="height:3.0279em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.734895em;"><span class="pstrut" style="height:3.0279em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0278999999999998em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqbo" style=""><span class="mord mathnormal mtight" style="margin-right:0.10764em">f</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbx" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="mclose mtight" style="">)</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.316995em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="delimsizing size4">)</span></span></span></span></span></span></span>場所がわかります<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathcal" style="margin-right:0.14736em;">N</span><span class="mopen">(</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span>。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">ma</span></span></span></span></span>これは標準偏差であり、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbu" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="mopen" style="">(</span><span class="mord" style="">.</span><span class="mclose" style="">)</span></span></span></span></span></span>運動量とは異なることに注意してください</p>。
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<p><a href="https://en.wikipedia.org/wiki/Scaled_inverse_chi-squared_distribution">スケーリングされた逆カイ二乗は</a>、正規分布の平均の二乗逆数の分布です。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqch" style=""><span class="mord mathnormal" style="">p</span></span></span></span></span></span><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em;"></span><span class="mord coloredeq eqch" style=""><span class="mord mathnormal" style="">p</span></span><span class="mord"><span class="delimsizing size4">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7348949999999999em;"><span style="top:-2.3419em;"><span class="pstrut" style="height:3.0279em;"></span><span class="mord"><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqcj" style="">t</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span><span style="top:-3.2579em;"><span class="pstrut" style="height:3.0279em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.734895em;"><span class="pstrut" style="height:3.0279em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0278999999999998em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqbo" style=""><span class="mord mathnormal mtight" style="margin-right:0.10764em">f</span><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mpunct mtight" style="">,</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbx" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="mclose mtight" style="">)</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-2.441336em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.316995em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="delimsizing size4">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.00744em;vertical-align:-0.686em;"></span><span class="mord coloredeq eqz" style=""><span class="mord text" style=""><span class="mord" style="">Scale-inv</span></span><span class="mord" style=""><span class="mord mathcal" style="margin-right:0.14643em">X</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">ρ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose">)</span></span></span></span></span></span>どこ<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbo" style=""><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqcj" style="">t</span></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span>。</p>
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<h3>整流</h3>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqby" style=""><span class="mord mathnormal" style="margin-right:0.03588em">ψ</span><span class="mopen" style="">(</span><span class="mord" style="">.</span><span class="mclose" style="">)</span></span></span></span></span></span>時間とともにばらつきが小さくなることを証明しています<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span></span></span></span></span>。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">.</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.190108em;vertical-align:-0.345em;"></span><span class="mord coloredeq eqz" style=""><span class="mord text" style=""><span class="mord" style="">Scale-inv</span></span><span class="mord" style=""><span class="mord mathcal" style="margin-right:0.14643em">X</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">ρ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463142857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose">)</span></span></span></span></span></p>
|
||
<p>したがって、分散は最大値<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span></span></span></span></span>、つまりで最小化されます。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.326216em;vertical-align:-0.481108em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mtight coloredeq eqbx" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.481108em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span></span>最小分散を次の式にしましょう <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqbi" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.07153em">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">va</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqci" style="">r</span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqby" style=""><span class="mord mathnormal" style="margin-right:0.03588em">ψ</span><span class="mopen" style="">(</span><span class="mord" style="">.</span><span class="mclose" style="">)</span></span></span></span></span></span>適応型学習率のばらつきが一貫していることを確認するために、差異を以下のように修正します。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqci" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span></span></span></span></span></p>
|
||
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.34em;vertical-align:-1.4200000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9199999999999997em;"><span style="top:-3.92em;"><span class="pstrut" style="height:3.769035em;"></span><span class="mord"><span class="mord coloredeq eqci" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7690350000000001em;"><span class="svg-align" style="top:-5em;"><span class="pstrut" style="height:5em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.2600000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbe" style=""><span class="mord mathnormal" style="">Va</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">[</span></span></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqby" style="margin-right:0.03588em">ψ</span><span class="mopen coloredeq eqby" style="">(</span><span class="mord coloredeq eqby" style="">.</span><span class="mclose coloredeq eqby" style="">)</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">]</span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbi" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.07153em">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">va</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqci" style="">r</span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.09001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.729035em;"><span class="pstrut" style="height:5em;"></span><span class="hide-tail" style="min-width:1.02em;height:3.08em;"><svg height="3.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 3240" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M473,2793
|
||
c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0
|
||
c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7
|
||
s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9
|
||
c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200
|
||
c0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26
|
||
s76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,
|
||
