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GitHub - yatindandi/Disentangled-Sequential-Autoencoder: Variational Autoencoder for Unsupervised and Disentangled Representation Learning of content and motion features in sequential data (Mandt et al.).
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8.351a1.312 1.312 0 0 1-1.146 1.954H1.33A1.313 1.313 0 0 1 .183 9.058ZM7 7V3H5v4Zm-1 3a1 1 0 1 0 0-2 1 1 0 0 0 0 2Z"></path> </svg> </span> <span></span> </div> </div> <div data-target="query-builder.screenReaderFeedback" aria-live="polite" aria-atomic="true" class="sr-only"></div> </query-builder></form> <div class="d-flex flex-row color-fg-muted px-3 text-small color-bg-default search-feedback-prompt"> <a target="_blank" href="https://docs.github.com/search-github/github-code-search/understanding-github-code-search-syntax" data-view-component="true" class="Link color-fg-accent text-normal ml-2"> Search syntax tips </a> <div class="d-flex flex-1"></div> </div> </div> </div> </div> </modal-dialog></div> </div> <div data-action="click:qbsearch-input#retract" class="dark-backdrop position-fixed" hidden data-target="qbsearch-input.darkBackdrop"></div> <div class="color-fg-default"> <dialog-helper> <dialog data-target="qbsearch-input.feedbackDialog" 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3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg></button> </div> </div> </div> <scrollable-region data-labelled-by="feedback-dialog-title"> <div data-view-component="true" class="Overlay-body"> <!-- '"` --><!-- </textarea></xmp> --></option></form><form id="code-search-feedback-form" data-turbo="false" action="/search/feedback" accept-charset="UTF-8" method="post"><input type="hidden" data-csrf="true" name="authenticity_token" value="S+asG7sA6n6SziCliIjwkJVFEmBPNji3wPVECesO7X8xsR+hdLgEUdAg1IF7ahZ4dFJhYFqaH9F7ZP0sDhNp6Q==" /> <p>We read every piece of feedback, and take your input very seriously.</p> <textarea name="feedback" class="form-control width-full mb-2" style="height: 120px" id="feedback"></textarea> <input name="include_email" id="include_email" aria-label="Include my email address so I can be contacted" class="form-control mr-2" type="checkbox"> 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class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDisentangled Sequential Autoencoder\u003c/h1\u003e\u003ca id=\"user-content-disentangled-sequential-autoencoder\" class=\"anchor\" aria-label=\"Permalink: Disentangled Sequential Autoencoder\" href=\"#disentangled-sequential-autoencoder\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eReproduction of the ICML 2018 publication \u003ca href=\"https://arxiv.org/abs/1803.02991\" rel=\"nofollow\"\u003eDisentangled Sequential Autoencoder by Yinghen Li and Stephen Mandt\u003c/a\u003e, a Variational Autoencoder Architecture for learning latent representations of high dimensional sequential data by approximately disentangling the time invariant and the time variable features, without any modification to the ELBO objective.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eNetwork Architecture\u003c/h1\u003e\u003ca id=\"user-content-network-architecture\" class=\"anchor\" aria-label=\"Permalink: Network Architecture\" href=\"#network-architecture\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ePrior of z:\u003c/h2\u003e\u003ca id=\"user-content-prior-of-z\" class=\"anchor\" aria-label=\"Permalink: Prior of z:\" href=\"#prior-of-z\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe prior of \u003ccode\u003ez\u003c/code\u003e is a Gaussian with mean and variance computed by the LSTM as follows\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"h_t, c_t = prior_lstm(z_t-1, (h_t, c_t)) where h_t is the hidden state and c_t is the cell state\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003eh_t, c_t = prior_lstm(z_t-1, (h_t, c_t)) where h_t is the hidden state and c_t is the cell state\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eNow the hidden state \u003ccode\u003eh_t\u003c/code\u003e is used to compute the mean and variance of \u003ccode\u003ez_t\u003c/code\u003e using an affine transform\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"z_mean, z_log_variance = affine_mean(h_t), affine_logvar(h_t)\nz = reparameterize(z_mean, z_log_variance)\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003ez_mean, z_log_variance = affine_mean(h_t), affine_logvar(h_t)\nz = reparameterize(z_mean, z_log_variance)\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe hidden state has dimension 512 and z has dimension 32\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eConvolutional Encoder:\u003c/h2\u003e\u003ca id=\"user-content-convolutional-encoder\" class=\"anchor\" aria-label=\"Permalink: Convolutional Encoder:\" href=\"#convolutional-encoder\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe convolutional encoder consists of 4 convolutional layers with 256 layers and a kernel size of 5\nEach convolution is followed by a batch normalization layer and a LeakyReLU(0.2) nonlinearity.