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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>
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<li class="toctree-l3"><a class="reference internal" href="nn.html#module"><span class="hidden-section">Module</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#sequential"><span class="hidden-section">Sequential</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#modulelist"><span class="hidden-section">ModuleList</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#parameterlist"><span class="hidden-section">ParameterList</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#convolution-layers">Convolution layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#conv1d"><span class="hidden-section">Conv1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#conv2d"><span class="hidden-section">Conv2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#conv3d"><span class="hidden-section">Conv3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#convtranspose1d"><span class="hidden-section">ConvTranspose1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#convtranspose2d"><span class="hidden-section">ConvTranspose2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#convtranspose3d"><span class="hidden-section">ConvTranspose3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#pooling-layers">Pooling layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#maxpool1d"><span class="hidden-section">MaxPool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#maxpool2d"><span class="hidden-section">MaxPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#maxpool3d"><span class="hidden-section">MaxPool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#maxunpool1d"><span class="hidden-section">MaxUnpool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#maxunpool2d"><span class="hidden-section">MaxUnpool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#maxunpool3d"><span class="hidden-section">MaxUnpool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#avgpool1d"><span class="hidden-section">AvgPool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#avgpool2d"><span class="hidden-section">AvgPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#avgpool3d"><span class="hidden-section">AvgPool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#fractionalmaxpool2d"><span class="hidden-section">FractionalMaxPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#lppool1d"><span class="hidden-section">LPPool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#lppool2d"><span class="hidden-section">LPPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptivemaxpool1d"><span class="hidden-section">AdaptiveMaxPool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptivemaxpool2d"><span class="hidden-section">AdaptiveMaxPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptivemaxpool3d"><span class="hidden-section">AdaptiveMaxPool3d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptiveavgpool1d"><span class="hidden-section">AdaptiveAvgPool1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptiveavgpool2d"><span class="hidden-section">AdaptiveAvgPool2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#adaptiveavgpool3d"><span class="hidden-section">AdaptiveAvgPool3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#padding-layers">Padding layers</a><ul>
<li class="toctree-l3"><a class="reference internal" href="nn.html#reflectionpad1d"><span class="hidden-section">ReflectionPad1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#reflectionpad2d"><span class="hidden-section">ReflectionPad2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#replicationpad1d"><span class="hidden-section">ReplicationPad1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#replicationpad2d"><span class="hidden-section">ReplicationPad2d</span></a></li>
<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#constantpad1d"><span class="hidden-section">ConstantPad1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#constantpad2d"><span class="hidden-section">ConstantPad2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#constantpad3d"><span class="hidden-section">ConstantPad3d</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#non-linear-activations-weighted-sum-nonlinearity">Non-linear activations (weighted sum, nonlinearity)</a><ul>
<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#hardshrink"><span class="hidden-section">Hardshrink</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#leakyrelu"><span class="hidden-section">LeakyReLU</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#prelu"><span class="hidden-section">PReLU</span></a></li>
<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#rrelu"><span class="hidden-section">RReLU</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#sigmoid"><span class="hidden-section">Sigmoid</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#tanh"><span class="hidden-section">Tanh</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#threshold"><span class="hidden-section">Threshold</span></a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="nn.html#non-linear-activations-other">Non-linear activations (other)</a><ul>
<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>
<li class="toctree-l3"><a class="reference internal" href="nn.html#layernorm"><span class="hidden-section">LayerNorm</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#localresponsenorm"><span class="hidden-section">LocalResponseNorm</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#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#clip-grad-value"><span class="hidden-section">clip_grad_value_</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>
<li class="toctree-l3"><a class="reference internal" href="nn.html#pad-sequence"><span class="hidden-section">pad_sequence</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#pack-sequence"><span class="hidden-section">pack_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#id20"><span class="hidden-section">conv1d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id21"><span class="hidden-section">conv2d</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id22"><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-pool1d"><span class="hidden-section">lp_pool1d</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#id23"><span class="hidden-section">threshold</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id24"><span class="hidden-section">relu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id25"><span class="hidden-section">hardtanh</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id26"><span class="hidden-section">relu6</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id27"><span class="hidden-section">elu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id28"><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#id29"><span class="hidden-section">prelu</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id30"><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#id31"><span class="hidden-section">logsigmoid</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id32"><span class="hidden-section">hardshrink</span></a></li>
<li class="toctree-l3"><a class="reference internal" href="nn.html#id33"><span class="hidden-section">tanhshrink</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><code class="docutils literal"><span class="pre">torch.autograd</span></code> provides classes and functions implementing automatic
differentiation of arbitrary scalar valued functions. It requires minimal
changes to the existing code - you only need to declare <code class="xref py py-class docutils literal"><span class="pre">Tensor</span></code> s
for which gradients should be computed with the <code class="docutils literal"><span class="pre">requires_grad=True</span></code> keyword.</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>tensors</em>, <em>grad_tensors=None</em>, <em>retain_graph=None</em>, <em>create_graph=False</em>, <em>grad_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 tensors 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">tensors</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_tensors</span></code>.
