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<h1>AdaBelief Optimizer</h1>
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<p>This is based from AdaBelief <a href="https://github.com/juntang-zhuang/Adabelief-Optimizer">official implementation</a> of the paper <a href="https://papers.labml.ai/paper/2010.07468">AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients</a>.</p>
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<p>This is implemented in <a href="https://pytorch.org">PyTorch</a> as an extension to <a href="radam.html">RAdam</a>.</p>
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<p>The main difference between Adam optimizer and AdaBelief is that, how it calculates the adaptive learning rate; instead of dividing by the exponential moving average of square of the gradients, AdaBelief divides by the exponential mean of variance.</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:10.518109999999997em;vertical-align:-5.009054999999998em;"></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:5.509054999999999em;"><span style="top:-8.040495em;"><span class="pstrut" style="height:3.3714399999999998em;"></span><span class="mord"><span class="mord coloredeq eqs" 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 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style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqw" 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></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:5.009054999999998em;"><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:5.509054999999999em;"><span style="top:-8.040495em;"><span class="pstrut" style="height:3.3714399999999998em;"></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 coloredeq eqm" 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="mord coloredeq eqo" 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:0.301108em;"><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 mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" 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 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 eqm" 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:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqr" 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 eqw" 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:-6.516386999999999em;"><span class="pstrut" style="height:3.3714399999999998em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="color:cyan">←</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord" style="color:cyan"><span class="mord coloredeq eqn" 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="mord" style="color:cyan"><span class="mord coloredeq eqp" style=""><span class="mord mathnormal" style="">s</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: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 mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" 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" style="color:cyan">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen" style="color:cyan">(</span><span class="mord" style="color:cyan">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="color:cyan">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style="color:cyan"><span class="mord coloredeq eqn" 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="color:cyan">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin" style="color:cyan">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style="color:cyan"><span class="mopen coloredeq eqi" style="">(</span><span class="mord coloredeq eqi" style=""><span class="mord coloredeq eqr" 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 eqw" 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 coloredeq eqi" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord coloredeq eqi" style=""><span class="mord coloredeq eqs" 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 eqw" 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 coloredeq eqi" style=""><span class="mclose" style="">)</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></span><span style="top:-4.7488269999999995em;"><span class="pstrut" style="height:3.3714399999999998em;"></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:-2.2321040000000005em;"><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"><span class="mord coloredeq eqm" 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:0.8778959999999999em;"><span style="top:-3.1473400000000002em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqw" style=""><span class="mord mathnormal mtight" style="">t</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 coloredeq eqs" 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 eqw" 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:0.9623359999999999em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2261610000000003em;"><span class="pstrut" style="height:3.3714399999999998em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel" style="color:cyan">←</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:1.2603300000000002em;"><span style="top:-2.2321040000000005em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="color:cyan"><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 eqn" 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 eqw" style="">t</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"><span class="mord" style="color:cyan"><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">s</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 eqw" 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 coloredeq eqd" style="">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style="color:red"><span class="mord mathnormal coloredeq eql" style="">ϵ</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:0.4076149999999985em;"><span class="pstrut" style="height:3.3714399999999998em;"></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 coloredeq eqj" 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 eqw" 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 class="mord coloredeq eqq" 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 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:1.37144em;"><span style="top:-2.25278em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.85722em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;color:cyan"><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="">s</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 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 eqw" 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 style="top:-2.81722em;"><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:0.18278000000000005em;"><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 coloredeq eql" style=""><span class="mord mathnormal" style="">ϵ</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"><span class="mord accent"><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">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">^</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"><span class="mord mtight coloredeq eqw" 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></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.93em;"><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:5.009054999999998em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>🤔 The paper calculates variance as <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 coloredeq eqi" style=""><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqr" 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 eqw" 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" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqs" 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 eqw" 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 class="mclose" style="">)</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>, but I feel it should use the bias corrected momentum <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="mopen">(</span><span class="mord coloredeq eqr" 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 eqw" 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><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord" style="color:orange"><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 eqw" 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="mclose"><span class="mclose">)</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>. I guess this doesn't affect things much because bias correction is <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="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">1</span></span></span></span></span> after the initial training steps.</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">36</span><span></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">Any</span>
|
||
<span class="lineno">37</span>
|
||
<span class="lineno">38</span><span class="kn">import</span> <span class="nn">torch</span>
|
||
<span class="lineno">39</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span>