\nFor the 3,64,64 frames (all image dimensions are in channel, width, height) in the sprites dataset the following dimension changes take place\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003e3,64,64 -\u0026gt; 256,64,64 -\u0026gt; 256,32,32 -\u0026gt; 256,16,16 -\u0026gt; 256,8,8 (where each -\u0026gt; consists of a convolution, batch normalization followed by LeakyReLU(0.2))\u003c/code\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe 8,8,256 tensor is unrolled into a vector of size \u003ccode\u003e8*8*256\u003c/code\u003e which is then made to undergo the following tansformations\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003e8*8*256 -\u0026gt; 4096 -\u0026gt; 2048 (where each -\u0026gt; consists of an affine transformation, batch normalization followed by LeakyReLU(0.2)) \u003c/code\u003e\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eApproximate Posterior For f:\u003c/h2\u003e\u003ca id=\"user-content-approximate-posterior-for-f\" class=\"anchor\" aria-label=\"Permalink: Approximate Posterior For f:\" href=\"#approximate-posterior-for-f\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe approximate posterior is parameterized by a bidirectional LSTM that takes the entire sequence of transformed \u003ccode\u003ex_t\u003c/code\u003es (after being fed into the convolutional encoder)\nas input in each timestep. The hidden layer dimension is 512\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThen the features from the unit corresponding to the last timestep of the forward LSTM and the unit corresponding to the first timestep of the\nbackward LSTM (as shown in the diagram in the paper) are concatenated and fed to two affine layers (without any added nonlinearity) to compute\nthe mean and variance of the Gaussian posterior for f\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eApproximate Posterior for z (Factorized q)\u003c/h2\u003e\u003ca id=\"user-content-approximate-posterior-for-z-factorized-q\" class=\"anchor\" aria-label=\"Permalink: Approximate Posterior for z (Factorized q)\" href=\"#approximate-posterior-for-z-factorized-q\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eEach \u003ccode\u003ex_t\u003c/code\u003e is first fed into an affine layer followed by a LeakyReLU(0.2) nonlinearity to generate an intermediate feature vector of dimension 512,\nwhich is then followed by two affine layers (without any added nonlinearity) to compute the mean and variance of the Gaussian Posterior of each \u003ccode\u003ez_t\u003c/code\u003e\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"inter_t = intermediate_affine(x_t)\nz_mean_t, z_log_variance_t = affine_mean(inter_t), affine_logvar(inter_t)\nz = reparameterize(z_mean_t, z_log_variance_t)\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003einter_t = intermediate_affine(x_t)\nz_mean_t, z_log_variance_t = affine_mean(inter_t), affine_logvar(inter_t)\nz = reparameterize(z_mean_t, z_log_variance_t)\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eApproximate Posterior for z (FULL q)\u003c/h2\u003e\u003ca id=\"user-content-approximate-posterior-for-z-full-q\" class=\"anchor\" aria-label=\"Permalink: Approximate Posterior for z (FULL q)\" href=\"#approximate-posterior-for-z-full-q\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe vector \u003ccode\u003ef\u003c/code\u003e is concatenated to each \u003ccode\u003ev_t\u003c/code\u003e where \u003ccode\u003ev_t\u003c/code\u003e is the encodings generated for each frame \u003ccode\u003ex_t\u003c/code\u003e by the convolutional encoder. This entire sequence is fed into a bi-LSTM\nof hidden layer dimension 512. Then the features of the forward and backward LSTMs are fed into an RNN having a hidden layer dimension 512. The output \u003ccode\u003eh_t\u003c/code\u003e of each timestep\nof this RNN transformed by two affine transformations (without any added nonlinearity) to compute the mean and variance of the Gaussian Posterior of each \u003ccode\u003ez_t\u003c/code\u003e\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"g_t = [v_t, f] for each timestep\nforward_features, backward_features = lstm(g_t for all timesteps)\nh_t = rnn([forward_features, backward_features])\nz_mean_t, z_log_variance_t = affine_mean(h_t), affine_logvar(h_t)\nz = reparameterize(z_mean_t, z_log_variance_t)\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003eg_t = [v_t, f] for each timestep\nforward_features, backward_features = lstm(g_t for all timesteps)\nh_t = rnn([forward_features, backward_features])\nz_mean_t, z_log_variance_t = affine_mean(h_t), affine_logvar(h_t)\nz = reparameterize(z_mean_t, z_log_variance_t)\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eConvolutional Decoder