606zM1001 80h400000v40H1017.7z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.270965em;"><span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.4200000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><h3>おおよその値 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbm" style=""><span class="mord mathnormal" style="">Va</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqby" style="margin-right:0.03588em">ψ</span><span class="mopen coloredeq eqby" style="">(</span><span class="mord coloredeq eqby" style="">.</span><span class="mclose coloredeq eqby" style="">)</span></span><span class="mclose" style="">]</span></span></span></span></span></span></h3>
|
||
<p>どう導き出されたのかわからなかった <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.24em;vertical-align:-0.30499999999999994em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.935em;"><span class="svg-align" style="top:-3.2em;"><span class="pstrut" style="height:3.2em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">.</span><span class="mclose">)</span></span></span><span style="top:-2.8950000000000005em;"><span class="pstrut" style="height:3.2em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.28em;"><svg height="1.28em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1296" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M263,681c0.7,0,18,39.7,52,119
|
||
c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120
|
||
c340,-704.7,510.7,-1060.3,512,-1067
|
||
l0 -0
|
||
c4.7,-7.3,11,-11,19,-11
|
||
H40000v40H1012.3
|
||
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232
|
||
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
|
||
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26
|
||
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
|
||
M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.30499999999999994em;"><span></span></span></span></span></span></span></span></span></span> 🤪 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbm" style=""><span class="mord mathnormal" style="">Va</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqby" style="margin-right:0.03588em">ψ</span><span class="mopen coloredeq eqby" style="">(</span><span class="mord coloredeq eqby" style="">.</span><span class="mclose coloredeq eqby" style="">)</span></span><span class="mclose" style="">]</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.62892em;vertical-align:-0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.10892em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">4</span><span class="mord mathbb mtight">E</span><span class="mopen mtight">[</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">ψ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463142857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mtight">.</span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">Va</span><span class="mord mtight coloredeq eqci" style=""><span class="mord mathnormal mtight" style="margin-right:0.02778em">r</span></span><span class="mopen mtight">[</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">ψ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913142857142857em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mtight">.</span><span class="mclose mtight">)]</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> の一次展開に基づいて見積もっています。</p>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="mord coloredeq eqz" style=""><span class="mord text" style=""><span class="mord" style="">Scale-inv</span></span><span class="mord" style=""><span class="mord mathcal" style="margin-right:0.14643em">X</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span></span></span></span></span></span></span></span></span></span>私たちが持っているディストリビューションから、</p>
|
||
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:5.398656000000001em;vertical-align:-2.4493280000000004em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.9493280000000004em;"><span style="top:-4.949328em;"><span class="pstrut" style="height:3.491108em;"></span><span class="mord"><span class="mord mathbb">E</span><span class="mord"><span class="delimsizing size1">[</span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">.</span><span class="mclose">)</span><span class="mord"><span class="delimsizing size1">]</span></span></span></span><span style="top:-2.27778em;"><span class="pstrut" style="height:3.491108em;"></span><span class="mord"><span class="mord mathnormal">Va</span><span class="mord coloredeq eqci" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span class="mord"><span class="delimsizing size1">[</span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">.</span><span class="mclose">)</span><span class="mord"><span class="delimsizing size1">]</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.4493280000000004em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.9493280000000004em;"><span style="top:-4.949328em;"><span class="pstrut" style="height:3.491108em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.491108em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="mord">/</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.27778em;"><span class="pstrut" style="height:3.491108em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.491108em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="mord">/</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.4493280000000004em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>これにより、<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbm" style=""><span class="mord mathnormal" style="">Va</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqby" style="margin-right:0.03588em">ψ</span><span class="mopen coloredeq eqby" style="">(</span><span class="mord coloredeq eqby" style="">.</span><span class="mclose coloredeq eqby" style="">)</span></span><span class="mclose" style="">]</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.04356em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mopen">(</span><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></p>
|
||
<h3>修正期間</h3>
|
||
<p>私たちは持っています</p>
|
||
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:5.683559999999999em;vertical-align:-2.591779999999999em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.09178em;"><span style="top:-5.09178em;"><span class="pstrut" style="height:3.769035em;"></span><span class="mord"><span class="mord coloredeq eqci" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span></span></span><span style="top:-2.4132550000000013em;"><span class="pstrut" style="height:3.769035em;"></span><span class="mord"><span class="mord coloredeq eqbm" style=""><span class="mord mathnormal" style="">Va</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="mopen" style="">[</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqby" style="margin-right:0.03588em">ψ</span><span class="mopen coloredeq eqby" style="">(</span><span class="mord coloredeq eqby" style="">.</span><span class="mclose coloredeq eqby" style="">)</span></span><span class="mclose" style="">]</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.591779999999999em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.09178em;"><span style="top:-5.09178em;"><span class="pstrut" style="height:3.769035em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.7690350000000001em;"><span class="svg-align" style="top:-5em;"><span class="pstrut" style="height:5em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em;"><span style="top:-2.2600000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbe" style=""><span class="mord mathnormal" style="">Va</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">[</span></span></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqby" style="margin-right:0.03588em">ψ</span><span class="mopen coloredeq eqby" style="">(</span><span class="mord coloredeq eqby" style="">.</span><span class="mclose coloredeq eqby" style="">)</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">]</span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbi" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.07153em">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">va</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqci" style="">r</span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.09001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.729035em;"><span class="pstrut" style="height:5em;"></span><span class="hide-tail" style="min-width:1.02em;height:3.08em;"><svg height="3.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 3240" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M473,2793