|
||
<span class="lineno">40</span>
|
||
<span class="lineno">41</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">42</span><span class="kn">from</span> <span class="nn">labml_nn.optimizers.radam</span> <span class="kn">import</span> <span class="n">RAdam</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>AdaBelief Optimizer</h2>
|
||
<p>This class extends from RAdam optimizer defined in <a href="radam.html"><code class="highlight"><span></span><span class="n">radam</span><span class="o">.</span><span class="n">py</span></code>
|
||
</a>.</p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">45</span><span class="k">class</span> <span class="nc">AdaBelief</span><span class="p">(</span><span class="n">RAdam</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>Initialize the optimizer</h3>
|
||
<ul><li><code class="highlight"><span></span><span class="n">params</span></code>
|
||
is the list of parameters </li>
|
||
<li><code class="highlight"><span></span><span class="n">lr</span></code>
|
||
is the learning rate <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 eqq" 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>
|
||
is a tuple of (<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 eqm" 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>, <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 eqn" 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>
|
||
is <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 accent"><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 coloredeq eql" style=""><span class="mord mathnormal" 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">^</span></span></span></span></span></span></span></span></span></span></span> or <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 eql" style=""><span class="mord mathnormal" style="">ϵ</span></span></span></span></span></span> based on <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>
|
||
is an instance of class <code class="highlight"><span></span><span class="n">WeightDecay</span></code>
|
||
defined in <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>
|
||
is a flag whether to optimize the bias correction of the second moment by doing it after adding <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 eql" 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>
|
||
is a flag indicating whether to use AMSGrad or fallback to plain Adam </li>
|
||
<li><code class="highlight"><span></span><span class="n">degenerate_to_sgd</span></code>
|
||
whether to use sgd when the rectification term <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"><span class="mord mathnormal" style="margin-right:0.02778em;">r</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 eqw" 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></span></span></span> is intractable </li>
|
||
<li><code class="highlight"><span></span><span class="n">rectify</span></code>
|
||
is whether to use RAdam update </li>
|
||
<li><code class="highlight"><span></span><span class="n">defaults</span></code>
|
||
is a dictionary of default for group values. This is useful when you want to extend the class <code class="highlight"><span></span><span class="n">AdaBelief</span></code>
|
||
.</li></ul>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">52</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-16</span><span class="p">,</span>
|
||
<span class="lineno">53</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="n">amsgrad</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
|
||
<span class="lineno">54</span> <span class="n">degenerate_to_sgd</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
|
||
<span class="lineno">55</span> <span class="n">rectify</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">73</span> <span class="n">defaults</span> <span class="o">=</span> <span class="p">{}</span> <span class="k">if</span> <span class="n">defaults</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">defaults</span>
|
||
<span class="lineno">74</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">amsgrad</span><span class="p">,</span> <span class="n">degenerate_to_sgd</span><span class="p">,</span> <span class="n">defaults</span><span class="p">)</span>
|
||
<span class="lineno">75</span> <span class="bp">self</span><span class="o">.</span><span class="n">rectify</span> <span class="o">=</span> <span class="n">rectify</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>Initialize a parameter state</h3>
|
||
<ul><li><code class="highlight"><span></span><span class="n">state</span></code>
|
||
is the optimizer state of the parameter (tensor) </li>
|
||
<li><code class="highlight"><span></span><span class="n">group</span></code>
|
||
stores optimizer attributes of the parameter group </li>
|
||
<li><code class="highlight"><span></span><span class="n">param</span></code>
|
||
is the parameter tensor <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 eqj" 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 eqw" 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">77</span> <span class="k">def</span> <span class="nf">init_state</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">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>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">85</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">0</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>Exponential moving average of gradient values </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">87</span> <span class="n">state</span><span class="p">[</span><span class="s1">'exp_avg'</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">preserve_format</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>Exponential moving average of variance </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">89</span> <span class="n">state</span><span class="p">[</span><span class="s1">'exp_avg_var'</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">preserve_format</span><span class="p">)</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>If <code class="highlight"><span></span><span class="n">amsgrad</span></code>
|
||
flag is <code class="highlight"><span></span><span class="kc">True</span></code>
|
||
for this parameter group, we maintain the maximum of exponential moving average of variance </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">93</span> <span class="k">if</span> <span class="n">group</span><span class="p">[</span><span class="s1">'amsgrad'</span><span class="p">]:</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-9'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-9'>#</a>
|
||
</div>
|
||
<p>Maintains max of all exp. moving avg. of sq. grad. values </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">95</span> <span class="n">state</span><span class="p">[</span><span class="s1">'max_exp_avg_var'</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">preserve_format</span><span class="p">)</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-10'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
||
<a href='#section-10'>#</a>
|
||
</div>
|
||
<h3>Calculate <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 eqs" 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 eqw" 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> and <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 equ" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</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 eqw" 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> or <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 eqf" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="">s</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: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="">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 class="mord mathnormal" style="">s</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: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="">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 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 eqp" style=""><span class="mord mathnormal" style="">s</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: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 mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" 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="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">s</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 eqw" 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></h3>
|
||
<ul><li><code class="highlight"><span></span><span class="n">state</span></code>
|
||
is the optimizer state of the parameter (tensor) </li>
|
||
<li><code class="highlight"><span></span><span class="n">group</span></code>
|
||
stores optimizer attributes of the parameter group </li>
|
||
<li><code class="highlight"><span></span><span class="n">grad</span></code>
|
||
