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<h1>Transformer XL</h1>
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<p>This is an implementation of
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<a href="https://arxiv.org/abs/1901.02860">Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context</a>
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in <a href="https://pytorch.org">PyTorch</a>.</p>
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<p>Transformer has a limited attention span,
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equal to the length of the sequence trained in parallel.
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All these positions have a fixed positional encoding.
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Transformer XL increases this attention span by letting
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each of the positions pay attention to precalculated past embeddings.
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For instance if the context length is $l$, it will keep the embeddings of
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all layers for previous batch of length $l$ and feed them to current step.
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If we use fixed-positional encodings these pre-calculated embeddings will have
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the same positions as the current context.
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They introduce relative positional encoding, where the positional encodings
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are introduced at the attention calculation.</p>
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<p>Annotated implementation of relative multi-headed attention is in <a href="relative_mha.html"><code>relative_mha.py</code></a>.</p>
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<p>Here’s <a href="experiment.html">the training code</a> and a notebook for training a transformer XL model on Tiny Shakespeare dataset.</p>
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<p><a href="https://colab.research.google.com/github/lab-ml/nn/blob/master/labml_nn/transformers/xl/experiment.ipynb"><img alt="Open In Colab" src="https://colab.research.google.com/assets/colab-badge.svg" /></a>
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<div class='code'>
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<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">List</span><span class="p">,</span> <span class="n">Optional</span>
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<span class="lineno">37</span>
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<span class="lineno">38</span><span class="kn">import</span> <span class="nn">torch</span>
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<span class="lineno">39</span><span class="kn">import</span> <span class="nn">torch.nn</span> <span class="k">as</span> <span class="nn">nn</span>
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<span class="lineno">40</span>
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<span class="lineno">41</span><span class="kn">from</span> <span class="nn">labml_helpers.module</span> <span class="kn">import</span> <span class="n">Module</span>
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<span class="lineno">42</span><span class="kn">from</span> <span class="nn">labml_nn.utils</span> <span class="kn">import</span> <span class="n">clone_module_list</span>
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<span class="lineno">43</span><span class="kn">from</span> <span class="nn">.relative_mha</span> <span class="kn">import</span> <span class="n">RelativeMultiHeadAttention</span>
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<span class="lineno">44</span><span class="kn">from</span> <span class="nn">..feed_forward</span> <span class="kn">import</span> <span class="n">FeedForward</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-1'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-1'>#</a>
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</div>
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<h2>Transformer XL Layer</h2>
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<p>The transformer XL model comprises of a number of these layers.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">47</span><span class="k">class</span> <span class="nc">TransformerXLLayer</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-2'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-2'>#</a>
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</div>
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<ul>
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<li><code>d_model</code> is the token embedding size</li>
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<li><code>self_attn</code> is the <a href="relative_mha.html">self attention module</a></li>
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<li><code>feed_forward</code> is the feed forward module</li>
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<li><code>dropout_prob</code> is the probability of dropping out after self attention and FFN</li>
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</ul>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">53</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="o">*</span><span class="p">,</span>
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<span class="lineno">54</span> <span class="n">d_model</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
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<span class="lineno">55</span> <span class="n">self_attn</span><span class="p">:</span> <span class="n">RelativeMultiHeadAttention</span><span class="p">,</span>
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<span class="lineno">56</span> <span class="n">feed_forward</span><span class="p">:</span> <span class="n">FeedForward</span><span class="p">,</span>
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<span class="lineno">57</span> <span class="n">dropout_prob</span><span class="p">:</span> <span class="nb">float</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-3'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-3'>#</a>
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</div>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">64</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
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<span class="lineno">65</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="n">d_model</span>
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<span class="lineno">66</span> <span class="bp">self</span><span class="o">.</span><span class="n">self_attn</span> <span class="o">=</span> <span class="n">self_attn</span>
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<span class="lineno">67</span> <span class="bp">self</span><span class="o">.</span><span class="n">feed_forward</span> <span class="o">=</span> <span class="n">feed_forward</span>
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<span class="lineno">68</span> <span class="bp">self</span><span class="o">.</span><span class="n">dropout</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Dropout</span><span class="p">(</span><span class="n">dropout_prob</span><span class="p">)</span>
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<span class="lineno">69</span> <span class="bp">self</span><span class="o">.</span><span class="n">norm_self_attn</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">LayerNorm</span><span class="p">([</span><span class="n">d_model</span><span class="p">])</span>
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<span class="lineno">70</span> <span class="bp">self</span><span class="o">.</span><span class="n">norm_ff</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">LayerNorm</span><span class="p">([</span><span class="n">d_model</span><span class="p">])</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-4'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-4'>#</a>
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</div>
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<ul>
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<li><code>x</code> is a tensor of the token level feature vectors of shape <code>[seq_len, batch_size, d_model]</code></li>
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<li><code>mem</code> is a tensor of the past token level feature vectors of shape <code>[mem_len, batch_size, d_model]</code></li>
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<li><code>mask</code> is a matrix of shape <code>[seq_len, mem_len + seq_len, batch_size]</code> or <code>[seq_len, mem_len + seq_len, 1]</code>.