|
||
c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0
|
||
c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7
|
||
s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9
|
||
c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200
|
||
c0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26
|
||
s76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,
|
||
606zM1001 80h400000v40H1017.7z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.270965em;"><span></span></span></span></span></span></span></span><span style="top:-2.4132550000000013em;"><span class="pstrut" style="height:3.769035em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mopen">(</span><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.591779999999999em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqbi" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.07153em">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">va</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqci" style="">r</span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em;"></span><span class="mord coloredeq eqbe" style=""><span class="mord mathnormal" style="">Va</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">[</span></span></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqby" style="margin-right:0.03588em">ψ</span><span class="mopen coloredeq eqby" style="">(</span><span class="mord coloredeq eqby" style="">.</span><span class="mclose coloredeq eqby" style="">)</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">]</span></span></span></span></span></span></span></span>どこが<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbp" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>.<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span></span></span></span></span><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord coloredeq eqcj" style=""><span class="mord mathnormal" style="">t</span></span></span></span></span></span>一歩を踏み出して<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>段階的な修正項になりなさい</p>。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord coloredeq eqcj" style=""><span class="mord mathnormal" style="">t</span></span></span></span></span></span>
|
||
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:4.68712em;vertical-align:-2.09356em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.59356em;"><span style="top:-4.59356em;"><span class="pstrut" style="height:3.10756em;"></span><span class="mord"><span class="mord coloredeq eqbi" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.07153em">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">va</span><span class="mord mtight" style=""><span class="mord mtight coloredeq eqci" style="">r</span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.10756em;"></span><span class="mord"><span class="mord mathnormal">Va</span><span class="mord coloredeq eqci" style=""><span class="mord mathnormal" style="margin-right:0.02778em">r</span></span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">...</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqcd" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mclose">)]</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.09356em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.59356em;"><span style="top:-4.59356em;"><span class="pstrut" style="height:3.10756em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqbp" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.10756em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mopen">(</span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:2.09356em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>これにより、</p>
|
||
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.34em;vertical-align:-1.4200000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9199999999999997em;"><span style="top:-3.92em;"><span class="pstrut" style="height:3.879375em;"></span><span class="mord"><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.4200000000000002em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9199999999999997em;"><span style="top:-3.92em;"><span class="pstrut" style="height:3.879375em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.879375em;"><span class="svg-align" style="top:-5em;"><span class="pstrut" style="height:5em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mord coloredeq eqbp" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.839375em;"><span class="pstrut" style="height:5em;"></span><span class="hide-tail" style="min-width:1.02em;height:3.08em;"><svg height="3.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 3240" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M473,2793
|
||
c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0
|
||
c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7
|
||
s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9
|
||
c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200
|
||
c0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26
|
||
s76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,
|
||
606zM1001 80h400000v40H1017.7z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.160625em;"><span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.4200000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></span>
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">139</span><span></span><span class="kn">import</span> <span class="nn">math</span>
|
||
<span class="lineno">140</span><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">Optional</span>
|
||
<span class="lineno">141</span>
|
||
<span class="lineno">142</span><span class="kn">import</span> <span class="nn">torch</span>
|
||
<span class="lineno">143</span>
|
||
<span class="lineno">144</span><span class="kn">from</span> <span class="nn">labml_nn.optimizers</span> <span class="kn">import</span> <span class="n">WeightDecay</span>
|
||
<span class="lineno">145</span><span class="kn">from</span> <span class="nn">labml_nn.optimizers.amsgrad</span> <span class="kn">import</span> <span class="n">AMSGrad</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-1'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
||
<a href='#section-1'>#</a>
|
||
</div>
|
||
<h2>レクティファイド・アダム・オプティマイザー</h2>
|
||
<p>このクラスは、で定義されている AmSadam オプティマイザを拡張したものです。<a href="amsadam.html"><code class="highlight"><span></span><span class="n">amsadam</span><span class="o">.</span><span class="n">py</span></code>
|
||
</a></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">148</span><span class="k">class</span> <span class="nc">RAdam</span><span class="p">(</span><span class="n">AMSGrad</span><span class="p">):</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-2'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
||
<a href='#section-2'>#</a>
|
||
</div>
|
||
<h3>オプティマイザを初期化</h3>
|
||
<ul><li><code class="highlight"><span></span><span class="n">params</span></code>
|
||
はパラメータのリストです</li>
|
||
<li><code class="highlight"><span></span><span class="n">lr</span></code>
|
||
は学習率 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqbz" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span></span></span></span></span></span></li>
|
||
<li><code class="highlight"><span></span><span class="n">betas</span></code>
|
||
(,) <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbw" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> のタプルです <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span></li>
|
||
<li><code class="highlight"><span></span><span class="n">eps</span></code>
|
||
<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqbj" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbv" style="">ϵ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord" style="">^</span></span></span></span></span></span></span></span></span></span></span></span><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqbv" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span></span>またはそれに基づいている <code class="highlight"><span></span><span class="n">optimized_update</span></code>
|
||
</li>
|
||
<li><code class="highlight"><span></span><span class="n">weight_decay</span></code>
|
||
<code class="highlight"><span></span><span class="n">WeightDecay</span></code>
|
||
で定義されているクラスのインスタンスです <a href="index.html"><code class="highlight"><span></span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span></code>
|
||
</a></li>
|
||
<li><code class="highlight"><span></span><span class="n">optimized_update</span></code>
|
||
セカンドモーメントのバイアス補正を加算してから行うことで最適化するか否かのフラグです <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqbv" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span></span></li>
|
||
<li><code class="highlight"><span></span><span class="n">amsgrad</span></code>
|
||
amsGradを使用するか、プレーンなAdamにフォールバックするかを示すフラグです</li>
|
||
<li><code class="highlight"><span></span><span class="n">degenerate_to_sgd</span></code>
|
||
<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>修正項が扱いにくい場合に sgd を使うかどうか。</li>
|
||
<li><code class="highlight"><span></span><span class="n">defaults</span></code>
|
||
グループ値のデフォルト辞書です。これは、クラスを拡張する場合に便利です<code class="highlight"><span></span><span class="n">RAdam</span></code>
|
||
。</li></ul>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">155</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span> <span class="n">betas</span><span class="o">=</span><span class="p">(</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.999</span><span class="p">),</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-8</span><span class="p">,</span>
|
||
<span class="lineno">156</span> <span class="n">weight_decay</span><span class="p">:</span> <span class="n">WeightDecay</span> <span class="o">=</span> <span class="n">WeightDecay</span><span class="p">(),</span>
|
||
<span class="lineno">157</span> <span class="n">optimized_update</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
|
||
<span class="lineno">158</span> <span class="n">amsgrad</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
|
||
<span class="lineno">159</span> <span class="n">degenerated_to_sgd</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">defaults</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-3'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-3'>#</a>
|
||
</div>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">175</span> <span class="bp">self</span><span class="o">.</span><span class="n">degenerated_to_sgd</span> <span class="o">=</span> <span class="n">degenerated_to_sgd</span>
|
||
<span class="lineno">176</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">lr</span><span class="p">,</span> <span class="n">betas</span><span class="p">,</span> <span class="n">eps</span><span class="p">,</span> <span class="n">weight_decay</span><span class="p">,</span> <span class="n">optimized_update</span><span class="p">,</span> <span class="n">amsgrad</span><span class="p">,</span> <span class="n">defaults</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-4'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
||
<a href='#section-4'>#</a>
|
||
</div>
|
||
<h3>与えられたパラメータテンソルの更新ステップを実行する</h3>
|
||
<ul><li><code class="highlight"><span></span><span class="n">state</span></code>
|
||
はパラメーター (テンソル) のオプティマイザー状態です</li>
|
||
<li><code class="highlight"><span></span><span class="n">group</span></code>
|
||
パラメータグループのオプティマイザ属性を格納します</li>
|
||
<li><code class="highlight"><span></span><span class="n">grad</span></code>
|
||
<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqcd" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>パラメータの現在の勾配テンソルです <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqbn" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span></span></span></li>
|
||
<li><code class="highlight"><span></span><span class="n">param</span></code>
|
||
はパラメータテンソル <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqbn" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span></span></span></li></ul>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">178</span> <span class="k">def</span> <span class="nf">step_param</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">state</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">],</span> <span class="n">group</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">],</span> <span class="n">grad</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">param</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">Parameter</span><span class="p">):</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-5'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-5'>#</a>
|
||
</div>
|
||
<p>体重減少の計算</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">189</span> <span class="n">grad</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">weight_decay</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">grad</span><span class="p">,</span> <span class="n">group</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-6'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-6'>#</a>
|
||
</div>
|
||
<p>Get <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqce" style=""><span class="mord" style=""><span class="mord mathnormal" style="">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span> と<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcg" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>; つまり<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbu" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="mopen" style="">(</span><span class="mord" style="">.</span><span class="mclose" style="">)</span></span></span></span></span></span>、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqby" style=""><span class="mord mathnormal" style="margin-right:0.03588em">ψ</span><span class="mopen" style="">(</span><span class="mord" style="">.</span><span class="mclose" style="">)</span></span></span></span></span></span>バイアス補正なし</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">192</span> <span class="n">m</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_mv</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">group</span><span class="p">,</span> <span class="n">grad</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-7'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-7'>#</a>
|
||
</div>
|
||
<p>オプティマイザーステップ数の計算 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord coloredeq eqcj" style=""><span class="mord mathnormal" style="">t</span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">195</span> <span class="n">state</span><span class="p">[</span><span class="s1">'step'</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-8'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-8'>#</a>
|
||
</div>
|
||
<p><em>RaDAM アップデートを実行</em></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">198</span> <span class="bp">self</span><span class="o">.</span><span class="n">r_adam_update</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">group</span><span class="p">,</span> <span class="n">param</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span></pre></div>
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<h3>修正期間の計算 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span></h3>
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<div class="highlight"><pre><span class="lineno">200</span> <span class="nd">@staticmethod</span>
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<span class="lineno">201</span> <span class="k">def</span> <span class="nf">calc_rectification_term</span><span class="p">(</span><span class="n">beta2</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">step</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="n">Optional</span><span class="p">[</span><span class="nb">float</span><span class="p">]:</span></pre></div>
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<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.072336em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbr" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
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<div class="highlight"><pre><span class="lineno">207</span> <span class="n">beta2_t</span> <span class="o">=</span> <span class="n">beta2</span> <span class="o">**</span> <span class="n">step</span></pre></div>
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<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbp" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.20188em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span></span></span></p>
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<div class="highlight"><pre><span class="lineno">209</span> <span class="n">rho_inf</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span></pre></div>
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<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.20188em;vertical-align:-0.8804400000000001em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8804400000000001em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.517232em;vertical-align:-0.9623359999999999em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5548959999999998em;"><span style="top:-2.2321040000000005em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqbr" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span><span class="mord coloredeq eqcj" style=""><span class="mord mathnormal" style="">t</span></span><span class="mord coloredeq eqbr" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9623359999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></p>
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<div class="highlight"><pre><span class="lineno">211</span> <span class="n">rho</span> <span class="o">=</span> <span class="n">rho_inf</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">step</span> <span class="o">*</span> <span class="n">beta2_t</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta2_t</span><span class="p">)</span></pre></div>
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<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.7335400000000001em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">>=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">4</span></span></span></span></span>どんなときでも扱いやすい。おおよその値なので、もう少し保守的にしています</p>
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<div class="highlight"><pre><span class="lineno">215</span> <span class="k">if</span> <span class="n">rho</span> <span class="o">>=</span> <span class="mi">5</span><span class="p">:</span></pre></div>
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<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.04em;vertical-align:-1.160625em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.879375em;"><span class="svg-align" style="top:-5em;"><span class="pstrut" style="height:5em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord"><span class="mord coloredeq eqcc" style=""><span class="mord mathnormal" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord coloredeq eqca" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">4</span><span class="mclose">)</span><span class="mord coloredeq eqbp" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqcc" style="">ρ</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">∞</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.839375em;"><span class="pstrut" style="height:5em;"></span><span class="hide-tail" style="min-width:1.02em;height:3.08em;"><svg height="3.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 3240" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M473,2793
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||
c339.3,-1799.3,509.3,-2700,510,-2702 l0 -0
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||
c3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7
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||
s-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9
|
||
c-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200
|
||
c0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26
|
||
s76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,
|
||
606zM1001 80h400000v40H1017.7z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.160625em;"><span></span></span></span></span></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">217</span> <span class="n">r2</span> <span class="o">=</span> <span class="p">(</span><span class="n">rho</span> <span class="o">-</span> <span class="mi">4</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">rho_inf</span> <span class="o">-</span> <span class="mi">4</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">rho</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="n">rho</span> <span class="o">*</span> <span class="n">rho_inf</span> <span class="o">/</span> <span class="p">(</span><span class="n">rho_inf</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span>
|
||
<span class="lineno">218</span> <span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">r2</span><span class="p">)</span>
|
||
<span class="lineno">219</span> <span class="k">else</span><span class="p">:</span>
|
||
<span class="lineno">220</span> <span class="k">return</span> <span class="kc">None</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-15'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
||
<a href='#section-15'>#</a>
|
||
</div>
|
||
<h3><em>RadAM</em> パラメータの更新を行います</h3>
|
||
<ul><li><code class="highlight"><span></span><span class="n">state</span></code>
|
||
はパラメーター (テンソル) のオプティマイザー状態です</li>
|
||
<li><code class="highlight"><span></span><span class="n">group</span></code>
|
||
パラメータグループのオプティマイザ属性を格納します</li>
|
||
<li><code class="highlight"><span></span><span class="n">param</span></code>
|
||
はパラメータテンソル <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqbn" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span></span></span></li>
|
||
<li><code class="highlight"><span></span><span class="n">m</span></code>
|
||
<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqce" style=""><span class="mord" style=""><span class="mord mathnormal" style="">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>未補正の第1モーメントと第2モーメントで、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcg" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqbu" style=""><span class="mord mathnormal" style="margin-right:0.03588em">σ</span><span class="mopen" style="">(</span><span class="mord" style="">.</span><span class="mclose" style="">)</span></span></span></span></span></span><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqby" style=""><span class="mord mathnormal" style="margin-right:0.03588em">ψ</span><span class="mopen" style="">(</span><span class="mord" style="">.</span><span class="mclose" style="">)</span></span></span></span></span></span>バイアス補正なし <code class="highlight"><span></span><span class="n">v</span></code>