is the current gradient tensor <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 eqr" 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 eqw" 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> for the parameter <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 eqj" 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 eqw" 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">97</span> <span class="k">def</span> <span class="nf">get_ms</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="n">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="n">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></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-11'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-11'>#</a>
|
||
</div>
|
||
<p>Get <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 eqm" 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> and <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 eqn" 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>
|
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|
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|
||
<div class='code'>
|
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<div class="highlight"><pre><span class="lineno">107</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>
|
||
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|
||
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|
||
<div class='section' id='section-12'>
|
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<div class='docs'>
|
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<div class='section-link'>
|
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<a href='#section-12'>#</a>
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|
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<p>Get <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqo" 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:0.301108em;"><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 mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" 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> and <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqp" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</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: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 mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" 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> </p>
|
||
|
||
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|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">110</span> <span class="n">m</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="n">state</span><span class="p">[</span><span class="s1">'exp_avg'</span><span class="p">],</span> <span class="n">state</span><span class="p">[</span><span class="s1">'exp_avg_var'</span><span class="p">]</span></pre></div>
|
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|
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|
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<div class='section' id='section-13'>
|
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<div class='docs'>
|
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<div class='section-link'>
|
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<a href='#section-13'>#</a>
|
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|
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<p>In-place calculation of <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 eqs" 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 eqw" 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-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 eqs" 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 eqw" 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:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqm" 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="mord coloredeq eqo" 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:0.301108em;"><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 mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" 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:1em;vertical-align:-0.25em;"></span><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><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqm" 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:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqr" 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 eqw" 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> </p>
|
||
|
||
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|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">114</span> <span class="n">m</span><span class="o">.</span><span class="n">mul_</span><span class="p">(</span><span class="n">beta1</span><span class="p">)</span><span class="o">.</span><span class="n">add_</span><span class="p">(</span><span class="n">grad</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta1</span><span class="p">)</span></pre></div>
|
||
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|
||
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|
||
<div class='section' id='section-14'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-14'>#</a>
|
||
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|
||
<p>Difference between gradient and momentum </p>
|
||
|
||
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|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">116</span> <span class="n">grad_residual</span> <span class="o">=</span> <span class="n">grad</span> <span class="o">-</span> <span class="n">m</span></pre></div>
|
||
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|
||
</div>
|
||
<div class='section' id='section-15'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-15'>#</a>
|
||
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|
||
<p>In-place calculation of <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 equ" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</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 eqw" 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-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 equ" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</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 eqw" 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:0.902771em;vertical-align:-0.208331em;"></span><span class="mord coloredeq eqn" 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="mord coloredeq eqp" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</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: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 mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" 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:1em;vertical-align:-0.25em;"></span><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><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqn" 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:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.1141079999999999em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqi" style=""><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord coloredeq eqr" 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 eqw" 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" style="">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style=""><span class="mord coloredeq eqs" 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 eqw" 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 class="mclose" style="">)</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></span></span></span></span> </p>
|
||
|
||
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|
||
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|
||
<div class="highlight"><pre><span class="lineno">119</span> <span class="n">s</span><span class="o">.</span><span class="n">mul_</span><span class="p">(</span><span class="n">beta2</span><span class="p">)</span><span class="o">.</span><span class="n">addcmul_</span><span class="p">(</span><span class="n">grad_residual</span><span class="p">,</span> <span class="n">grad_residual</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="mi">1</span> <span class="o">-</span> <span class="n">beta2</span><span class="p">)</span></pre></div>
|
||
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|
||
</div>
|
||
<div class='section' id='section-16'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-16'>#</a>
|
||
</div>
|
||
<p>If this parameter group is using <code class="highlight"><span></span><span class="n">amsgrad</span></code>
|
||
</p>
|
||
|
||
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|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">122</span> <span class="k">if</span> <span class="n">group</span><span class="p">[</span><span class="s1">'amsgrad'</span><span class="p">]:</span></pre></div>
|
||
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|
||
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|
||
<div class='section' id='section-17'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-17'>#</a>
