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<!DOCTYPE html>
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<title>Automatic differentiation package - torch.autograd — PyTorch master documentation</title>
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<p class="caption"><span class="caption-text">Notes</span></p>
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<li class="toctree-l1"><a class="reference internal" href="notes/autograd.html">Autograd mechanics</a><ul>
<li class="toctree-l2"><a class="reference internal" href="notes/autograd.html#excluding-subgraphs-from-backward">Excluding subgraphs from backward</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="nn.html#replicationpad3d"><span class="hidden-section">ReplicationPad3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#zeropad2d"><span class="hidden-section">ZeroPad2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#constantpad2d"><span class="hidden-section">ConstantPad2d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#non-linear-activations">Non-linear Activations</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#relu"><span class="hidden-section">ReLU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#relu6"><span class="hidden-section">ReLU6</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#elu"><span class="hidden-section">ELU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#selu"><span class="hidden-section">SELU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#prelu"><span class="hidden-section">PReLU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#leakyrelu"><span class="hidden-section">LeakyReLU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#threshold"><span class="hidden-section">Threshold</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#hardtanh"><span class="hidden-section">Hardtanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#sigmoid"><span class="hidden-section">Sigmoid</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#tanh"><span class="hidden-section">Tanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#logsigmoid"><span class="hidden-section">LogSigmoid</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#softplus"><span class="hidden-section">Softplus</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#softshrink"><span class="hidden-section">Softshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#softsign"><span class="hidden-section">Softsign</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#tanhshrink"><span class="hidden-section">Tanhshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#softmin"><span class="hidden-section">Softmin</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#softmax"><span class="hidden-section">Softmax</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#softmax2d"><span class="hidden-section">Softmax2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#logsoftmax"><span class="hidden-section">LogSoftmax</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#normalization-layers">Normalization layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#batchnorm1d"><span class="hidden-section">BatchNorm1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#batchnorm2d"><span class="hidden-section">BatchNorm2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#batchnorm3d"><span class="hidden-section">BatchNorm3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#instancenorm1d"><span class="hidden-section">InstanceNorm1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#instancenorm2d"><span class="hidden-section">InstanceNorm2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#instancenorm3d"><span class="hidden-section">InstanceNorm3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#recurrent-layers">Recurrent layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#rnn"><span class="hidden-section">RNN</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#lstm"><span class="hidden-section">LSTM</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#gru"><span class="hidden-section">GRU</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#rnncell"><span class="hidden-section">RNNCell</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#lstmcell"><span class="hidden-section">LSTMCell</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#grucell"><span class="hidden-section">GRUCell</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#linear-layers">Linear layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#linear"><span class="hidden-section">Linear</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#bilinear"><span class="hidden-section">Bilinear</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#dropout-layers">Dropout layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#dropout"><span class="hidden-section">Dropout</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#dropout2d"><span class="hidden-section">Dropout2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#dropout3d"><span class="hidden-section">Dropout3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#alphadropout"><span class="hidden-section">AlphaDropout</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#sparse-layers">Sparse layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#embedding"><span class="hidden-section">Embedding</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#embeddingbag"><span class="hidden-section">EmbeddingBag</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#distance-functions">Distance functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#cosinesimilarity"><span class="hidden-section">CosineSimilarity</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#pairwisedistance"><span class="hidden-section">PairwiseDistance</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#loss-functions">Loss functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#l1loss"><span class="hidden-section">L1Loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#mseloss"><span class="hidden-section">MSELoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#crossentropyloss"><span class="hidden-section">CrossEntropyLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#nllloss"><span class="hidden-section">NLLLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#poissonnllloss"><span class="hidden-section">PoissonNLLLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#nllloss2d"><span class="hidden-section">NLLLoss2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#kldivloss"><span class="hidden-section">KLDivLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#bceloss"><span class="hidden-section">BCELoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#bcewithlogitsloss"><span class="hidden-section">BCEWithLogitsLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#marginrankingloss"><span class="hidden-section">MarginRankingLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#hingeembeddingloss"><span class="hidden-section">HingeEmbeddingLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#multilabelmarginloss"><span class="hidden-section">MultiLabelMarginLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#smoothl1loss"><span class="hidden-section">SmoothL1Loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#softmarginloss"><span class="hidden-section">SoftMarginLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#multilabelsoftmarginloss"><span class="hidden-section">MultiLabelSoftMarginLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#cosineembeddingloss"><span class="hidden-section">CosineEmbeddingLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#multimarginloss"><span class="hidden-section">MultiMarginLoss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#tripletmarginloss"><span class="hidden-section">TripletMarginLoss</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#vision-layers">Vision layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#pixelshuffle"><span class="hidden-section">PixelShuffle</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#upsample"><span class="hidden-section">Upsample</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#upsamplingnearest2d"><span class="hidden-section">UpsamplingNearest2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#upsamplingbilinear2d"><span class="hidden-section">UpsamplingBilinear2d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#dataparallel-layers-multi-gpu-distributed">DataParallel layers (multi-GPU, distributed)</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#dataparallel"><span class="hidden-section">DataParallel</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#distributeddataparallel"><span class="hidden-section">DistributedDataParallel</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#utilities">Utilities</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#clip-grad-norm"><span class="hidden-section">clip_grad_norm</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#weight-norm"><span class="hidden-section">weight_norm</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#remove-weight-norm"><span class="hidden-section">remove_weight_norm</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#packedsequence"><span class="hidden-section">PackedSequence</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#pack-padded-sequence"><span class="hidden-section">pack_padded_sequence</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#pad-packed-sequence"><span class="hidden-section">pad_packed_sequence</span></a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="nn.html#torch-nn-functional">torch.nn.functional</a><ul>
<li class="toctree-l2"><a class="reference internal" href="nn.html#convolution-functions">Convolution functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id14"><span class="hidden-section">conv1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id15"><span class="hidden-section">conv2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id16"><span class="hidden-section">conv3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#conv-transpose1d"><span class="hidden-section">conv_transpose1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#conv-transpose2d"><span class="hidden-section">conv_transpose2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#conv-transpose3d"><span class="hidden-section">conv_transpose3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#pooling-functions">Pooling functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#avg-pool1d"><span class="hidden-section">avg_pool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#avg-pool2d"><span class="hidden-section">avg_pool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#avg-pool3d"><span class="hidden-section">avg_pool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#max-pool1d"><span class="hidden-section">max_pool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#max-pool2d"><span class="hidden-section">max_pool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#max-pool3d"><span class="hidden-section">max_pool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#max-unpool1d"><span class="hidden-section">max_unpool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#max-unpool2d"><span class="hidden-section">max_unpool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#max-unpool3d"><span class="hidden-section">max_unpool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#lp-pool2d"><span class="hidden-section">lp_pool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptive-max-pool1d"><span class="hidden-section">adaptive_max_pool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptive-max-pool2d"><span class="hidden-section">adaptive_max_pool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptive-max-pool3d"><span class="hidden-section">adaptive_max_pool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptive-avg-pool1d"><span class="hidden-section">adaptive_avg_pool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptive-avg-pool2d"><span class="hidden-section">adaptive_avg_pool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptive-avg-pool3d"><span class="hidden-section">adaptive_avg_pool3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#non-linear-activation-functions">Non-linear activation functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id17"><span class="hidden-section">threshold</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id18"><span class="hidden-section">relu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id19"><span class="hidden-section">hardtanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id20"><span class="hidden-section">relu6</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id21"><span class="hidden-section">elu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id22"><span class="hidden-section">selu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#leaky-relu"><span class="hidden-section">leaky_relu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id23"><span class="hidden-section">prelu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#rrelu"><span class="hidden-section">rrelu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#glu"><span class="hidden-section">glu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id24"><span class="hidden-section">logsigmoid</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#hardshrink"><span class="hidden-section">hardshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id25"><span class="hidden-section">tanhshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id26"><span class="hidden-section">softsign</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id27"><span class="hidden-section">softplus</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id28"><span class="hidden-section">softmin</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id29"><span class="hidden-section">softmax</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id30"><span class="hidden-section">softshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#log-softmax"><span class="hidden-section">log_softmax</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id31"><span class="hidden-section">tanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id32"><span class="hidden-section">sigmoid</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#normalization-functions">Normalization functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#batch-norm"><span class="hidden-section">batch_norm</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#normalize"><span class="hidden-section">normalize</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#linear-functions">Linear functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id33"><span class="hidden-section">linear</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#dropout-functions">Dropout functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id34"><span class="hidden-section">dropout</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#alpha-dropout"><span class="hidden-section">alpha_dropout</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id35"><span class="hidden-section">dropout2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id36"><span class="hidden-section">dropout3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#id37">Distance functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#pairwise-distance"><span class="hidden-section">pairwise_distance</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#cosine-similarity"><span class="hidden-section">cosine_similarity</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#id38">Loss functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#binary-cross-entropy"><span class="hidden-section">binary_cross_entropy</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#poisson-nll-loss"><span class="hidden-section">poisson_nll_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#cosine-embedding-loss"><span class="hidden-section">cosine_embedding_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#cross-entropy"><span class="hidden-section">cross_entropy</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#hinge-embedding-loss"><span class="hidden-section">hinge_embedding_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#kl-div"><span class="hidden-section">kl_div</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#l1-loss"><span class="hidden-section">l1_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#mse-loss"><span class="hidden-section">mse_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#margin-ranking-loss"><span class="hidden-section">margin_ranking_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#multilabel-margin-loss"><span class="hidden-section">multilabel_margin_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#multilabel-soft-margin-loss"><span class="hidden-section">multilabel_soft_margin_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#multi-margin-loss"><span class="hidden-section">multi_margin_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#nll-loss"><span class="hidden-section">nll_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#binary-cross-entropy-with-logits"><span class="hidden-section">binary_cross_entropy_with_logits</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#smooth-l1-loss"><span class="hidden-section">smooth_l1_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#soft-margin-loss"><span class="hidden-section">soft_margin_loss</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#triplet-margin-loss"><span class="hidden-section">triplet_margin_loss</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#vision-functions">Vision functions</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#pixel-shuffle"><span class="hidden-section">pixel_shuffle</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#pad"><span class="hidden-section">pad</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id40"><span class="hidden-section">upsample</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#upsample-nearest"><span class="hidden-section">upsample_nearest</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#upsample-bilinear"><span class="hidden-section">upsample_bilinear</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#grid-sample"><span class="hidden-section">grid_sample</span></a></li>
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<div class="section" id="module-torch.autograd">
<span id="automatic-differentiation-package-torch-autograd"></span><h1>Automatic differentiation package - torch.autograd<a class="headerlink" href="#module-torch.autograd" title="Permalink to this headline">¶</a></h1>
<p>torch.autograd provides classes and functions implementing automatic
differentiation of arbitrary scalar valued functions. It requires minimal
changes to the existing code - you only need to wrap all tensors in
<a class="reference internal" href="#torch.autograd.Variable" title="torch.autograd.Variable"><code class="xref py py-class docutils literal"><span class="pre">Variable</span></code></a> objects.</p>
<dl class="function">
<dt id="torch.autograd.backward">
<code class="descclassname">torch.autograd.</code><code class="descname">backward</code><span class="sig-paren">(</span><em>variables</em>, <em>grad_variables=None</em>, <em>retain_graph=None</em>, <em>create_graph=None</em>, <em>retain_variables=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd.html#backward"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.backward" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the sum of gradients of given variables w.r.t. graph leaves.</p>
<p>The graph is differentiated using the chain rule. If any of <code class="docutils literal"><span class="pre">variables</span></code>
are non-scalar (i.e. their data has more than one element) and require
gradient, the function additionally requires specifying <code class="docutils literal"><span class="pre">grad_variables</span></code>.
It should be a sequence of matching length, that contains gradient of
the differentiated function w.r.t. corresponding variables (<code class="docutils literal"><span class="pre">None</span></code> is an
acceptable value for all variables that don’t need gradient tensors).</p>
<p>This function accumulates gradients in the leaves - you might need to zero
them before calling it.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>variables</strong> (<em>sequence of Variable</em>) – Variables of which the derivative will be
computed.</li>
<li><strong>grad_variables</strong> (<em>sequence of</em><em> (</em><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a><em>, </em><a class="reference internal" href="#torch.autograd.Variable" title="torch.autograd.Variable"><em>Variable</em></a><em> or </em><a class="reference external" href="https://docs.python.org/2/library/constants.html#None" title="(in Python v2.7)"><em>None</em></a><em>)</em><em></em>) – Gradients w.r.t.
each element of corresponding variables. Any tensors will be
automatically converted to Variables that are volatile unless
<code class="docutils literal"><span class="pre">create_graph</span></code> is <code class="docutils literal"><span class="pre">True</span></code>. None values can be specified for scalar
Variables or ones that don’t require grad. If a None value would
be acceptable for all grad_variables, then this argument is optional.</li>
<li><strong>retain_graph</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a><em>, </em><em>optional</em>) – If <code class="docutils literal"><span class="pre">False</span></code>, the graph used to compute the grad
will be freed. Note that in nearly all cases setting this option to <code class="docutils literal"><span class="pre">True</span></code>
is not needed and often can be worked around in a much more efficient
way. Defaults to the value of <code class="docutils literal"><span class="pre">create_graph</span></code>.</li>
<li><strong>create_graph</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a><em>, </em><em>optional</em>) – If <code class="docutils literal"><span class="pre">True</span></code>, graph of the derivative will
be constructed, allowing to compute higher order derivative products.
