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<!DOCTYPE html>
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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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<li class="toctree-l2"><a class="reference internal" href="nn.html#id46">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>
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<li class="toctree-l3"><a class="reference internal" href="nn.html#multilabel-margin-loss"><span class="hidden-section">multilabel_margin_loss</span></a></li>
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<li class="toctree-l4"><a class="reference internal" href="#optimizer-step"><code class="docutils literal"><span class="pre">optimizer.step()</span></code></a></li>
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<div class="section" id="module-torch.optim">
<span id="torch-optim"></span><h1>torch.optim<a class="headerlink" href="#module-torch.optim" title="Permalink to this headline">¶</a></h1>
<p><a class="reference internal" href="#module-torch.optim" title="torch.optim"><code class="xref py py-mod docutils literal"><span class="pre">torch.optim</span></code></a> is a package implementing various optimization algorithms.
Most commonly used methods are already supported, and the interface is general
enough, so that more sophisticated ones can be also easily integrated in the
future.</p>
<div class="section" id="how-to-use-an-optimizer">
<h2>How to use an optimizer<a class="headerlink" href="#how-to-use-an-optimizer" title="Permalink to this headline">¶</a></h2>
<p>To use <a class="reference internal" href="#module-torch.optim" title="torch.optim"><code class="xref py py-mod docutils literal"><span class="pre">torch.optim</span></code></a> you have to construct an optimizer object, that will hold
the current state and will update the parameters based on the computed gradients.</p>
<div class="section" id="constructing-it">
<h3>Constructing it<a class="headerlink" href="#constructing-it" title="Permalink to this headline">¶</a></h3>
<p>To construct an <a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><code class="xref py py-class docutils literal"><span class="pre">Optimizer</span></code></a> you have to give it an iterable containing the
parameters (all should be <code class="xref py py-class docutils literal"><span class="pre">Variable</span></code> s) to optimize. Then,
you can specify optimizer-specific options such as the learning rate, weight decay, etc.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p>If you need to move a model to GPU via <cite>.cuda()</cite>, please do so before
constructing optimizers for it. Parameters of a model after <cite>.cuda()</cite> will
be different objects with those before the call.</p>
<p class="last">In general, you should make sure that optimized parameters live in
consistent locations when optimizers are constructed and used.</p>
</div>
<p>Example:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="n">lr</span> <span class="o">=</span> <span class="mf">0.01</span><span class="p">,</span> <span class="n">momentum</span><span class="o">=</span><span class="mf">0.9</span><span class="p">)</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">optim</span><span class="o">.</span><span class="n">Adam</span><span class="p">([</span><span class="n">var1</span><span class="p">,</span> <span class="n">var2</span><span class="p">],</span> <span class="n">lr</span> <span class="o">=</span> <span class="mf">0.0001</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="per-parameter-options">
<h3>Per-parameter options<a class="headerlink" href="#per-parameter-options" title="Permalink to this headline">¶</a></h3>
<p><a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><code class="xref py py-class docutils literal"><span class="pre">Optimizer</span></code></a> s also support specifying per-parameter options. To do this, instead
of passing an iterable of <code class="xref py py-class docutils literal"><span class="pre">Variable</span></code> s, pass in an iterable of
<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.6)"><code class="xref py py-class docutils literal"><span class="pre">dict</span></code></a> s. Each of them will define a separate parameter group, and should contain
a <code class="docutils literal"><span class="pre">params</span></code> key, containing a list of parameters belonging to it. Other keys
should match the keyword arguments accepted by the optimizers, and will be used
as optimization options for this group.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">You can still pass options as keyword arguments. They will be used as
defaults, in the groups that didn’t override them. This is useful when you
only want to vary a single option, while keeping all others consistent
between parameter groups.</p>
</div>
<p>For example, this is very useful when one wants to specify per-layer learning rates:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">optim</span><span class="o">.</span><span class="n">SGD</span><span class="p">([</span>
<span class="p">{</span><span class="s1">'params'</span><span class="p">:</span> <span class="n">model</span><span class="o">.</span><span class="n">base</span><span class="o">.</span><span class="n">parameters</span><span class="p">()},</span>
<span class="p">{</span><span class="s1">'params'</span><span class="p">:</span> <span class="n">model</span><span class="o">.</span><span class="n">classifier</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="s1">'lr'</span><span class="p">:</span> <span class="mf">1e-3</span><span class="p">}</span>
<span class="p">],</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-2</span><span class="p">,</span> <span class="n">momentum</span><span class="o">=</span><span class="mf">0.9</span><span class="p">)</span>
</pre></div>
</div>
<p>This means that <code class="docutils literal"><span class="pre">model.base</span></code>‘s parameters will use the default learning rate of <code class="docutils literal"><span class="pre">1e-2</span></code>,
<code class="docutils literal"><span class="pre">model.classifier</span></code>‘s parameters will use a learning rate of <code class="docutils literal"><span class="pre">1e-3</span></code>, and a momentum of
<code class="docutils literal"><span class="pre">0.9</span></code> will be used for all parameters</p>
</div>
<div class="section" id="taking-an-optimization-step">
<h3>Taking an optimization step<a class="headerlink" href="#taking-an-optimization-step" title="Permalink to this headline">¶</a></h3>
<p>All optimizers implement a <a class="reference internal" href="#torch.optim.Optimizer.step" title="torch.optim.Optimizer.step"><code class="xref py py-func docutils literal"><span class="pre">step()</span></code></a> method, that updates the
parameters. It can be used in two ways:</p>
<div class="section" id="optimizer-step">
<h4><code class="docutils literal"><span class="pre">optimizer.step()</span></code><a class="headerlink" href="#optimizer-step" title="Permalink to this headline">¶</a></h4>
<p>This is a simplified version supported by most optimizers. The function can be
called once the gradients are computed using e.g.