It should be a sequence of matching length, that contains gradient of
the differentiated function w.r.t. corresponding tensors (<code class="docutils literal"><span class="pre">None</span></code> is an
acceptable value for all tensors 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>tensors</strong> (<em>sequence of Tensor</em>) – Tensors of which the derivative will be
computed.</li>
<li><strong>grad_tensors</strong> (<em>sequence of</em><em> (</em><a class="reference internal" href="tensors.html#torch.Tensor" title="torch.Tensor"><em>Tensor</em></a><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.6)"><em>None</em></a><em>)</em><em></em>) – Gradients w.r.t.
each element of corresponding tensors. None values can be specified for
scalar Tensors or ones that don’t require grad. If a None value would
be acceptable for all grad_tensors, then this argument is optional.</li>
<li><strong>retain_graph</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.6)"><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/3/library/functions.html#bool" title="(in Python v3.6)"><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>.</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=False</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>).</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 Tensor</em>) – outputs of the differentiated function.</li>
<li><strong>inputs</strong> (<em>sequence of Tensor</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>) – Gradients w.r.t. each output.
None values can be specified for scalar Tensors or ones that don’t require
grad. If a None value would be acceptable for all grad_tensors, then this
argument is optional. Default: None.</li>
<li><strong>retain_graph</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.6)"><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/3/library/functions.html#bool" title="(in Python v3.6)"><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.
Default: <code class="docutils literal"><span class="pre">False</span></code>.</li>
<li><strong>allow_unused</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.6)"><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="locally-disabling-gradient-computation">
<span id="locally-disable-grad"></span><h2>Locally disabling gradient computation<a class="headerlink" href="#locally-disabling-gradient-computation" title="Permalink to this headline">¶</a></h2>
<dl class="class">
<dt id="torch.autograd.no_grad">
<em class="property">class </em><code class="descclassname">torch.autograd.</code><code class="descname">no_grad</code><a class="reference internal" href="_modules/torch/autograd/grad_mode.html#no_grad"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.no_grad" title="Permalink to this definition">¶</a></dt>
<dd><p>Context-manager that disabled gradient calculation.</p>
<p>Disabling gradient calculation is useful for inference, when you are sure
that you will not call <code class="xref py py-meth docutils literal"><span class="pre">Tensor.backward()</span></code>. It will reduce memory
consumption for computations that would otherwise have <cite>requires_grad=True</cite>.
In this mode, the result of every computation will have
<cite>requires_grad=False</cite>, even when the inputs have <cite>requires_grad=True</cite>.</p>
<p>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">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="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">no_grad</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">requires_grad</span>
<span class="go">False</span>
</pre></div>
</div>
</dd></dl>
<dl class="class">
<dt id="torch.autograd.enable_grad">
<em class="property">class </em><code class="descclassname">torch.autograd.</code><code class="descname">enable_grad</code><a class="reference internal" href="_modules/torch/autograd/grad_mode.html#enable_grad"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.enable_grad" title="Permalink to this definition">¶</a></dt>
<dd><p>Context-manager that enables gradient calculation.</p>
<p>Enables gradient calculation inside a <a class="reference internal" href="#torch.autograd.no_grad" title="torch.autograd.no_grad"><code class="xref py py-class docutils literal"><span class="pre">no_grad</span></code></a> context. This has
no effect outside of <a class="reference internal" href="#torch.autograd.no_grad" title="torch.autograd.no_grad"><code class="xref py py-class docutils literal"><span class="pre">no_grad</span></code></a>.</p>
<p>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">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="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">no_grad</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">enable_grad</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">requires_grad</span>
<span class="go">True</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="n">x</span><span class="o">.</span><span class="n">grad</span>
</pre></div>
</div>
</dd></dl>
<dl class="class">
<dt id="torch.autograd.set_grad_enabled">
<em class="property">class </em><code class="descclassname">torch.autograd.</code><code class="descname">set_grad_enabled</code><span class="sig-paren">(</span><em>mode</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/autograd/grad_mode.html#set_grad_enabled"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.autograd.set_grad_enabled" title="Permalink to this definition">¶</a></dt>
<dd><p>Context-manager that sets gradient calculation to on or off.</p>
<p><code class="docutils literal"><span class="pre">set_grad_enabled</span></code> will enable or disable grads based on its argument <code class="xref py py-attr docutils literal"><span class="pre">mode</span></code>.