Defaults to <code class="docutils literal"><span class="pre">False</span></code>, unless <code class="docutils literal"><span class="pre">grad_variables</span></code> contains at least one
non-volatile Variable.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="torch.autograd.grad">
<code class="descclassname">torch.autograd.</code><code class="descname">grad</code><span class="sig-paren">(</span><em>outputs</em>, <em>inputs</em>, <em>grad_outputs=None</em>, <em>retain_graph=None</em>, <em>create_graph=None</em>, <em>only_inputs=True</em>, <em>allow_unused=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd.html#grad"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.grad" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes and returns the sum of gradients of outputs w.r.t. the inputs.</p>
<p><code class="docutils literal"><span class="pre">grad_outputs</span></code> should be a sequence of length matching <code class="docutils literal"><span class="pre">output</span></code>
containing the pre-computed gradients w.r.t. each of the outputs. If an
output doesn’t require_grad, then the gradient can be <code class="docutils literal"><span class="pre">None</span></code>).
Gradients can be given as Tensors when one doesn’t need the graph of the
derivative, or as Variables, in which case the graph will be created.</p>
<p>If <code class="docutils literal"><span class="pre">only_inputs</span></code> is <code class="docutils literal"><span class="pre">True</span></code>, the function will only return a list of gradients
w.r.t the specified inputs. If it’s <code class="docutils literal"><span class="pre">False</span></code>, then gradient w.r.t. all remaining
leaves will still be computed, and will be accumulated into their <code class="docutils literal"><span class="pre">.grad</span></code>
attribute.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>outputs</strong> (<em>sequence of Variable</em>) – outputs of the differentiated function.</li>
<li><strong>inputs</strong> (<em>sequence of Variable</em>) – Inputs w.r.t. which the gradient will be
returned (and not accumulated into <code class="docutils literal"><span class="pre">.grad</span></code>).</li>
<li><strong>grad_outputs</strong> (<em>sequence of Tensor</em><em> or </em><a class="reference internal" href="#torch.autograd.Variable" title="torch.autograd.Variable"><em>Variable</em></a>) – Gradients w.r.t. each output.
Any tensors will be automatically converted to Variables that are
volatile unless <code class="docutils literal"><span class="pre">create_graph</span></code> is <code class="docutils literal"><span class="pre">True</span></code>. None values can be
specified for scalar Variables or ones that don’t require grad.
If a None value would be acceptable for all grad_variables, then
this argument is optional.</li>
<li><strong>retain_graph</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a><em>, </em><em>optional</em>) – If <code class="docutils literal"><span class="pre">False</span></code>, the graph used to compute the grad
will be freed. Note that in nearly all cases setting this option to <code class="docutils literal"><span class="pre">True</span></code>
is not needed and often can be worked around in a much more efficient
way. Defaults to the value of <code class="docutils literal"><span class="pre">create_graph</span></code>.</li>
<li><strong>create_graph</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a><em>, </em><em>optional</em>) – If <code class="docutils literal"><span class="pre">True</span></code>, graph of the derivative will
be constructed, allowing to compute higher order derivative products.
Defaults to <code class="docutils literal"><span class="pre">False</span></code>, unless <code class="docutils literal"><span class="pre">grad_variables</span></code> contains at least one
non-volatile Variable.</li>
<li><strong>only_inputs</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a><em>, </em><em>optional</em>) – If <code class="docutils literal"><span class="pre">True</span></code>, gradient w.r.t. leaves that are
part of the graph, but don’t appear in <code class="docutils literal"><span class="pre">inputs</span></code> won’t be computed
and accumulated. Defaults to <code class="docutils literal"><span class="pre">True</span></code>.</li>
<li><strong>allow_unused</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a><em>, </em><em>optional</em>) – If <code class="docutils literal"><span class="pre">False</span></code>, specifying inputs that were not
used when computing outputs (and therefore their grad is always zero)
is an error. Defaults to <code class="docutils literal"><span class="pre">False</span></code>.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<div class="section" id="variable">
<h2>Variable<a class="headerlink" href="#variable" title="Permalink to this headline">¶</a></h2>
<div class="section" id="api-compatibility">
<h3>API compatibility<a class="headerlink" href="#api-compatibility" title="Permalink to this headline">¶</a></h3>
<p>Variable API is nearly the same as regular Tensor API (with the exception
of a couple in-place methods, that would overwrite inputs required for
gradient computation). In most cases Tensors can be safely replaced with
Variables and the code will remain to work just fine. Because of this,
we’re not documenting all the operations on variables, and you should
refer to <a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><code class="xref py py-class docutils literal"><span class="pre">torch.Tensor</span></code></a> docs for this purpose.</p>
</div>
<div class="section" id="in-place-operations-on-variables">