<code class="xref py py-func docutils literal"><span class="pre">backward()</span></code>.</p>
<p>Example:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="nb">input</span><span class="p">,</span> <span class="n">target</span> <span class="ow">in</span> <span class="n">dataset</span><span class="p">:</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">zero_grad</span><span class="p">()</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">loss_fn</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="n">loss</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">step</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="section" id="optimizer-step-closure">
<h4><code class="docutils literal"><span class="pre">optimizer.step(closure)</span></code><a class="headerlink" href="#optimizer-step-closure" title="Permalink to this headline">¶</a></h4>
<p>Some optimization algorithms such as Conjugate Gradient and LBFGS need to
reevaluate the function multiple times, so you have to pass in a closure that
allows them to recompute your model. The closure should clear the gradients,
compute the loss, and return it.</p>
<p>Example:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="nb">input</span><span class="p">,</span> <span class="n">target</span> <span class="ow">in</span> <span class="n">dataset</span><span class="p">:</span>
<span class="k">def</span> <span class="nf">closure</span><span class="p">():</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">zero_grad</span><span class="p">()</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">loss_fn</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="n">loss</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="k">return</span> <span class="n">loss</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">step</span><span class="p">(</span><span class="n">closure</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="section" id="algorithms">
<h2>Algorithms<a class="headerlink" href="#algorithms" title="Permalink to this headline">¶</a></h2>
<dl class="class">
<dt id="torch.optim.Optimizer">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">Optimizer</code><span class="sig-paren">(</span><em>params</em>, <em>defaults</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer" title="Permalink to this definition">¶</a></dt>
<dd><p>Base class for all optimizers.</p>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">Parameters need to be specified as collections that have a deterministic
ordering that is consistent between runs. Examples of objects that don’t
satisfy those properties are sets and iterators over values of dictionaries.</p>
</div>
<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>params</strong> (<em>iterable</em>) – an iterable of <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> s or
<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.6)"><code class="xref py py-class docutils literal"><span class="pre">dict</span></code></a> s. Specifies what Tensors should be optimized.</li>
<li><strong>defaults</strong> – (dict): a dict containing default values of optimization
options (used when a parameter group doesn’t specify them).</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.Optimizer.add_param_group">
<code class="descname">add_param_group</code><span class="sig-paren">(</span><em>param_group</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.add_param_group"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.add_param_group" title="Permalink to this definition">¶</a></dt>
<dd><p>Add a param group to the <a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><code class="xref py py-class docutils literal"><span class="pre">Optimizer</span></code></a> s <cite>param_groups</cite>.</p>
<p>This can be useful when fine tuning a pre-trained network as frozen layers can be made
trainable and added to the <a class="reference internal" href="#torch.optim.Optimizer" title="torch.optim.Optimizer"><code class="xref py py-class docutils literal"><span class="pre">Optimizer</span></code></a> as training progresses.</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>param_group</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.6)"><em>dict</em></a>) – Specifies what Tensors should be optimized along with group</li>
<li><strong>optimization options.</strong> (<em>specific</em>) – </li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.load_state_dict">
<code class="descname">load_state_dict</code><span class="sig-paren">(</span><em>state_dict</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.load_state_dict"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.load_state_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Loads the optimizer state.</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>state_dict</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.6)"><em>dict</em></a>) – optimizer state. Should be an object returned
from a call to <a class="reference internal" href="#torch.optim.Optimizer.state_dict" title="torch.optim.Optimizer.state_dict"><code class="xref py py-meth docutils literal"><span class="pre">state_dict()</span></code></a>.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.state_dict">
<code class="descname">state_dict</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.state_dict"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.state_dict" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the state of the optimizer as a <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.6)"><code class="xref py py-class docutils literal"><span class="pre">dict</span></code></a>.</p>
<p>It contains two entries:</p>
<ul class="simple">