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<code>mask[i, j]</code> is true if token at <code>i</code> can see token at <code>j</code>.</li>
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</ul>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">72</span> <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span>
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<span class="lineno">73</span> <span class="n">x</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span>
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<span class="lineno">74</span> <span class="n">mem</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">],</span>
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<span class="lineno">75</span> <span class="n">mask</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>
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</div>
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</div>
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<div class='section' id='section-5'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-5'>#</a>
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</div>
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<p>Normalize the vectors before doing self attention</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">83</span> <span class="n">z</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">norm_self_attn</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-6'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-6'>#</a>
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</div>
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<p>If there is memory</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">85</span> <span class="k">if</span> <span class="n">mem</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-7'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-7'>#</a>
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</div>
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<p>Normalize it</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">87</span> <span class="n">mem</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">norm_self_attn</span><span class="p">(</span><span class="n">mem</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-8'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-8'>#</a>
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</div>
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<p>Concatenate with <code>z</code></p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">89</span> <span class="n">m_z</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cat</span><span class="p">((</span><span class="n">mem</span><span class="p">,</span> <span class="n">z</span><span class="p">),</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-9'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-9'>#</a>
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</div>
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<p>Ignore if there is no memory</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">91</span> <span class="k">else</span><span class="p">:</span>
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<span class="lineno">92</span> <span class="n">m_z</span> <span class="o">=</span> <span class="n">z</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-10'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-10'>#</a>
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</div>
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<p>Attention</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">94</span> <span class="n">self_attn</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">self_attn</span><span class="p">(</span><span class="n">query</span><span class="o">=</span><span class="n">z</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="n">m_z</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="n">m_z</span><span class="p">,</span> <span class="n">mask</span><span class="o">=</span><span class="n">mask</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-11'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-11'>#</a>
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</div>
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<p>Add the attention results</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">96</span> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">dropout</span><span class="p">(</span><span class="n">self_attn</span><span class="p">)</span></pre></div>
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</div>
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</div>
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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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</div>
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<p>Normalize for feed-forward</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">99</span> <span class="n">z</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">norm_ff</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></pre></div>
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</div>
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</div>
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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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</div>
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<p>Pass through the feed-forward network</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">101</span> <span class="n">ff</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">feed_forward</span><span class="p">(</span><span class="n">z</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-14'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-14'>#</a>
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</div>
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<p>Add the feed-forward results back</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">103</span> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">dropout</span><span class="p">(</span><span class="n">ff</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-15'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-15'>#</a>
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</div>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">106</span> <span class="k">return</span> <span class="n">x</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-16'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-16'>#</a>
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</div>
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<h2>Transformer XL Model</h2>
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<p>This consists of multiple transformer XL layers</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">109</span><span class="k">class</span> <span class="nc">TransformerXL</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
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<a href='#section-17'>#</a>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">116</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">layer</span><span class="p">:</span> <span class="n">TransformerXLLayer</span><span class="p">,</span> <span class="n">n_layers</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
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<span class="lineno">117</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span></pre></div>
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<a href='#section-18'>#</a>
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<p>Make copies of the transformer layer</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">119</span> <span class="bp">self</span><span class="o">.</span><span class="n">layers</span> <span class="o">=</span> <span class="n">clone_module_list</span><span class="p">(</span><span class="n">layer</span><span class="p">,</span> <span class="n">n_layers</span><span class="p">)</span></pre></div>
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<a href='#section-19'>#</a>
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<p>Final normalization layer</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">121</span> <span class="bp">self</span><span class="o">.</span><span class="n">norm</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">LayerNorm</span><span class="p">([</span><span class="n">layer</span><span class="o">.</span><span class="n">size</span><span class="p">])</span></pre></div>
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<div class='docs doc-strings'>
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<a href='#section-20'>#</a>
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<ul>
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<li><code>x</code> is a tensor of the token embeddings vectors of shape <code>[seq_len, batch_size, d_model]</code></li>
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<li><code>mem</code> is a list of tensors of the past token level feature vectors of shape
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<code>[mem_len, batch_size, d_model]</code> for each layer</li>
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<li><code>mask</code> is the masking matrix</li>
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</ul>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">123</span> <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</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">mem</span><span class="p">:</span> <span class="n">List</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">mask</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>
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<div class='section' id='section-21'>
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<a href='#section-21'>#</a>
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<p>List to store token level feature vectors,
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which will become the memories for the next sequential batch.</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">132</span> <span class="n">new_mem</span> <span class="o">=</span> <span class="p">[]</span></pre></div>
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<div class='section' id='section-22'>
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<a href='#section-22'>#</a>
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<p>Run through each transformer layer</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">134</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">layer</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">layers</span><span class="p">):</span></pre></div>
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<a href='#section-23'>#</a>
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<p>Add to the list of feature vectors</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">136</span> <span class="n">new_mem</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">detach</span><span class="p">())</span></pre></div>
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<a href='#section-24'>#</a>
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<p>Memory</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">138</span> <span class="n">m</span> <span class="o">=</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">if</span> <span class="n">mem</span> <span class="k">else</span> <span class="kc">None</span></pre></div>
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<div class='section' id='section-25'>
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<a href='#section-25'>#</a>
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<p>Run through the transformer XL layer</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">140</span> <span class="n">x</span> <span class="o">=</span> <span class="n">layer</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">mem</span><span class="o">=</span><span class="n">m</span><span class="p">,</span> <span class="n">mask</span><span class="o">=</span><span class="n">mask</span><span class="p">)</span></pre></div>
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<a href='#section-26'>#</a>
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<p>Finally, normalize the vectors</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">142</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">new_mem</span></pre></div>
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