For Conditional Distribution\u003c/h2\u003e\u003ca id=\"user-content-convolutional-decoder-for-conditional-distribution\" class=\"anchor\" aria-label=\"Permalink: Convolutional Decoder For Conditional Distribution\" href=\"#convolutional-decoder-for-conditional-distribution\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe architecture is symmetric to that of the convolutional encoder. The vector \u003ccode\u003ef\u003c/code\u003e is concatenated to each \u003ccode\u003ez_t\u003c/code\u003e, which then undergoes two subsequent\naffine transforms, causing the following change in dimensions\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003e256 + 32 -\u0026gt; 4096 -\u0026gt; 8*8*256\u003c/code\u003e (where each -\u0026gt; consists of an affine transformation, batch normalization followed by LeakyReLU(0.2))\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe \u003ccode\u003e8*8*256\u003c/code\u003e tensor is reshaped into a tensor of shape 256,8,8 and then undergoes the following dimension changes\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003e256,8,8 -\u0026gt; 256,16,16 -\u0026gt; 256,32,32 -\u0026gt; 256,64,64 -\u0026gt; 3,64,64\u003c/code\u003e (where each -\u0026gt; consists of a transposed convolution, batch normalization followed by LeakyReLU(0.2)\nwith the exception of the last layer that does not have batchnorm and uses tanh nonlinearity)\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eOptimizer\u003c/h1\u003e\u003ca id=\"user-content-optimizer\" class=\"anchor\" aria-label=\"Permalink: Optimizer\" href=\"#optimizer\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe model is trained with the Adam optimizer with a learning rate of 0.0002, betas of 0.9 and 0.999, with a batch size of 25 for 200 epochs\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch1 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eHyperparameters:\u003c/h1\u003e\u003ca id=\"user-content-hyperparameters\" class=\"anchor\" aria-label=\"Permalink: Hyperparameters:\" href=\"#hyperparameters\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eDimension of the content encoding f : 256\u003c/li\u003e\n\u003cli\u003eDimension of the dynamics encoding of a frame z_t : 32\u003c/li\u003e\n\u003cli\u003eNumber of frames in the video : 8\u003c/li\u003e\n\u003cli\u003eDimension of the hidden states of the RNNs : 512\u003c/li\u003e\n\u003cli\u003eNonlinearity used in convolutional and deconvolutional layers : LeakyReLU(0.2) in intermediate layers, Tanh in last layer of deconvolutional (Chosen arbitrarily, not stated in the paper)\u003c/li\u003e\n\u003cli\u003eNumber of channels in the convolutional and deconvolutional layers : 256\u003c/li\u003e\n\u003cli\u003eDimension of convolutional encoding generated from the video frames: 2048 (Chosen arbitrarily, not stated in the paper)\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/article\u003e","loaded":true,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":[{"level":1,"text":"Disentangled Sequential Autoencoder","anchor":"disentangled-sequential-autoencoder","htmlText":"Disentangled Sequential Autoencoder"},{"level":1,"text":"Network Architecture","anchor":"network-architecture","htmlText":"Network Architecture"},{"level":2,"text":"Prior of z:","anchor":"prior-of-z","htmlText":"Prior of z:"},{"level":2,"text":"Convolutional Encoder:","anchor":"convolutional-encoder","htmlText":"Convolutional Encoder:"},{"level":2,"text":"Approximate Posterior For f:","anchor":"approximate-posterior-for-f","htmlText":"Approximate Posterior For f:"},{"level":2,"text":"Approximate Posterior for z (Factorized q)","anchor":"approximate-posterior-for-z-factorized-q","htmlText":"Approximate Posterior for z (Factorized q)"},{"level":2,"text":"Approximate Posterior for z (FULL q)","anchor":"approximate-posterior-for-z-full-q","htmlText":"Approximate Posterior for z (FULL q)"},{"level":2,"text":"Convolutional Decoder For Conditional Distribution","anchor":"convolutional-decoder-for-conditional-distribution","htmlText":"Convolutional Decoder For Conditional Distribution"},{"level":1,"text":"Optimizer","anchor":"optimizer","htmlText":"Optimizer"},{"level":1,"text":"Hyperparameters:","anchor":"hyperparameters","htmlText":"Hyperparameters:"}],"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2Fyatindandi%2FDisentangled-Sequential-Autoencoder"}}],"overviewFilesProcessingTime":0}},"appPayload":{"helpUrl":"https://docs.github.com","findFileWorkerPath":"/assets-cdn/worker/find-file-worker-1583894afd38.js","findInFileWorkerPath":"/assets-cdn/worker/find-in-file-worker-67668e8c2caa.js","githubDevUrl":null,"enabled_features":{"code_nav_ui_events":false,"overview_shared_code_dropdown_button":false,"react_blob_overlay":false,"copilot_conversational_ux_embedding_update":false,"copilot_smell_icebreaker_ux":true,"copilot_workspace":false,"accessible_code_button":true}}}}</script> <div data-target="react-partial.reactRoot"><style data-styled="true" data-styled-version="5.3.11">.iVEunk{margin-top:16px;margin-bottom:16px;}/*!sc*/ 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.018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Reproduction of the ICML 2018 publication <a href="https://arxiv.org/abs/1803.02991" rel="nofollow">Disentangled Sequential Autoencoder by Yinghen Li and Stephen Mandt</a>, a Variational Autoencoder Architecture for learning latent representations of high dimensional sequential data by approximately disentangling the time invariant and the time variable features, without any modification to the ELBO objective.