<li><dl class="first docutils">
<dt>state - a dict holding current optimization state. Its content</dt>
<dd>differs between optimizer classes.</dd>
</dl>
</li>
<li>param_groups - a dict containing all parameter groups</li>
</ul>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>closure</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step (parameter update).</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>closure</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#callable" title="(in Python v3.6)"><em>callable</em></a>) – A closure that reevaluates the model and
returns the loss. Optional for most optimizers.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="torch.optim.Optimizer.zero_grad">
<code class="descname">zero_grad</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/optimizer.html#Optimizer.zero_grad"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Optimizer.zero_grad" title="Permalink to this definition">¶</a></dt>
<dd><p>Clears the gradients of all optimized <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> s.</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adadelta">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">Adadelta</code><span class="sig-paren">(</span><em>params</em>, <em>lr=1.0</em>, <em>rho=0.9</em>, <em>eps=1e-06</em>, <em>weight_decay=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adadelta.html#Adadelta"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adadelta" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements Adadelta algorithm.</p>
<p>It has been proposed in <a class="reference external" href="https://arxiv.org/abs/1212.5701">ADADELTA: An Adaptive Learning Rate Method</a>.</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>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>rho</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.6)"><em>float</em></a><em>, </em><em>optional</em>) – coefficient used for computing a running average
of squared gradients (default: 0.9)</li>
<li><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.6)"><em>float</em></a><em>, </em><em>optional</em>) – term added to the denominator to improve
numerical stability (default: 1e-6)</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.6)"><em>float</em></a><em>, </em><em>optional</em>) – coefficient that scale delta before it is applied
to the parameters (default: 1.0)</li>
<li><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.6)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.Adadelta.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adadelta.html#Adadelta.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adadelta.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</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>closure</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#callable" title="(in Python v3.6)"><em>callable</em></a><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adagrad">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">Adagrad</code><span class="sig-paren">(</span><em>params</em>, <em>lr=0.01</em>, <em>lr_decay=0</em>, <em>weight_decay=0</em>, <em>initial_accumulator_value=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adagrad.html#Adagrad"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adagrad" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements Adagrad algorithm.</p>
<p>It has been proposed in <a class="reference external" href="http://jmlr.org/papers/v12/duchi11a.html">Adaptive Subgradient Methods for Online Learning
and Stochastic Optimization</a>.</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>params</strong> (<em>iterable</em>) – iterable of parameters to optimize or dicts defining
parameter groups</li>
<li><strong>lr</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.6)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate (default: 1e-2)</li>
<li><strong>lr_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.6)"><em>float</em></a><em>, </em><em>optional</em>) – learning rate decay (default: 0)</li>
<li><strong>weight_decay</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.6)"><em>float</em></a><em>, </em><em>optional</em>) – weight decay (L2 penalty) (default: 0)</li>
</ul>
</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="torch.optim.Adagrad.step">
<code class="descname">step</code><span class="sig-paren">(</span><em>closure=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adagrad.html#Adagrad.step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adagrad.step" title="Permalink to this definition">¶</a></dt>
<dd><p>Performs a single optimization step.</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>closure</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#callable" title="(in Python v3.6)"><em>callable</em></a><em>, </em><em>optional</em>) – A closure that reevaluates the model
and returns the loss.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="torch.optim.Adam">
<em class="property">class </em><code class="descclassname">torch.optim.</code><code class="descname">Adam</code><span class="sig-paren">(</span><em>params</em>, <em>lr=0.001</em>, <em>betas=(0.9</em>, <em>0.999)</em>, <em>eps=1e-08</em>, <em>weight_decay=0</em>, <em>amsgrad=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/torch/optim/adam.html#Adam"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#torch.optim.Adam" title="Permalink to this definition">¶</a></dt>
<dd><p>Implements Adam algorithm.</p>
<p>It has been proposed in <a class="reference external" href="https://arxiv.org/abs/1412.6980">Adam: A Method for Stochastic Optimization</a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />