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<span class="mdl-layout-title toc">Table Of Contents</span>
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<li class="toctree-l1 current"><a class="reference internal" href="../../index.html">Python Tutorials</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="../index.html">Getting Started</a><ul class="current">
<li class="toctree-l3 current"><a class="reference internal" href="index.html">Crash Course</a><ul class="current">
<li class="toctree-l4"><a class="reference internal" href="1-ndarray.html">Manipulate data with <code class="docutils literal notranslate"><span class="pre">ndarray</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="2-nn.html">Create a neural network</a></li>
<li class="toctree-l4 current"><a class="current reference internal" href="#">Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="4-train.html">Train the neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="5-predict.html">Predict with a pre-trained model</a></li>
<li class="toctree-l4"><a class="reference internal" href="6-use_gpus.html">Use GPUs</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li>
<li class="toctree-l3"><a class="reference internal" href="../logistic_regression_explained.html">Logistic regression explained</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li>
</ul>
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<li class="toctree-l2"><a class="reference internal" href="../../packages/index.html">Packages</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../packages/autograd/index.html">Automatic Differentiation</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../packages/gluon/index.html">Gluon</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/gluon/blocks/index.html">Blocks</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/custom-layer.html">Custom Layers</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/custom_layer_beginners.html">Customer Layers (Beginners)</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/hybridize.html">Hybridize</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/init.html">Initialization</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/naming.html">Parameter and Block Naming</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/nn.html">Layers and Blocks</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/parameters.html">Parameter Management</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../packages/gluon/data/index.html">Data Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/data_augmentation.html">Image Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/data_augmentation.html#Spatial-Augmentation">Spatial Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/data_augmentation.html#Color-Augmentation">Color Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/data_augmentation.html#Composed-Augmentations">Composed Augmentations</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/image/pretrained_models.html">Using pre-trained models in MXNet</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/loss/loss.html">Loss functions</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/training/trainer.html">Trainer</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../../packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/training/normalization/index.html">Normalization Blocks</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../packages/kvstore/index.html">KVStore</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../packages/ndarray/index.html">NDArray</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/02-ndarray-operations.html">NDArray Operations</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/sparse/index.html">Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/ndarray/sparse/train.html">Train a Linear Regression Model with Sparse Symbols</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/ndarray/sparse/train_gluon.html">Sparse NDArrays with Gluon</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../packages/onnx/index.html">ONNX</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/onnx/fine_tuning_gluon.html">Fine-tuning an ONNX model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/onnx/inference_on_onnx_model.html">Running inference on MXNet/Gluon from an ONNX model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/onnx/super_resolution.html">Importing an ONNX model into MXNet</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/deploy/export/onnx.html">Export ONNX Models</a></li>
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<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/visualize_graph">Visualize networks</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../performance/index.html">Performance</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../performance/compression/index.html">Compression</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../performance/compression/int8.html">Deploy with int-8</a></li>
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<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/gradient_compression">Gradient Compression</a></li>
<li class="toctree-l4"><a class="reference external" href="https://gluon-cv.mxnet.io/build/examples_deployment/int8_inference.html">GluonCV with Quantized Models</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../performance/backend/index.html">Accelerated Backend Tools</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../performance/backend/mkldnn/index.html">Intel MKL-DNN</a><ul>
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<li class="toctree-l5"><a class="reference internal" href="../../performance/backend/mkldnn/mkldnn_quantization.html#Improving-accuracy-with-Intel®-Neural-Compressor">Improving accuracy with Intel® Neural Compressor</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../performance/backend/mkldnn/mkldnn_readme.html">Install MXNet with MKL-DNN</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../performance/backend/tensorrt/index.html">TensorRT</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../performance/backend/tensorrt/tensorrt.html">Optimizing Deep Learning Computation Graphs with TensorRT</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../performance/backend/profiler.html">Profiling MXNet Models</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../performance/backend/amp.html">Using AMP: Automatic Mixed Precision</a></li>
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<li class="toctree-l1 current"><a class="reference internal" href="../../index.html">Python Tutorials</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="../index.html">Getting Started</a><ul class="current">
<li class="toctree-l3 current"><a class="reference internal" href="index.html">Crash Course</a><ul class="current">