|
||
</li></ul>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">222</span> <span class="k">def</span> <span class="nf">r_adam_update</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">state</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">],</span> <span class="n">group</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="nb">any</span><span class="p">],</span> <span class="n">param</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">Parameter</span><span class="p">,</span>
|
||
<span class="lineno">223</span> <span class="n">m</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">):</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-16'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-16'>#</a>
|
||
</div>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbw" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>取得して <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">235</span> <span class="n">beta1</span><span class="p">,</span> <span class="n">beta2</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s1">'betas'</span><span class="p">]</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-17'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-17'>#</a>
|
||
</div>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqbs" style=""><span class="mord" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="">m</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord" style="">^</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>のバイアス補正用語 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.072336em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbk" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqbw" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">237</span> <span class="n">bias_correction1</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">beta1</span> <span class="o">**</span> <span class="n">state</span><span class="p">[</span><span class="s1">'step'</span><span class="p">]</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-18'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-18'>#</a>
|
||
</div>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqbt" style=""><span class="mord" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord" style="">^</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>のバイアス補正用語 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.072336em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbl" style=""><span class="mord" style="">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqbr" style=""><span class="mord" style=""><span class="mord coloredeq eqbx" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">239</span> <span class="n">bias_correction2</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span> <span class="o">**</span> <span class="n">state</span><span class="p">[</span><span class="s1">'step'</span><span class="p">]</span>
|
||
<span class="lineno">240</span>
|
||
<span class="lineno">241</span> <span class="n">r</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_rectification_term</span><span class="p">(</span><span class="n">beta2</span><span class="p">,</span> <span class="n">state</span><span class="p">[</span><span class="s1">'step'</span><span class="p">])</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-19'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-19'>#</a>
|
||
</div>
|
||
<p>学習率を取得</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">244</span> <span class="n">lr</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_lr</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">group</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-20'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-20'>#</a>
|
||
</div>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>治りにくい場合</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">247</span> <span class="k">if</span> <span class="n">r</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-21'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-21'>#</a>
|
||
</div>
|
||
<p>スカラー計算を組み合わせて計算を最適化するかどうか</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">249</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">optimized_update</span><span class="p">:</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-22'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-22'>#</a>
|
||
</div>
|
||
<p>分母 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.31472em;"></span><span class="mord coloredeq eqba" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.72528em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em"><span class="mord" style=""><span class="mord coloredeq eqcg" style=""><span class="mord mathnormal" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.68528em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.31472em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord accent coloredeq eqbj" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord mathnormal coloredeq eqbv" style="">ϵ</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord" style="">^</span></span></span></span></span></span></span></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">251</span> <span class="n">denominator</span> <span class="o">=</span> <span class="n">v</span><span class="o">.</span><span class="n">sqrt</span><span class="p">()</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s1">'eps'</span><span class="p">])</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-23'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-23'>#</a>
|
||
</div>
|
||
<p>ステップサイズ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.31472em;"></span><span class="mord coloredeq eqbz" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.72528em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.68528em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.31472em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.822356em;vertical-align:-0.49275599999999986em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296000000000001em;"><span style="top:-2.643352em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mtight coloredeq eqbw" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7809257142857142em;"><span style="top:-2.841582857142857em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5734925em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0801535714285715em;"><span class="svg-align" style="top:-3.428571428571429em;"><span class="pstrut" style="height:3.428571428571429em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mtight coloredeq eqbr" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbx" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7809257142857142em;"><span style="top:-2.841582857142857em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0521535714285717em;"><span class="pstrut" style="height:3.428571428571429em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5428571428571431em;"><svg height="1.5428571428571431em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.37641785714285714em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.49275599999999986em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">253</span> <span class="n">step_size</span> <span class="o">=</span> <span class="n">lr</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">bias_correction2</span><span class="p">)</span> <span class="o">*</span> <span class="n">r</span> <span class="o">/</span> <span class="n">bias_correction1</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-24'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-24'>#</a>
|
||
</div>
|
||
<p>パラメータを更新 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">←</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqbn" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.822356em;vertical-align:-0.49275599999999986em;"></span><span class="mord coloredeq eqbz" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.72528em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.68528em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.31472em;"><span></span></span></span></span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3296000000000001em;"><span style="top:-2.643352em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mtight coloredeq eqbw" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7809257142857142em;"><span style="top:-2.841582857142857em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5734925em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0801535714285715em;"><span class="svg-align" style="top:-3.428571428571429em;"><span class="pstrut" style="height:3.428571428571429em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mtight coloredeq eqbr" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbx" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7809257142857142em;"><span style="top:-2.841582857142857em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0521535714285717em;"><span class="pstrut" style="height:3.428571428571429em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5428571428571431em;"><svg height="1.5428571428571431em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.37641785714285714em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.49275599999999986em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.2704084999999998em;vertical-align:-0.5589165em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqba" style=""><span class="mord sqrt mtight" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.734405em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em"><span class="mord mtight" style=""><span class="mord mtight coloredeq eqcg" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em;"><span style="top:-2.357em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.6944049999999997em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.30559500000000006em;"><span></span></span></span></span></span><span class="mbin mtight" style="">+</span><span class="mord mtight" style=""><span class="mord accent mtight coloredeq eqbj" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqbv" style="">ϵ</span></span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord mtight" style="">^</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4101em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqce" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.5589165em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">256</span> <span class="n">param</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">addcdiv_</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">denominator</span><span class="p">,</span> <span class="n">value</span><span class="o">=-</span><span class="n">step_size</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-25'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-25'>#</a>
|
||
</div>
|
||
<p>最適化なしの計算</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">258</span> <span class="k">else</span><span class="p">:</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-26'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-26'>#</a>
|
||
</div>
|
||
<p>分母 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.8676em;vertical-align:-0.8295999999999999em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.038em;"><span style="top:-2.4338925em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0801535714285715em;"><span class="svg-align" style="top:-3.428571428571429em;"><span class="pstrut" style="height:3.428571428571429em;"></span><span class="mord mtight" style="padding-left:1.19em;"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mtight coloredeq eqbr" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqbx" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7809257142857142em;"><span style="top:-2.841582857142857em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0521535714285717em;"><span class="pstrut" style="height:3.428571428571429em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.5428571428571431em;"><svg height="1.5428571428571431em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.37641785714285714em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5239165em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.734405em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight coloredeq eqcg" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03588em">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em;"><span style="top:-2.357em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.6944049999999997em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.30559500000000006em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.8295999999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqbv" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">260</span> <span class="n">denominator</span> <span class="o">=</span> <span class="p">(</span><span class="n">v</span><span class="o">.</span><span class="n">sqrt</span><span class="p">()</span> <span class="o">/</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">bias_correction2</span><span class="p">))</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s1">'eps'</span><span class="p">])</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-27'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-27'>#</a>
|
||
</div>
|
||
<p>ステップサイズ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.5307559999999998em;vertical-align:-0.49275599999999986em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.038em;"><span style="top:-2.643352em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mtight coloredeq eqbw" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7809257142857142em;"><span style="top:-2.841582857142857em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.5239165em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqbz" style=""><span class="mord mathnormal mtight" style="margin-right:0.0037em">α</span></span><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.734405em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight coloredeq eqcf" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em;"><span style="top:-2.357em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.6944049999999997em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.30559500000000006em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.49275599999999986em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">262</span> <span class="n">step_size</span> <span class="o">=</span> <span class="n">lr</span> <span class="o">*</span> <span class="n">r</span> <span class="o">/</span> <span class="n">bias_correction1</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-28'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-28'>#</a>
|
||
</div>
|
||