It can be used as a context-manager or as a function.</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>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.6)"><em>bool</em></a>) – Flag whether to enable grad (<code class="docutils literal"><span class="pre">True</span></code>), or disable
(<code class="docutils literal"><span class="pre">False</span></code>). This can be used to conditionally enable
gradients.</td>
</tr>
</tbody>
</table>
<p>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">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="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">is_train</span> <span class="o">=</span> <span class="kc">False</span>
<span class="gp">>>> </span><span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">set_grad_enabled</span><span class="p">(</span><span class="n">is_train</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">requires_grad</span>
<span class="go">False</span>
<span class="gp">>>> </span><span class="n">set_grad_enabled</span><span class="p">(</span><span class="kc">True</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">requires_grad</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">set_grad_enabled</span><span class="p">(</span><span class="kc">False</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">requires_grad</span>
<span class="go">True</span>
</pre></div>
</div>
</dd></dl>
</div>
<div class="section" id="in-place-operations-on-tensors">
<h2>In-place operations on Tensors<a class="headerlink" href="#in-place-operations-on-tensors" title="Permalink to this headline">¶</a></h2>
<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 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 <code class="xref py py-class docutils literal"><span class="pre">Tensor</span></code> s keep track of in-place operations applied to them, and
if the implementation detects that a tensor 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>
</div>
</div>
<div class="section" id="variable-deprecated">
<h2>Variable (deprecated)<a class="headerlink" href="#variable-deprecated" title="Permalink to this headline">¶</a></h2>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p>The Variable API has been deprecated: Variables are no longer necessary to
use autograd with tensors. Autograd automatically supports Tensors with
<code class="docutils literal"><span class="pre">requires_grad</span></code> set to <code class="docutils literal"><span class="pre">True</span></code>. Below please find a quick guide on what
has changed:</p>
<ul class="simple">
<li><code class="docutils literal"><span class="pre">Variable(tensor)</span></code> and <code class="docutils literal"><span class="pre">Variable(tensor,</span> <span class="pre">requires_grad)</span></code> still work as expected,
but they return Tensors instead of Variables.</li>
<li><code class="docutils literal"><span class="pre">var.data</span></code> is the same thing as <code class="docutils literal"><span class="pre">tensor.data</span></code>.</li>
<li>Methods such as <code class="docutils literal"><span class="pre">var.backward(),</span> <span class="pre">var.detach(),</span> <span class="pre">var.register_hook()</span></code> now work on tensors
with the same method names.</li>
</ul>
<p>In addition, one can now create tensors with <code class="docutils literal"><span class="pre">requires_grad=True</span></code> using factory
methods such as <a class="reference internal" href="torch.html#torch.randn" title="torch.randn"><code class="xref py py-func docutils literal"><span class="pre">torch.randn()</span></code></a>, <a class="reference internal" href="torch.html#torch.zeros" title="torch.zeros"><code class="xref py py-func docutils literal"><span class="pre">torch.zeros()</span></code></a>, <a class="reference internal" href="torch.html#torch.ones" title="torch.ones"><code class="xref py py-func docutils literal"><span class="pre">torch.ones()</span></code></a>, and others
like the following:</p>
<p class="last"><code class="docutils literal"><span class="pre">autograd_tensor</span> <span class="pre">=</span> <span class="pre">torch.randn((2,</span> <span class="pre">3,</span> <span class="pre">4),</span> <span class="pre">requires_grad=True)</span></code></p>
</div>
</div>
<div class="section" id="tensor-autograd-functions">
<h2>Tensor autograd functions<a class="headerlink" href="#tensor-autograd-functions" title="Permalink to this headline">¶</a></h2>
<dl class="class">
<dt id="torch.Tensor">
<em class="property">class </em><code class="descclassname">torch.</code><code class="descname">Tensor</code><a class="headerlink" href="#torch.Tensor" title="Permalink to this definition">¶</a></dt>
<dd><dl class="method">
<dt id="torch.Tensor.backward">
<code class="descname">backward</code><span class="sig-paren">(</span><em>gradient=None</em>, <em>retain_graph=None</em>, <em>create_graph=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/tensor.html#Tensor.backward"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.Tensor.backward" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the gradient of current tensor w.r.t. graph leaves.</p>
<p>The graph is differentiated using the chain rule. If the tensor 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> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.6)"><em>None</em></a>) – Gradient w.r.t. the
tensor. If it is a tensor, it will be automatically converted
to a Tensor that does not require grad unless <code class="docutils literal"><span class="pre">create_graph</span></code> is True.
None values can be specified for scalar Tensors 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/3/library/functions.html#bool" title="(in Python v3.6)"><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/3/library/functions.html#bool" title="(in Python v3.6)"><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>.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.Tensor.detach">
<code class="descname">detach</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.Tensor.detach" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a new Tensor, detached from the current graph.</p>
<p>The result will never require gradient.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Returned Tensor uses the same data tensor as the original one.
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.Tensor.detach_">
<code class="descname">detach_</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#torch.Tensor.detach_" title="Permalink to this definition">¶</a></dt>
<dd><p>Detaches the Tensor from the graph that created it, making it a leaf.
Views cannot be detached in-place.</p>
</dd></dl>
<dl class="method">
<dt id="torch.Tensor.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/tensor.html#Tensor.register_hook"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.Tensor.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
Tensor 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">Tensor</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">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">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="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">]))</span>
<span class="gp">>>> </span><span class="n">v</span><span class="o">.</span><span class="n">grad</span>
</pre></div>
</div>