<li class="toctree-l4"><a class="reference internal" href="1-ndarray.html">Manipulate data with <code class="docutils literal notranslate"><span class="pre">ndarray</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="2-nn.html">Create a neural network</a></li>
<li class="toctree-l4 current"><a class="current reference internal" href="#">Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="4-train.html">Train the neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="5-predict.html">Predict with a pre-trained model</a></li>
<li class="toctree-l4"><a class="reference internal" href="6-use_gpus.html">Use GPUs</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li>
<li class="toctree-l3"><a class="reference internal" href="../logistic_regression_explained.html">Logistic regression explained</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../packages/index.html">Packages</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../packages/autograd/index.html">Automatic Differentiation</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../packages/gluon/index.html">Gluon</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/gluon/blocks/index.html">Blocks</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/custom-layer.html">Custom Layers</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/custom_layer_beginners.html">Customer Layers (Beginners)</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/hybridize.html">Hybridize</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/init.html">Initialization</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/naming.html">Parameter and Block Naming</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/nn.html">Layers and Blocks</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/parameters.html">Parameter Management</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../packages/gluon/data/index.html">Data Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/data_augmentation.html">Image Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/data_augmentation.html#Spatial-Augmentation">Spatial Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/data_augmentation.html#Color-Augmentation">Color Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/data_augmentation.html#Composed-Augmentations">Composed Augmentations</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/image/image-augmentation.html">Image Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/image/pretrained_models.html">Using pre-trained models in MXNet</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../packages/gluon/loss/index.html">Losses</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/loss/custom-loss.html">Custom Loss Blocks</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/loss/loss.html">Loss functions</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../packages/gluon/text/index.html">Text Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/text/transformer.html">Machine Translation with Transformer</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../packages/gluon/training/index.html">Training</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/training/trainer.html">Trainer</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../../packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../../packages/gluon/training/normalization/index.html">Normalization Blocks</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../packages/kvstore/index.html">KVStore</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../packages/ndarray/index.html">NDArray</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/02-ndarray-operations.html">NDArray Operations</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/ndarray/sparse/index.html">Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/ndarray/sparse/train.html">Train a Linear Regression Model with Sparse Symbols</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/ndarray/sparse/train_gluon.html">Sparse NDArrays with Gluon</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../packages/onnx/index.html">ONNX</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/onnx/fine_tuning_gluon.html">Fine-tuning an ONNX model</a></li>
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<!--- Licensed to the Apache Software Foundation (ASF) under one --><!--- or more contributor license agreements. See the NOTICE file --><!--- distributed with this work for additional information --><!--- regarding copyright ownership. The ASF licenses this file --><!--- to you under the Apache License, Version 2.0 (the --><!--- "License"); you may not use this file except in compliance --><!--- with the License. You may obtain a copy of the License at --><!--- http://www.apache.org/licenses/LICENSE-2.0 --><!--- Unless required by applicable law or agreed to in writing, --><!--- software distributed under the License is distributed on an --><!--- "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY --><!--- KIND, either express or implied. See the License for the --><!--- specific language governing permissions and limitations --><!--- under the License. --><div class="section" id="Automatic-differentiation-with-autograd">
<h1>Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code><a class="headerlink" href="#Automatic-differentiation-with-autograd" title="Permalink to this headline"></a></h1>
<p>We train models to get better and better as a function of experience. Usually, getting better means minimizing a loss function. To achieve this goal, we often iteratively compute the gradient of the loss with respect to weights and then update the weights accordingly. While the gradient calculations are straightforward through a chain rule, for complex models, working it out by hand can be a pain.</p>
<p>Before diving deep into the model training, let’s go through how MXNet’s <code class="docutils literal notranslate"><span class="pre">autograd</span></code> package expedites this work by automatically calculating derivatives.</p>
<div class="section" id="Basic-usage">
<h2>Basic usage<a class="headerlink" href="#Basic-usage" title="Permalink to this headline"></a></h2>
<p>Let’s first import the <code class="docutils literal notranslate"><span class="pre">autograd</span></code> package.</p>
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<span></span><span class="kn">from</span> <span class="nn">mxnet</span> <span class="kn">import</span> <span class="n">nd</span>
<span class="kn">from</span> <span class="nn">mxnet</span> <span class="kn">import</span> <span class="n">autograd</span>
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<p>As a toy example, let’s say that we are interested in differentiating a function <span class="math notranslate nohighlight">\(f(x) = 2 x^2\)</span> with respect to parameter <span class="math notranslate nohighlight">\(x\)</span>. We can start by assigning an initial value of <span class="math notranslate nohighlight">\(x\)</span>.</p>