</p> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Network Architecture</h1><a id="user-content-network-architecture" class="anchor" aria-label="Permalink: Network Architecture" href="#network-architecture"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Prior of z:</h2><a id="user-content-prior-of-z" class="anchor" aria-label="Permalink: Prior of z:" href="#prior-of-z"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The prior of <code>z</code> is a Gaussian with mean and variance computed by the LSTM as follows</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="h_t, c_t = prior_lstm(z_t-1, (h_t, c_t)) where h_t is the hidden state and c_t is the cell state"><pre class="notranslate"><code>h_t, c_t = prior_lstm(z_t-1, (h_t, c_t)) where h_t is the hidden state and c_t is the cell state </code></pre></div> <p dir="auto">Now the hidden state <code>h_t</code> is used to compute the mean and variance of <code>z_t</code> using an affine transform</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="z_mean, z_log_variance = affine_mean(h_t), affine_logvar(h_t) z = reparameterize(z_mean, z_log_variance)"><pre class="notranslate"><code>z_mean, z_log_variance = affine_mean(h_t), affine_logvar(h_t) z = reparameterize(z_mean, z_log_variance) </code></pre></div> <p dir="auto">The hidden state has dimension 512 and z has dimension 32</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Convolutional Encoder:</h2><a id="user-content-convolutional-encoder" class="anchor" aria-label="Permalink: Convolutional Encoder:" href="#convolutional-encoder"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The convolutional encoder consists of 4 convolutional layers with 256 layers and a kernel size of 5 Each convolution is followed by a batch normalization layer and a LeakyReLU(0.2) nonlinearity. For the 3,64,64 frames (all image dimensions are in channel, width, height) in the sprites dataset the following dimension changes take place</p> <p dir="auto"><code>3,64,64 -> 256,64,64 -> 256,32,32 -> 256,16,16 -> 256,8,8 (where each -> consists of a convolution, batch normalization followed by LeakyReLU(0.2))</code></p> <p dir="auto">The 8,8,256 tensor is unrolled into a vector of size <code>8*8*256</code> which is then made to undergo the following tansformations</p> <p dir="auto"><code>8*8*256 -> 4096 -> 2048 (where each -> consists of an affine transformation, batch normalization followed by LeakyReLU(0.2)) </code></p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Approximate Posterior For f:</h2><a id="user-content-approximate-posterior-for-f" class="anchor" aria-label="Permalink: Approximate Posterior For f:" href="#approximate-posterior-for-f"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The approximate posterior is parameterized by a bidirectional LSTM that takes the entire sequence of transformed <code>x_t</code>s (after being fed into the convolutional encoder) as input in each timestep. The hidden layer dimension is 512</p> <p dir="auto">Then the features from the unit corresponding to the last timestep of the forward LSTM and the unit corresponding to the first timestep of the backward LSTM (as shown in the diagram in the paper) are concatenated and fed to two affine layers (without any added nonlinearity) to compute the mean and variance of the Gaussian posterior for f</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Approximate Posterior for z (Factorized q)</h2><a id="user-content-approximate-posterior-for-z-factorized-q" class="anchor" aria-label="Permalink: Approximate Posterior for z (Factorized q)" href="#approximate-posterior-for-z-factorized-q"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Each <code>x_t</code> is first fed into an affine layer followed by a LeakyReLU(0.2) nonlinearity to generate an intermediate feature vector of dimension 512, which is then followed by two affine layers (without any added nonlinearity) to compute the mean and variance of the Gaussian Posterior of each <code>z_t</code></p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="inter_t = intermediate_affine(x_t) z_mean_t, z_log_variance_t = affine_mean(inter_t), affine_logvar(inter_t) z = reparameterize(z_mean_t, z_log_variance_t)"><pre