http://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&feed=atom&action=historygenerating text with recurrent neural networks - Revision history2024-03-29T00:05:18ZRevision history for this page on the wikiMediaWiki 1.41.0http://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27730&oldid=prevConversion script: Conversion script moved page Generating text with recurrent neural networks to generating text with recurrent neural networks: Converting page titles to lowercase2017-08-30T13:46:31Z<p>Conversion script moved page <a href="/statwiki/index.php?title=Generating_text_with_recurrent_neural_networks" class="mw-redirect" title="Generating text with recurrent neural networks">Generating text with recurrent neural networks</a> to <a href="/statwiki/index.php?title=generating_text_with_recurrent_neural_networks" title="generating text with recurrent neural networks">generating text with recurrent neural networks</a>: Converting page titles to lowercase</p>
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</td></tr></table>Conversion scripthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27319&oldid=prevTrttse: /* The RNN as a Generative Model */2015-12-15T05:10:19Z<p><span dir="auto"><span class="autocomment">The RNN as a Generative Model</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= The RNN as a Generative Model =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= The RNN as a Generative Model =</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The goal of the model is to predict the next character given a string of characters. More formally, given a training sequence <math>(x_1,...,x_T)</math>, the RNN uses its output vectors <math>(o_1,...,o_T)</math> to obtain a sequence of predictive distributions <math>P(x_{t+1}|x_{\le t})</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The goal of the model is to predict the next character given a string of characters. More formally, given a training sequence <math>(x_1,...,x_T)</math>, the RNN uses its output vectors <math>(o_1,...,o_T)</math> to obtain a sequence of predictive distributions <math>P(x_{t+1}|x_{\le t}<ins style="font-weight: bold; text-decoration: none;">) = softmax(o_t</ins>)</math><ins style="font-weight: bold; text-decoration: none;">.</ins></div></td></tr>
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</table>Trttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27318&oldid=prevTrttse: /* The RNN as a Generative Model */2015-12-15T05:09:14Z<p><span dir="auto"><span class="autocomment">The RNN as a Generative Model</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= The RNN as a Generative Model =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= The RNN as a Generative Model =</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The goal of the model is to predict the next character given a string of characters. More formally, given a training sequence <math>(x_1,...,x_T)</math>, the RNN uses its output vectors <math>(o_1,...,o_T)</math> to obtain a sequence of predictive distributions <math>P(x_{t+1}|<del style="font-weight: bold; text-decoration: none;">x</del>)</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The goal of the model is to predict the next character given a string of characters. More formally, given a training sequence <math>(x_1,...,x_T)</math>, the RNN uses its output vectors <math>(o_1,...,o_T)</math> to obtain a sequence of predictive distributions <math>P(x_{t+1}|<ins style="font-weight: bold; text-decoration: none;">x_{\le t}</ins>)</math></div></td></tr>
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</table>Trttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27317&oldid=prevTrttse: /* The RNN as a Generative Model */2015-12-15T05:07:23Z<p><span dir="auto"><span class="autocomment">The RNN as a Generative Model</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= The RNN as a Generative Model =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= The RNN as a Generative Model =</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The goal of the model is to predict the next character given a string of characters. More formally, given a training sequence <math>(x_1,...,x_T)</math>, the RNN uses its output vectors <math>(o_1,...,o_T)</math> to obtain a sequence of predictive distributions</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The goal of the model is to predict the next character given a string of characters. More formally, given a training sequence <math>(x_1,...,x_T)</math>, the RNN uses its output vectors <math>(o_1,...,o_T)</math> to obtain a sequence of predictive distributions <ins style="font-weight: bold; text-decoration: none;"><math>P(x_{t+1}|x)</math></ins></div></td></tr>
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</table>Trttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27316&oldid=prevTrttse: /* The RNN as a Generative Model */2015-12-15T05:06:34Z<p><span dir="auto"><span class="autocomment">The RNN as a Generative Model</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= The RNN as a Generative Model =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= The RNN as a Generative Model =</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The goal of the model is to predict the next character given a string of characters. More formally, given a training sequence <math>(x_1,...,x_T)</math>, the RNN uses its output vectors <math>(o_1,...,o_T)</math> to obtain a sequence of predictive distributions</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
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</table>Trttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27315&oldid=prevTrttse at 05:02, 15 December 20152015-12-15T05:02:19Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the experiments described below, an MRNN is trained via Hessian Free optimization on sequences of 250 characters. The first 50 characters used to condition the hidden state, so only 200 predictions are generated per sequence. 1500 hidden units were used, along with 1500 factors (i.e. multiplicative gates, or the triangles in the figure above), yielding an unrolled network of 500 layers if the multiplicative units are treated as forming a layer. Training was performed with a parallelized system consisting of 8 GPUs. A vocabulary of 86 characters was used in all cases.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the experiments described below, an MRNN is trained via Hessian Free optimization on sequences of 250 characters. The first 50 characters used to condition the hidden state, so only 200 predictions are generated per sequence. 1500 hidden units were used, along with 1500 factors (i.e. multiplicative gates, or the triangles in the figure above), yielding an unrolled network of 500 layers if the multiplicative units are treated as forming a layer. Training was performed with a parallelized system consisting of 8 GPUs. A vocabulary of 86 characters was used in all cases.</div></td></tr>
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</table>Trttsehttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27297&oldid=prevMgohari2 at 19:04, 14 December 20152015-12-14T19:04:58Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>\ h_t = <del style="font-weight: bold; text-decoration: none;">\</del>tanh(W_{hi}i_t + W_{hh}h_{t-1} + b_h) </math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>\ h_t = tanh(W_{hi}i_t + W_{hh}h_{t-1} + b_h) </math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>While this optimization technique is described elsewhere in Martens (2010) <ref> Martens, J. [http://icml2010.haifa.il.ibm.com/papers/458.pdf "Deep learning via Hessian-free optimization."] ICML, (2010) </ref></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>While this optimization technique is described elsewhere in Martens (2010) <ref> Martens, J. [http://icml2010.haifa.il.ibm.com/papers/458.pdf "Deep learning via Hessian-free optimization."] ICML, (2010) </ref></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>, its use is essential to obtaining the successful results reported in this paper. In brief, the technique involves uses information about the 2nd derivatives of the cost function to perform more intelligent parameter updates. This information is helpful because in cases where the gradient is changing very slowly on a particular dimension, it is more efficient to take larger steps in the direction of descent along this dimension. Alternatively, if the the gradient is changing very rapidly on a particular dimension, then it makes sense to take smaller steps to avoid 'bouncing' off of a step incline in the cost function and moving to a less desirable location in parameter space. The relevant 2nd order information is computed using the method of finite differences to avoid computing the Hessian of the cost function. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>, its use is essential to obtaining the successful results reported in this paper. In brief, the technique involves uses information about the 2nd derivatives of the cost function to perform more intelligent parameter updates. This information is helpful because in cases where the gradient is changing very slowly on a particular dimension, it is more efficient to take larger steps in the direction of descent along this dimension. Alternatively, if the the gradient is changing very rapidly on a particular dimension, then it makes sense to take smaller steps to avoid 'bouncing' off of a step incline in the cost function and moving to a less desirable location in parameter space. The relevant 2nd order information is computed using the method of finite differences to avoid computing the Hessian of the cost function<ins style="font-weight: bold; text-decoration: none;">.In fact instead of computing and inverting the H matrix when updating equations, the Gauss-Newton approximation is used for the Hessian matrix which is quite good approximation to the Hessian and practically cheaper to compute</ins>. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>What is important about this technique is that it provides a solution to problem of vanishing and exploding gradients during the training of recurrent neural networks. Vanishing gradients are accommodated by descending much more rapidly along the cost function in areas where it has relatively low curvature (e.g., when the cost function is nearly flat), while exploding gradients are accommodated by descending much more slowly along the cost function in areas where it has relatively high curvature (e.g., when there is a steep cliff). The figure below illustrates how hessian free optimization improves the training of neural networks in general. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>What is important about this technique is that it provides a solution to problem of vanishing and exploding gradients during the training of recurrent neural networks. Vanishing gradients are accommodated by descending much more rapidly along the cost function in areas where it has relatively low curvature (e.g., when the cost function is nearly flat), while exploding gradients are accommodated by descending much more slowly along the cost function in areas where it has relatively high curvature (e.g., when there is a steep cliff). The figure below illustrates how hessian free optimization improves the training of neural networks in general. </div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Discussion =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Discussion =</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>One aspect of this work that is worth considering concerns the degree to which the use of input-dependent gating of the information being passed <del style="font-weight: bold; text-decoration: none;">between </del>hidden <del style="font-weight: bold; text-decoration: none;">states </del>actually improves the results above the use of a standard recurrent neural network. Presumably, the use of hessian<del style="font-weight: bold; text-decoration: none;">-</del>free optimization allows such a network <del style="font-weight: bold; text-decoration: none;">to be successfully trained</del>, so it would be helpful to <del style="font-weight: bold; text-decoration: none;">compare with </del>the results obtained using an MRNN. MRNNs already learn surprisingly good language models using only 1500 hidden units, and unlike other approaches such as the sequence <del style="font-weight: bold; text-decoration: none;">memorizer </del>and PAQ, they are easy to extend along various dimensions. Otherwise, it is hard to discern the relative importance of the optimization technique and the network architecture in achieving the good language <del style="font-weight: bold; text-decoration: none;">modeling </del>results reported in this paper.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>One aspect of this work that is worth considering concerns the degree to which the use of input-dependent gating of the information being passed <ins style="font-weight: bold; text-decoration: none;">from </ins>hidden <ins style="font-weight: bold; text-decoration: none;">state to hidden state </ins>actually improves the results <ins style="font-weight: bold; text-decoration: none;">over and </ins>above the use of a standard recurrent neural network. Presumably, the use of hessian free optimization allows <ins style="font-weight: bold; text-decoration: none;">one to successfully train </ins>such a network, so it would be helpful to <ins style="font-weight: bold; text-decoration: none;">see a comparison to </ins>the results obtained using an MRNN.MRNNs already learn surprisingly good language models</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>using only 1500 hidden units, and unlike other approaches such as the sequence <ins style="font-weight: bold; text-decoration: none;">memoizer </ins>and PAQ, they are easy to extend along various dimensions. Otherwise, it is hard to discern the relative importance of the optimization technique and the network architecture in achieving the good language <ins style="font-weight: bold; text-decoration: none;">modelling </ins>results reported in this paper.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The MRNN assigns probability to plausible words that do not exist in the training set. This is a good property that enabled the MRNN to deal with real words that it did not see in the training set. <del style="font-weight: bold; text-decoration: none;">One </del>advantage of this model is that <del style="font-weight: bold; text-decoration: none;">it </del>avoids using a huge softmax over all known words by predicting the next word based on a sequence of character predictions, while some word-level language models actually make up binary spellings of words in a way that they can predict them one bit at each time<del style="font-weight: bold; text-decoration: none;">.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The MRNN assigns probability to plausible words that do not exist in the training set. This is a good property<ins style="font-weight: bold; text-decoration: none;">, </ins>that enabled the MRNN to deal with real words that it did not see in the training set. <ins style="font-weight: bold; text-decoration: none;">one </ins>advantage of this model is that<ins style="font-weight: bold; text-decoration: none;">, this model </ins>avoids using a huge softmax over all known words by predicting the next word based on a sequence of character predictions, while some word-level language models actually make up binary spellings of words in a way that they can predict them one bit at each time.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Although this paper is strictly concerned with producing very strong character-level models, I think it would be interesting to somehow combine the results of a character-level and word-level RNN into a larger text-generation model. The text generated by this model appears to perform well with grammar and on words that are unseen, but it seems to struggle with carrying a "train of thought". The sentences it generates are not very sensible in most cases, and a higher-level word model might be able to control some of that. However, I am not sure how to combine the word level with the character model, but a convolutional approach could certainly work</del>.</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Bibliography = </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Bibliography = </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><references /></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><references /></div></td></tr>
</table>Mgohari2http://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27296&oldid=prevAlcateri: /* Discussion */ Cleaned up the discussion and added a new idea about combining character and word level models.2015-12-14T18:47:42Z<p><span dir="auto"><span class="autocomment">Discussion: </span> Cleaned up the discussion and added a new idea about combining character and word level models.</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:47, 14 December 2015</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Discussion =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Discussion =</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>One aspect of this work that is worth considering concerns the degree to which the use of input-dependent gating of the information being passed <del style="font-weight: bold; text-decoration: none;">from </del>hidden <del style="font-weight: bold; text-decoration: none;">state to hidden state </del>actually improves the results <del style="font-weight: bold; text-decoration: none;">over and </del>above the use of a standard recurrent neural network. Presumably, the use of hessian free optimization allows <del style="font-weight: bold; text-decoration: none;">one to successfully train </del>such a network, so it would be helpful to <del style="font-weight: bold; text-decoration: none;">see a comparison to </del>the results obtained using an MRNN.MRNNs already learn surprisingly good language models</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>One aspect of this work that is worth considering concerns the degree to which the use of input-dependent gating of the information being passed <ins style="font-weight: bold; text-decoration: none;">between </ins>hidden <ins style="font-weight: bold; text-decoration: none;">states </ins>actually improves the results above the use of a standard recurrent neural network. Presumably, the use of hessian<ins style="font-weight: bold; text-decoration: none;">-</ins>free optimization allows such a network <ins style="font-weight: bold; text-decoration: none;">to be successfully trained</ins>, so it would be helpful to <ins style="font-weight: bold; text-decoration: none;">compare with </ins>the results obtained using an MRNN. MRNNs already learn surprisingly good language models using only 1500 hidden units, and unlike other approaches such as the sequence <ins style="font-weight: bold; text-decoration: none;">memorizer </ins>and PAQ, they are easy to extend along various dimensions. Otherwise, it is hard to discern the relative importance of the optimization technique and the network architecture in achieving the good language <ins style="font-weight: bold; text-decoration: none;">modeling </ins>results reported in this paper.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>using only 1500 hidden units, and unlike other approaches such as the sequence <del style="font-weight: bold; text-decoration: none;">memoizer </del>and PAQ, they are easy to extend along various dimensions. Otherwise, it is hard to discern the relative importance of the optimization technique and the network architecture in achieving the good language <del style="font-weight: bold; text-decoration: none;">modelling </del>results reported in this paper.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The MRNN assigns probability to plausible words that do not exist in the training set. This is a good property<del style="font-weight: bold; text-decoration: none;">, </del>that enabled the MRNN to deal with real words that it did not see in the training set. <del style="font-weight: bold; text-decoration: none;">one </del>advantage of this model is that<del style="font-weight: bold; text-decoration: none;">, this model </del>avoids using a huge softmax over all known words by predicting the next word based on a sequence of character predictions, while some word-level language models actually make up binary spellings of words in a way that they can predict them one bit at each time.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The MRNN assigns probability to plausible words that do not exist in the training set. This is a good property that enabled the MRNN to deal with real words that it did not see in the training set. <ins style="font-weight: bold; text-decoration: none;">One </ins>advantage of this model is that <ins style="font-weight: bold; text-decoration: none;">it </ins>avoids using a huge softmax over all known words by predicting the next word based on a sequence of character predictions, while some word-level language models actually make up binary spellings of words in a way that they can predict them one bit at each time<ins style="font-weight: bold; text-decoration: none;">.</ins></div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Although this paper is strictly concerned with producing very strong character-level models, I think it would be interesting to somehow combine the results of a character-level and word-level RNN into a larger text-generation model. The text generated by this model appears to perform well with grammar and on words that are unseen, but it seems to struggle with carrying a "train of thought". The sentences it generates are not very sensible in most cases, and a higher-level word model might be able to control some of that. However, I am not sure how to combine the word level with the character model, but a convolutional approach could certainly work</ins>.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Bibliography = </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Bibliography = </div></td></tr>