<h3>In-place operations on Variables<a class="headerlink" href="#in-place-operations-on-variables" title="Permalink to this headline">¶</a></h3>
<p>Supporting in-place operations in autograd is a hard matter, and we discourage
their use in most cases. Autograd’s aggressive buffer freeing and reuse makes
it very efficient and there are very few occasions when in-place operations
actually lower memory usage by any significant amount. Unless you’re operating
under heavy memory pressure, you might never need to use them.</p>
</div>
<div class="section" id="in-place-correctness-checks">
<h3>In-place correctness checks<a class="headerlink" href="#in-place-correctness-checks" title="Permalink to this headline">¶</a></h3>
<p>All <a class="reference internal" href="#torch.autograd.Variable" title="torch.autograd.Variable"><code class="xref py py-class docutils literal"><span class="pre">Variable</span></code></a> s keep track of in-place operations applied to them, and
if the implementation detects that a variable was saved for backward in one of
the functions, but it was modified in-place afterwards, an error will be raised
once backward pass is started. This ensures that if you’re using in-place
functions and not seeing any errors, you can be sure that the computed
gradients are correct.</p>
<dl class="class">
<dt id="torch.autograd.Variable">
<em class="property">class </em><code class="descclassname">torch.autograd.</code><code class="descname">Variable</code><a class="reference internal" href="_modules/torch/autograd/variable.html#Variable"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.Variable" title="Permalink to this definition">¶</a></dt>
<dd><p>Wraps a tensor and records the operations applied to it.</p>
<p>Variable is a thin wrapper around a Tensor object, that also holds
the gradient w.r.t. to it, and a reference to a function that created it.
This reference allows retracing the whole chain of operations that
created the data. If the Variable has been created by the user, its grad_fn
will be <code class="docutils literal"><span class="pre">None</span></code> and we call such objects <em>leaf</em> Variables.</p>
<p>Since autograd only supports scalar valued function differentiation, grad
size always matches the data size. Also, grad is normally only allocated
for leaf variables, and will be always zero otherwise.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Variables:</th><td class="field-body"><ul class="first simple">
<li><strong>data</strong> – Wrapped tensor of any type.</li>
<li><strong>grad</strong> – Variable holding the gradient of type and location matching
the <code class="docutils literal"><span class="pre">.data</span></code>. This attribute is lazily allocated and can’t
be reassigned.</li>
<li><strong>requires_grad</strong> – Boolean indicating whether the Variable has been
created by a subgraph containing any Variable, that requires it.
See <a class="reference internal" href="notes/autograd.html#excluding-subgraphs"><span class="std std-ref">Excluding subgraphs from backward</span></a> for more details.
Can be changed only on leaf Variables.</li>
<li><strong>volatile</strong> – Boolean indicating that the Variable should be used in
inference mode, i.e. don’t save the history. See
<a class="reference internal" href="notes/autograd.html#excluding-subgraphs"><span class="std std-ref">Excluding subgraphs from backward</span></a> for more details.
Can be changed only on leaf Variables.</li>
<li><strong>is_leaf</strong> – Boolean indicating if the Variable is a graph leaf (i.e
if it was created by the user).</li>
<li><strong>grad_fn</strong> – Gradient function graph trace.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>data</strong> (<em>any tensor class</em>) – Tensor to wrap.</li>
<li><strong>requires_grad</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a>) – Value of the requires_grad flag. <strong>Keyword only.</strong></li>
<li><strong>volatile</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a>) – Value of the volatile flag. <strong>Keyword only.</strong></li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.autograd.Variable.backward">
<code class="descname">backward</code><span class="sig-paren">(</span><em>gradient=None</em>, <em>retain_graph=None</em>, <em>create_graph=None</em>, <em>retain_variables=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/variable.html#Variable.backward"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.Variable.backward" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the gradient of current variable w.r.t. graph leaves.</p>
<p>The graph is differentiated using the chain rule. If the variable is
non-scalar (i.e. its data has more than one element) and requires
gradient, the function additionally requires specifying <code class="docutils literal"><span class="pre">gradient</span></code>.
It should be a tensor of matching type and location, that contains
the gradient of the differentiated function w.r.t. <code class="docutils literal"><span class="pre">self</span></code>.</p>
<p>This function accumulates gradients in the leaves - you might need to
zero them before calling it.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>gradient</strong> (<a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a><em>, </em><a class="reference internal" href="#torch.autograd.Variable" title="torch.autograd.Variable"><em>Variable</em></a><em> or </em><a class="reference external" href="https://docs.python.org/2/library/constants.html#None" title="(in Python v2.7)"><em>None</em></a>) – Gradient w.r.t. the
variable. If it is a tensor, it will be automatically converted
to a Variable that is volatile unless <code class="docutils literal"><span class="pre">create_graph</span></code> is True.