class="notranslate"><code>inter_t = intermediate_affine(x_t) z_mean_t, z_log_variance_t = affine_mean(inter_t), affine_logvar(inter_t) z = reparameterize(z_mean_t, z_log_variance_t) </code></pre></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Approximate Posterior for z (FULL q)</h2><a id="user-content-approximate-posterior-for-z-full-q" class="anchor" aria-label="Permalink: Approximate Posterior for z (FULL q)" href="#approximate-posterior-for-z-full-q"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The vector <code>f</code> is concatenated to each <code>v_t</code> where <code>v_t</code> is the encodings generated for each frame <code>x_t</code> by the convolutional encoder. This entire sequence is fed into a bi-LSTM of hidden layer dimension 512. Then the features of the forward and backward LSTMs are fed into an RNN having a hidden layer dimension 512. The output <code>h_t</code> of each timestep of this RNN transformed by two affine transformations (without any added nonlinearity) to compute the mean and variance of the Gaussian Posterior of each <code>z_t</code></p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="g_t = [v_t, f] for each timestep forward_features, backward_features = lstm(g_t for all timesteps) h_t = rnn([forward_features, backward_features]) z_mean_t, z_log_variance_t = affine_mean(h_t), affine_logvar(h_t) z = reparameterize(z_mean_t, z_log_variance_t)"><pre class="notranslate"><code>g_t = [v_t, f] for each timestep forward_features, backward_features = lstm(g_t for all timesteps) h_t = rnn([forward_features, backward_features]) z_mean_t, z_log_variance_t = affine_mean(h_t), affine_logvar(h_t) z = reparameterize(z_mean_t, z_log_variance_t) </code></pre></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Convolutional Decoder For Conditional Distribution</h2><a id="user-content-convolutional-decoder-for-conditional-distribution" class="anchor" aria-label="Permalink: Convolutional Decoder For Conditional Distribution" href="#convolutional-decoder-for-conditional-distribution"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The architecture is symmetric to that of the convolutional encoder. The vector <code>f</code> is concatenated to each <code>z_t</code>, which then undergoes two subsequent affine transforms, causing the following change in dimensions</p> <p dir="auto"><code>256 + 32 -> 4096 -> 8*8*256</code> (where each -> consists of an affine transformation, batch normalization followed by LeakyReLU(0.2))</p> <p dir="auto">The <code>8*8*256</code> tensor is reshaped into a tensor of shape 256,8,8 and then undergoes the following dimension changes</p> <p dir="auto"><code>256,8,8 -> 256,16,16 -> 256,32,32 -> 256,64,64 -> 3,64,64</code> (where each -> consists of a transposed convolution, batch normalization followed by LeakyReLU(0.2) with the exception of the last layer that does not have batchnorm and uses tanh nonlinearity)</p> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Optimizer</h1><a id="user-content-optimizer" class="anchor" aria-label="Permalink: Optimizer" href="#optimizer"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The model is trained with the Adam optimizer with a learning rate of 0.0002, betas of 0.9 and 0.999, with a batch size of 25 for 200 epochs</p> <div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Hyperparameters:</h1><a id="user-content-hyperparameters" class="anchor" aria-label="Permalink: Hyperparameters:" href="#hyperparameters"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li>Dimension of the content encoding f : 256</li> <li>Dimension of the dynamics encoding of a frame z_t : 32</li> <li>Number of frames in the video : 8</li> <li>Dimension of the hidden states of the RNNs : 512</li> <li>Nonlinearity used in convolutional and deconvolutional layers : LeakyReLU(0.2) in intermediate layers, Tanh in last layer of deconvolutional (Chosen arbitrarily, not stated in the paper)</li> <li>Number of channels in the convolutional and deconvolutional layers : 256</li> <li>Dimension of convolutional encoding generated from the video frames: 2048 (Chosen arbitrarily, not stated in the paper)</li> </ul> </article></div></div></div></div></div> <!-- --> <!-- --> <script type="application/json" id="__PRIMER_DATA_:R0:__">{"resolvedServerColorMode":"day"}</script></div> </react-partial> <input type="hidden" data-csrf="true" value="POXtWN3e0sJcfnwwEP7lb9ZH12Rju0B7f2JGNcIaLBoW0MbPxmyPMHQJMO46GAKBGQgNJLUJLgax5K2A7fslaQ==" /> </div> <div data-view-component="true" class="Layout-sidebar"> <div class="BorderGrid about-margin" data-pjax> <div class="BorderGrid-row"> <div class="BorderGrid-cell"> <div class="hide-sm hide-md"> <h2 class="mb-3 h4">About</h2> <p class="f4 my-3"> Variational Autoencoder for Unsupervised and Disentangled Representation Learning 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