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</table>Alcaterihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27295&oldid=prevAlcateri: /* Introduction */2015-12-14T18:34:06Z<p><span dir="auto"><span class="autocomment">Introduction</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:<math>\ h_t = tanh(W_{hi}i_t + W_{hh}h_{t-1} + b_h) </math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:<math>\ h_t = <ins style="font-weight: bold; text-decoration: none;">\</ins>tanh(W_{hi}i_t + W_{hh}h_{t-1} + b_h) </math></div></td></tr>
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</table>Alcaterihttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=generating_text_with_recurrent_neural_networks&diff=27272&oldid=prevFatemehKarimi: /* Multiplicative Recurrent Neural Networks */2015-12-13T21:54:37Z<p><span dir="auto"><span class="autocomment">Multiplicative Recurrent Neural Networks</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Multiplicative Recurrent Neural Networks = </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Multiplicative Recurrent Neural Networks = </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The authors report that using a standard neural network trained via Hessian-free optimization produces only mediocre results. As such, they introduce a new architecture called a multiplicative recurrent neural network (MRNN). The motivating intuition behind this architecture is that the input at a given time step should both additively contribute to the hidden state (though the mapping performed by the input-to-hidden weights) and additionally determine the weights on the recurrent connections to the hidden state. In other words, the idea is to define a unique weight matrix <math>\ W_{hh} </math> for each possible input. The reason this design is hypothesized to the improve the predictive adequacy of the model is due to the idea that the ''conjunction'' of the input at one time step and the hidden state at the previous time step is important. Capturing this conjunction requires the input to influence the contribution of the previous hidden state to the current hidden state. Otherwise, the previous hidden state and the current input will make entirely independent contributions to the calculation of the current hidden state. Formally, this changes the calculation of the hidden state at a given time step as follows:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The authors report that using a standard neural network trained via Hessian-free optimization produces only mediocre results. As such, they introduce a new architecture called a multiplicative recurrent neural network (MRNN). The motivating intuition behind this architecture is that the input at a given time step should both additively contribute to the hidden state (though the mapping performed by the input-to-hidden weights) and additionally determine the weights on the recurrent connections to the hidden state<ins style="font-weight: bold; text-decoration: none;">. This approach came from viewing an RNN as a model of an tree in which each node is a hidden state vector and each edge is labelled by a character that determines how the parent node gives rise to the child node</ins>. In other words, the idea is to define a unique weight matrix <math>\ W_{hh} </math> for each possible input. The reason this design is hypothesized to the improve the predictive adequacy of the model is due to the idea that the ''conjunction'' of the input at one time step and the hidden state at the previous time step is important. Capturing this conjunction requires the input to influence the contribution of the previous hidden state to the current hidden state. Otherwise, the previous hidden state and the current input will make entirely independent contributions to the calculation of the current hidden state. Formally, this changes the calculation of the hidden state at a given time step as follows:</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[File:MRNN.png | frame | centre | A depiction of a multiplicative recurrent neural network unrolled through three time steps.]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[File:MRNN.png | frame | centre | A depiction of a multiplicative recurrent neural network unrolled through three time steps.]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the experiments described below, an MRNN is trained via Hessian Free optimization on sequences of 250 characters. The first 50 characters used to condition the hidden state, so only 200 predictions are generated per sequence. 1500 hidden units were used, along with 1500 factors (i.e. multiplicative gates, or the triangles in the figure above), yielding an unrolled network of 500 layers if the multiplicative units are treated as forming a layer. Training was performed with a parallelized system consisting of 8 GPUs. A vocabulary of 86 characters was used in all cases. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the experiments described below, an MRNN is trained via Hessian Free optimization on sequences of 250 characters. The first 50 characters used to condition the hidden state, so only 200 predictions are generated per sequence. 1500 hidden units were used, along with 1500 factors (i.e. multiplicative gates, or the triangles in the figure above), yielding an unrolled network of 500 layers if the multiplicative units are treated as forming a layer. Training was performed with a parallelized system consisting of 8 GPUs. A vocabulary of 86 characters was used in all cases.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Quantitative Experiments =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Quantitative Experiments =</div></td></tr>
</table>FatemehKarimi