None values can be specified for scalar Variables or ones that
don’t require grad. If a None value would be acceptable then
this argument is optional.</li>
<li><strong>retain_graph</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a><em>, </em><em>optional</em>) – If <code class="docutils literal"><span class="pre">False</span></code>, the graph used to compute
the grads will be freed. Note that in nearly all cases setting
this option to True is not needed and often can be worked around
in a much more efficient way. Defaults to the value of
<code class="docutils literal"><span class="pre">create_graph</span></code>.</li>
<li><strong>create_graph</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a><em>, </em><em>optional</em>) – If <code class="docutils literal"><span class="pre">True</span></code>, graph of the derivative will
be constructed, allowing to compute higher order derivative
products. Defaults to <code class="docutils literal"><span class="pre">False</span></code>, unless <code class="docutils literal"><span class="pre">gradient</span></code> is a volatile
Variable.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.autograd.Variable.detach">
<code class="descname">detach</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/variable.html#Variable.detach"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.Variable.detach" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a new Variable, detached from the current graph.</p>
<p>Result will never require gradient. If the input is volatile, the output
will be volatile too.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Returned Variable uses the same data tensor, as the original one, and
in-place modifications on either of them will be seen, and may trigger
errors in correctness checks.</p>
</div>
</dd></dl>
<dl class="method">
<dt id="torch.autograd.Variable.detach_">
<code class="descname">detach_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/variable.html#Variable.detach_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.Variable.detach_" title="Permalink to this definition">¶</a></dt>
<dd><p>Detaches the Variable from the graph that created it, making it a
leaf.</p>
</dd></dl>
<dl class="method">
<dt id="torch.autograd.Variable.register_hook">
<code class="descname">register_hook</code><span class="sig-paren">(</span><em>hook</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/variable.html#Variable.register_hook"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.Variable.register_hook" title="Permalink to this definition">¶</a></dt>
<dd><p>Registers a backward hook.</p>
<p>The hook will be called every time a gradient with respect to the
variable is computed. The hook should have the following signature:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">hook</span><span class="p">(</span><span class="n">grad</span><span class="p">)</span> <span class="o">-></span> <span class="n">Variable</span> <span class="ow">or</span> <span class="kc">None</span>
</pre></div>
</div>
<p>The hook should not modify its argument, but it can optionally return
a new gradient which will be used in place of <a class="reference internal" href="#torch.autograd.grad" title="torch.autograd.grad"><code class="xref py py-attr docutils literal"><span class="pre">grad</span></code></a>.</p>
<p>This function returns a handle with a method <code class="docutils literal"><span class="pre">handle.remove()</span></code>
that removes the hook from the module.</p>
<p class="rubric">Example</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">v</span> <span class="o">=</span> <span class="n">Variable</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="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">h</span> <span class="o">=</span> <span class="n">v</span><span class="o">.</span><span class="n">register_hook</span><span class="p">(</span><span class="k">lambda</span> <span class="n">grad</span><span class="p">:</span> <span class="n">grad</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span> <span class="c1"># double the gradient</span>
<span class="gp">>>> </span><span class="n">v</span><span class="o">.</span><span class="n">backward</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="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]))</span>
<span class="gp">>>> </span><span class="n">v</span><span class="o">.</span><span class="n">grad</span><span class="o">.</span><span class="n">data</span>
<span class="go"> 2</span>
<span class="go"> 2</span>
<span class="go"> 2</span>
<span class="go">[torch.FloatTensor of size 3]</span>
<span class="gp">>>> </span><span class="n">h</span><span class="o">.</span><span class="n">remove</span><span class="p">()</span> <span class="c1"># removes the hook</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="torch.autograd.Variable.retain_grad">
<code class="descname">retain_grad</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/variable.html#Variable.retain_grad"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.Variable.retain_grad" title="Permalink to this definition">¶</a></dt>
<dd><p>Enables .grad attribute for non-leaf Variables.</p>
</dd></dl>
</dd></dl>
</div>
</div>
<div class="section" id="function">
<h2><span class="hidden-section">Function</span><a class="headerlink" href="#function" title="Permalink to this headline">¶</a></h2>
<dl class="class">
<dt id="torch.autograd.Function">
<em class="property">class </em><code class="descclassname">torch.autograd.</code><code class="descname">Function</code><a class="reference internal" href="_modules/torch/autograd/function.html#Function"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.Function" title="Permalink to this definition">¶</a></dt>
<dd><p>Records operation history and defines formulas for differentiating ops.</p>
<p>Every operation performed on <a class="reference internal" href="#torch.autograd.Variable" title="torch.autograd.Variable"><code class="xref py py-class docutils literal"><span class="pre">Variable</span></code></a> s creates a new function
object, that performs the computation, and records that it happened.