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<span></span><span class="n">x</span> <span class="o">=</span> <span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]])</span>
<span class="n">x</span>
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<p>Once we compute the gradient of <span class="math notranslate nohighlight">\(f(x)\)</span> with respect to <span class="math notranslate nohighlight">\(x\)</span>, we’ll need a place to store it. In MXNet, we can tell an NDArray that we plan to store a gradient by invoking its <code class="docutils literal notranslate"><span class="pre">attach_grad</span></code> method.</p>
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<span></span><span class="n">x</span><span class="o">.</span><span class="n">attach_grad</span><span class="p">()</span>
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<p>Now we’re going to define the function <span class="math notranslate nohighlight">\(y=f(x)\)</span>. To let MXNet store <span class="math notranslate nohighlight">\(y\)</span>, so that we can compute gradients later, we need to put the definition inside a <code class="docutils literal notranslate"><span class="pre">autograd.record()</span></code> scope.</p>
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<span></span><span class="k">with</span> <span class="n">autograd</span><span class="o">.</span><span class="n">record</span><span class="p">():</span>
<span class="n">y</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">x</span> <span class="o">*</span> <span class="n">x</span>
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<p>Let’s invoke back propagation (backprop) by calling <code class="docutils literal notranslate"><span class="pre">y.backward()</span></code>. When <span class="math notranslate nohighlight">\(y\)</span> has more than one entry, <code class="docutils literal notranslate"><span class="pre">y.backward()</span></code> is equivalent to <code class="docutils literal notranslate"><span class="pre">y.sum().backward()</span></code>.</p>
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<span></span><span class="n">y</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
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<p>Now, let’s see if this is the expected output. Note that <span class="math notranslate nohighlight">\(y=2x^2\)</span> and <span class="math notranslate nohighlight">\(\frac{dy}{dx} = 4x\)</span>, which should be <code class="docutils literal notranslate"><span class="pre">[[4,</span> <span class="pre">8],[12,</span> <span class="pre">16]]</span></code>. Let’s check the automatically computed results:</p>
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<span></span><span class="n">x</span><span class="o">.</span><span class="n">grad</span>
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<div class="section" id="Using-Python-control-flows">
<h2>Using Python control flows<a class="headerlink" href="#Using-Python-control-flows" title="Permalink to this headline"></a></h2>
<p>Sometimes we want to write dynamic programs where the execution depends on some real-time values. MXNet will record the execution trace and compute the gradient as well.</p>
<p>Consider the following function <code class="docutils literal notranslate"><span class="pre">f</span></code>: it doubles the inputs until it’s <code class="docutils literal notranslate"><span class="pre">norm</span></code> reaches 1000. Then it selects one element depending on the sum of its elements.</p>
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<span></span><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span>
<span class="k">while</span> <span class="n">b</span><span class="o">.</span><span class="n">norm</span><span class="p">()</span><span class="o">.</span><span class="n">asscalar</span><span class="p">()</span> <span class="o">&lt;</span> <span class="mi">1000</span><span class="p">:</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">b</span> <span class="o">*</span> <span class="mi">2</span>
<span class="k">if</span> <span class="n">b</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span><span class="o">.</span><span class="n">asscalar</span><span class="p">()</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="k">return</span> <span class="n">c</span>
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<p>We record the trace and feed in a random value:</p>
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<span></span><span class="n">a</span> <span class="o">=</span> <span class="n">nd</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">a</span><span class="o">.</span><span class="n">attach_grad</span><span class="p">()</span>
<span class="k">with</span> <span class="n">autograd</span><span class="o">.</span><span class="n">record</span><span class="p">():</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="n">c</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
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<p>We know that <code class="docutils literal notranslate"><span class="pre">b</span></code> is a linear function of <code class="docutils literal notranslate"><span class="pre">a</span></code>, and <code class="docutils literal notranslate"><span class="pre">c</span></code> is chosen from <code class="docutils literal notranslate"><span class="pre">b</span></code>. Then the gradient with respect to <code class="docutils literal notranslate"><span class="pre">a</span></code> be will be either <code class="docutils literal notranslate"><span class="pre">[c/a[0],</span> <span class="pre">0]</span></code> or <code class="docutils literal notranslate"><span class="pre">[0,</span> <span class="pre">c/a[1]]</span></code>, depending on which element from <code class="docutils literal notranslate"><span class="pre">b</span></code> we picked. Let’s find the results:</p>
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<span></span><span class="p">[</span><span class="n">a</span><span class="o">.</span><span class="n">grad</span><span class="p">,</span> <span class="n">c</span><span class="o">/</span><span class="n">a</span><span class="p">]</span>
</pre></div>
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<span class="caption-text">Table Of Contents</span>
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<ul>
<li><a class="reference internal" href="#">Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code></a><ul>
<li><a class="reference internal" href="#Basic-usage">Basic usage</a></li>
<li><a class="reference internal" href="#Using-Python-control-flows">Using Python control flows</a></li>
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