<p>パラメータを更新 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">←</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqbn" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.31472em;"></span><span class="mord coloredeq eqbz" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.72528em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.68528em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.31472em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.434208em;vertical-align:-0.5379999999999999em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8962079999999999em;"><span style="top:-2.5835585em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord sqrt mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.866345em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em;"><span class="mord mtight coloredeq eqbt" style=""><span class="mord mtight" style=""><span class="mord accent mtight" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mathnormal mtight" style="margin-right:0.03588em">v</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.22222em;"><span class="mord mtight" style="">^</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em;"><span style="top:-2.357em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-2.826345em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em;"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
|
||
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
|
||
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
|
||
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
|
||
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
|
||
c69,-144,104.5,-217.7,106.5,-221
|
||
l0 -0
|
||
c5.3,-9.3,12,-14,20,-14
|
||
H400000v40H845.2724
|
||
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
|
||
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
|
||
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.173655em;"><span></span></span></span></span></span><span class="mbin mtight">+</span><span class="mord mtight coloredeq eqbv" style=""><span class="mord mathnormal mtight" style="">ϵ</span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4101em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqbs" style=""><span class="mord mtight" style=""><span class="mord accent mtight" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="mord mathnormal mtight" style="">m</span></span><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord mtight" style="">^</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.5379999999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">265</span> <span class="n">param</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">addcdiv_</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">denominator</span><span class="p">,</span> <span class="n">value</span><span class="o">=-</span><span class="n">step_size</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-29'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-29'>#</a>
|
||
</div>
|
||
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span>手に負えないなら勢いをつけてSGDをやりましょう</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">268</span> <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">degenerated_to_sgd</span><span class="p">:</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-30'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-30'>#</a>
|
||
</div>
|
||
<p>ステップサイズ <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.188148em;vertical-align:-0.49275599999999986em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.695392em;"><span style="top:-2.643352em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mtight coloredeq eqbw" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.05278em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7809257142857142em;"><span style="top:-2.841582857142857em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqbz" style=""><span class="mord mathnormal mtight" style="margin-right:0.0037em">α</span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.49275599999999986em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
|
||
|
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</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">270</span> <span class="n">step_size</span> <span class="o">=</span> <span class="n">lr</span> <span class="o">/</span> <span class="n">bias_correction1</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-31'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-31'>#</a>
|
||
</div>
|
||
<p>パラメータを更新 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqcj" style=""><span class="mord mathnormal mtight" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">←</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqbn" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.44445em;vertical-align:0em;"></span><span class="mord coloredeq eqbz" style=""><span class="mord mathnormal" style="margin-right:0.0037em">α</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqbs" style=""><span class="mord" style=""><span class="mord accent" style=""><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="">m</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord" style="">^</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
|
||
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</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">273</span> <span class="n">param</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=-</span><span class="n">step_size</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-32'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
||
<a href='#section-32'>#</a>
|
||
</div>
|
||
<h3><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord coloredeq eqcf" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqci" style="margin-right:0.02778em">r</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqcj" style="">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord coloredeq eqcj" style=""><span class="mord mathnormal" style="">t</span></span></span></span></span></span>さまざまなプロット対象 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqbx" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.05278em">β</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.05278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></span></h3>
|
||
<p><img alt="Plot of r_t" src="radam_r_t.png"></p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">276</span><span class="k">def</span> <span class="nf">_test_rectification_term</span><span class="p">():</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-33'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-33'>#</a>
|
||
</div>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">282</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||
<span class="lineno">283</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||
<span class="lineno">284</span>
|
||
<span class="lineno">285</span> <span class="n">beta2</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.9999</span><span class="p">,</span> <span class="mf">0.999</span><span class="p">,</span> <span class="mf">0.99</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">]</span>
|
||
<span class="lineno">286</span> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5_000</span><span class="p">),</span> <span class="p">[[</span><span class="n">RAdam</span><span class="o">.</span><span class="n">calc_rectification_term</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">beta2</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5_000</span><span class="p">)])</span>
|
||
<span class="lineno">287</span> <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">beta2</span><span class="p">)</span>
|
||
<span class="lineno">288</span> <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Optimizer"</span><span class="p">)</span>
|
||
<span class="lineno">289</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
<span class="lineno">290</span>
|
||
<span class="lineno">291</span>
|
||
<span class="lineno">292</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
|
||
<span class="lineno">293</span> <span class="n">_test_rectification_term</span><span class="p">()</span></pre></div>
|
||
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|
||
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