|
||
</div>
|
||
<p>Get <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="mop">max</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">s</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:0em;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 class="mord mathnormal">s</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:0em;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:0.15em;"><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 eqp" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</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: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 mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" 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="mclose">)</span></span></span></span></span>. </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">124</span> <span class="n">s_max</span> <span class="o">=</span> <span class="n">state</span><span class="p">[</span><span class="s1">'max_exp_avg_var'</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>Calculate <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 eqf" style=""><span class="mop" style=""><span style="">m</span><span style="">a</span><span style="">x</span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="">s</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: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="">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 class="mord mathnormal" style="">s</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: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="">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 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 eqp" style=""><span class="mord mathnormal" style="">s</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: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 mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" 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="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style=""><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">s</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 eqw" 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>. </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">126</span> <span class="n">torch</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">s_max</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="n">s_max</span><span class="p">)</span>
|
||
<span class="lineno">127</span>
|
||
<span class="lineno">128</span> <span class="k">return</span> <span class="n">m</span><span class="p">,</span> <span class="n">s_max</span>
|
||
<span class="lineno">129</span> <span class="k">else</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><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 eqs" 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 eqw" 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> and <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 equ" style=""><span class="mord" style=""><span class="mord mathnormal" style="">s</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 eqw" 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> otherwise </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">131</span> <span class="k">return</span> <span class="n">m</span><span class="p">,</span> <span class="n">s</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-20'>
|
||
<div class='docs doc-strings'>
|
||
<div class='section-link'>
|
||
<a href='#section-20'>#</a>
|
||
</div>
|
||
<h3>Take an update step for a given parameter tensor</h3>
|
||
<ul><li><code class="highlight"><span></span><span class="n">state</span></code>
|
||
is the optimizer state of the parameter (tensor) </li>
|
||
<li><code class="highlight"><span></span><span class="n">group</span></code>
|
||
stores optimizer attributes of the parameter group </li>
|
||
<li><code class="highlight"><span></span><span class="n">grad</span></code>
|
||
is the current gradient tensor <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 eqr" 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 eqw" 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> for the parameter <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 eqj" 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 eqw" 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>
|
||
is the parameter tensor <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 eqj" 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 eqw" 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">133</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-21'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-21'>#</a>
|
||
</div>
|
||
<p>Calculate weight decay </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">144</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-22'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-22'>#</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 eqs" 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 eqw" 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> and <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 eqv" 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 eqw" 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>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">147</span> <span class="n">m</span><span class="p">,</span> <span class="n">s</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_ms</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-23'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-23'>#</a>
|
||
</div>
|
||
<p>Increment <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 eqw" style=""><span class="mord mathnormal" style="">t</span></span></span></span></span></span> the number of optimizer steps </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">150</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>
|
||
<span class="lineno">151</span>
|
||
<span class="lineno">152</span> <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">rectify</span><span class="p">:</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>Perform <em>Adam</em> update, defined in <a href="adam.html"><code class="highlight"><span></span><span class="n">adam</span><span class="o">.</span><span class="n">py</span></code>
|
||
</a>, with <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord" style="color:cyan"><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">s</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 eqw" 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 coloredeq eqd" style="">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style="color:red"><span class="mord mathnormal coloredeq eql" style="">ϵ</span></span></span></span></span></span></span> in place of <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 eqv" 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 eqw" 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>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">155</span> <span class="bp">self</span><span class="o">.</span><span class="n">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">s</span> <span class="o">+</span> <span class="n">group</span><span class="p">[</span><span class="s1">'eps'</span><span class="p">])</span>
|
||
<span class="lineno">156</span> <span class="k">else</span><span class="p">:</span></pre></div>
|
||
</div>
|
||
</div>
|
||
<div class='section' id='section-25'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
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<a href='#section-25'>#</a>
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</div>
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<p>Perform <em>Rectified Adam</em> update defined in <a href="radam.html"><code class="highlight"><span></span><span class="n">radam</span><span class="o">.</span><span class="n">py</span></code>
|
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</a>, with <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord" style="color:cyan"><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">s</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 eqw" 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 coloredeq eqd" style="">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord" style="color:red"><span class="mord mathnormal coloredeq eql" style="">ϵ</span></span></span></span></span></span></span> in place of <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 eqv" 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 eqw" 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>
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<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">159</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">s</span> <span class="o">+</span> <span class="n">group</span><span class="p">[</span><span class="s1">'eps'</span><span class="p">])</span></pre></div>
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