The history is retained in the form of a DAG of functions, with edges
denoting data dependencies (<code class="docutils literal"><span class="pre">input</span> <span class="pre"><-</span> <span class="pre">output</span></code>). Then, when backward is
called, the graph is processed in the topological ordering, by calling
<a class="reference internal" href="#torch.autograd.backward" title="torch.autograd.backward"><code class="xref py py-func docutils literal"><span class="pre">backward()</span></code></a> methods of each <a class="reference internal" href="#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal"><span class="pre">Function</span></code></a> object, and passing
returned gradients on to next <a class="reference internal" href="#torch.autograd.Function" title="torch.autograd.Function"><code class="xref py py-class docutils literal"><span class="pre">Function</span></code></a> s.</p>
<p>Normally, the only way users interact with functions is by creating
subclasses and defining new operations. This is a recommended way of
extending torch.autograd.</p>
<p>Each function is meant to be used only once (in the forward pass).</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Variables:</th><td class="field-body"><strong>requires_grad</strong> – Boolean indicating whether the <a class="reference internal" href="#torch.autograd.backward" title="torch.autograd.backward"><code class="xref py py-func docutils literal"><span class="pre">backward()</span></code></a> will
ever need to be called.</td>
</tr>
</tbody>
</table>
<p>Examples:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">class</span> <span class="nc">Exp</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="go">>>></span>
<span class="gp">>>> </span> <span class="nd">@staticmethod</span>
<span class="gp">>>> </span> <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
<span class="gp">>>> </span> <span class="n">result</span> <span class="o">=</span> <span class="n">i</span><span class="o">.</span><span class="n">exp</span><span class="p">()</span>
<span class="gp">>>> </span> <span class="n">ctx</span><span class="o">.</span><span class="n">save_for_backward</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
<span class="gp">>>> </span> <span class="k">return</span> <span class="n">result</span>
<span class="go">>>></span>
<span class="gp">>>> </span> <span class="nd">@staticmethod</span>
<span class="gp">>>> </span> <span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="gp">>>> </span> <span class="n">result</span><span class="p">,</span> <span class="o">=</span> <span class="n">ctx</span><span class="o">.</span><span class="n">saved_variables</span>
<span class="gp">>>> </span> <span class="k">return</span> <span class="n">grad_output</span> <span class="o">*</span> <span class="n">result</span>
</pre></div>
</div>
<dl class="staticmethod">
<dt id="torch.autograd.Function.backward">
<em class="property">static </em><code class="descname">backward</code><span class="sig-paren">(</span><em>ctx</em>, <em>*grad_outputs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/function.html#Function.backward"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.Function.backward" title="Permalink to this definition">¶</a></dt>
<dd><p>Defines a formula for differentiating the operation.</p>
<p>This function is to be overriden by all subclasses.</p>
<p>It must accept a context ctx as the first argument, followed by as many
outputs did <a class="reference internal" href="#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-func docutils literal"><span class="pre">forward()</span></code></a> return, and it should return as many
tensors, as there were inputs to <a class="reference internal" href="#torch.autograd.Function.forward" title="torch.autograd.Function.forward"><code class="xref py py-func docutils literal"><span class="pre">forward()</span></code></a>. Each argument is the
gradient w.r.t the given output, and each returned value should be the
gradient w.r.t. the corresponding input.</p>
<p>The context can be used to retrieve variables saved during the forward
pass.</p>
</dd></dl>
<dl class="staticmethod">
<dt id="torch.autograd.Function.forward">
<em class="property">static </em><code class="descname">forward</code><span class="sig-paren">(</span><em>ctx</em>, <em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/function.html#Function.forward"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.Function.forward" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs the operation.</p>
<p>This function is to be overriden by all subclasses.</p>
<p>It must accept a context ctx as the first argument, followed by any
number of arguments (tensors or other types).</p>
<p>The context can be used to store variables that can be then retrieved
during the backward pass.</p>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="profiler">
<h2>Profiler<a class="headerlink" href="#profiler" title="Permalink to this headline">¶</a></h2>
<p>Autograd includes a profiler that lets you inspect the cost of different
operators inside your model - both on the CPU and GPU. There are two modes
implemented at the moment - CPU-only using <a class="reference internal" href="#torch.autograd.profiler.profile" title="torch.autograd.profiler.profile"><code class="xref py py-class docutils literal"><span class="pre">profile</span></code></a>.
and nvprof based (registers both CPU and GPU activity) using
<a class="reference internal" href="#torch.autograd.profiler.emit_nvtx" title="torch.autograd.profiler.emit_nvtx"><code class="xref py py-class docutils literal"><span class="pre">emit_nvtx</span></code></a>.</p>
<dl class="class">
<dt id="torch.autograd.profiler.profile">
<em class="property">class </em><code class="descclassname">torch.autograd.profiler.</code><code class="descname">profile</code><span class="sig-paren">(</span><em>enabled=True</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/profiler.html#profile"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.profiler.profile" title="Permalink to this definition">¶</a></dt>
<dd><p>Context manager that manages autograd profiler state and holds a summary of results.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>enabled</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#bool" title="(in Python v2.7)"><em>bool</em></a><em>, </em><em>optional</em>) – Setting this to False makes this context manager a no-op.
Default: <code class="docutils literal"><span class="pre">True</span></code>.</td>
</tr>
</tbody>
</table>
<p class="rubric">Example</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">autograd</span><span class="o">.</span><span class="n">profiler</span><span class="o">.</span><span class="n">profile</span><span class="p">()</span> <span class="k">as</span> <span class="n">prof</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">y</span> <span class="o">=</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">2</span>
<span class="gp">... </span> <span class="n">y</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="gp">>>> </span><span class="c1"># NOTE: some columns were removed for brevity</span>
<span class="gp">... </span><span class="nb">print</span><span class="p">(</span><span class="n">prof</span><span class="p">)</span>
<span class="go">------------------------------------- --------------- ---------------</span>
<span class="go">Name CPU time CUDA time</span>
<span class="go">------------------------------------- --------------- ---------------</span>
<span class="go">PowConstant 142.036us 0.000us</span>
<span class="go">N5torch8autograd9GraphRootE 63.524us 0.000us</span>
<span class="go">PowConstantBackward 184.228us 0.000us</span>
<span class="go">MulConstant 50.288us 0.000us</span>
<span class="go">PowConstant 28.439us 0.000us</span>
<span class="go">Mul 20.154us 0.000us</span>
<span class="go">N5torch8autograd14AccumulateGradE 13.790us 0.000us</span>
<span class="go">N5torch8autograd5CloneE 4.088us 0.000us</span>
</pre></div>
</div>
<dl class="method">
<dt id="torch.autograd.profiler.profile.export_chrome_trace">
<code class="descname">export_chrome_trace</code><span class="sig-paren">(</span><em>path</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/profiler.html#profile.export_chrome_trace"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.profiler.profile.export_chrome_trace" title="Permalink to this definition">¶</a></dt>
<dd><p>Exports an EventList as a Chrome tracing tools file.</p>
<p>The checkpoint can be later loaded and inspected under <code class="docutils literal"><span class="pre">chrome://tracing</span></code> URL.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>path</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#str" title="(in Python v2.7)"><em>str</em></a>) – Path where the trace will be written.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.autograd.profiler.profile.key_averages">
<code class="descname">key_averages</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/profiler.html#profile.key_averages"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.profiler.profile.key_averages" title="Permalink to this definition">¶</a></dt>
<dd><p>Averages all function events over their keys.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">An EventList containing FunctionEventAvg objects.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.autograd.profiler.profile.table">
<code class="descname">table</code><span class="sig-paren">(</span><em>sort_by=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/profiler.html#profile.table"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.profiler.profile.table" title="Permalink to this definition">¶</a></dt>
<dd><p>Prints an EventList as a nicely formatted table.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>sort_by</strong> (<a class="reference external" href="https://docs.python.org/2/library/functions.html#str" title="(in Python v2.7)"><em>str</em></a><em>, </em><em>optional</em>) – Attribute used to sort entries. By default
they are printed in the same order as they were registered.
Valid keys include: <code class="docutils literal"><span class="pre">cpu_time</span></code>, <code class="docutils literal"><span class="pre">cuda_time</span></code>, <code class="docutils literal"><span class="pre">cpu_time_total</span></code>,
<code class="docutils literal"><span class="pre">cuda_time_total</span></code>, <code class="docutils literal"><span class="pre">count</span></code>.</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">A string containing the table.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.autograd.profiler.profile.total_average">
<code class="descname">total_average</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/profiler.html#profile.total_average"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.profiler.profile.total_average" title="Permalink to this definition">¶</a></dt>