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<title>Step 4: Train the neural network &#8212; Apache MXNet documentation</title>
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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">Getting started with NP on MXNet</a><ul class="current">
<li class="toctree-l4"><a class="reference internal" href="1-ndarray.html">Step 1: Manipulate data with NP on MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="2-nn.html">Step 2: Create a neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="3-autograd.html">Step 3: Automatic differentiation with autograd</a></li>
<li class="toctree-l4 current"><a class="current reference internal" href="#">Step 4: Train the neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="5-predict.html">Step 5: Predict with a pretrained model</a></li>
<li class="toctree-l4"><a class="reference internal" href="6-use_gpus.html">Step 6: Use GPUs to increase efficiency</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>
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<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-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-l5"><a class="reference internal" href="../../packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li>
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<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-l4"><a class="reference internal" href="../../packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../packages/legacy/ndarray/index.html">NDArray</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/legacy/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/legacy/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/legacy/ndarray/sparse/index.html">Tutorials</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../../packages/legacy/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../packages/legacy/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../packages/legacy/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/np/index.html">What is NP on MXNet</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/np/cheat-sheet.html">The NP on MXNet cheat sheet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/np/np-vs-numpy.html">Differences between NP on MXNet and NumPy</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 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-l3"><a class="reference internal" href="../../packages/viz/index.html">Visualization</a><ul>
<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-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>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/float16">Float16</a></li>
<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-l4"><a class="reference internal" href="../../performance/backend/mkldnn/index.html">Intel MKL-DNN</a><ul>
<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 class="simple">
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<li class="toctree-l4"><a class="reference internal" href="../../performance/backend/tvm.html">Use TVM</a></li>
<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-l3"><a class="reference internal" href="../../deploy/export/index.html">Export</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../deploy/export/onnx.html">Exporting to ONNX format</a></li>
<li class="toctree-l4"><a class="reference external" href="https://gluon-cv.mxnet.io/build/examples_deployment/export_network.html">Export Gluon CV Models</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/blocks/save_load_params.html">Save / Load Parameters</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../deploy/inference/index.html">Inference</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../deploy/inference/cpp.html">Deploy into C++</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../deploy/inference/image_classification_jetson.html">Image Classication using pretrained ResNet-50 model on Jetson module</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../deploy/run-on-aws/index.html">Run on AWS</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../deploy/run-on-aws/use_ec2.html">Run on an EC2 Instance</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../deploy/run-on-aws/use_sagemaker.html">Run on Amazon SageMaker</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../deploy/run-on-aws/cloud.html">MXNet on the Cloud</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../extend/index.html">Extend</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../extend/customop.html">Custom Numpy Operators</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/faq/new_op">New Operator Creation</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/faq/add_op_in_backend">New Operator in MXNet Backend</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/faq/using_rtc">Using RTC for CUDA kernels</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../../api/index.html">Python API</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="../../../api/np/arrays.html">Array objects</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/arrays.ndarray.html">The N-dimensional array (<code class="xref py py-class docutils literal notranslate"><span class="pre">ndarray</span></code>)</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.html">mxnet.np.ndarray</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.shape.html">mxnet.np.ndarray.shape</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.ndim.html">mxnet.np.ndarray.ndim</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.size.html">mxnet.np.ndarray.size</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.dtype.html">mxnet.np.ndarray.dtype</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.T.html">mxnet.np.ndarray.T</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.item.html">mxnet.np.ndarray.item</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.copy.html">mxnet.np.ndarray.copy</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.tolist.html">mxnet.np.ndarray.tolist</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.astype.html">mxnet.np.ndarray.astype</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.reshape.html">mxnet.np.ndarray.reshape</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.transpose.html">mxnet.np.ndarray.transpose</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.swapaxes.html">mxnet.np.ndarray.swapaxes</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.flatten.html">mxnet.np.ndarray.flatten</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.squeeze.html">mxnet.np.ndarray.squeeze</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.nonzero.html">mxnet.np.ndarray.nonzero</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.take.html">mxnet.np.ndarray.take</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.repeat.html">mxnet.np.ndarray.repeat</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.max.html">mxnet.np.ndarray.max</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.argmax.html">mxnet.np.ndarray.argmax</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.min.html">mxnet.np.ndarray.min</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.argmin.html">mxnet.np.ndarray.argmin</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.clip.html">mxnet.np.ndarray.clip</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.sum.html">mxnet.np.ndarray.sum</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.mean.html">mxnet.np.ndarray.mean</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.prod.html">mxnet.np.ndarray.prod</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.cumsum.html">mxnet.np.ndarray.cumsum</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.var.html">mxnet.np.ndarray.var</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.std.html">mxnet.np.ndarray.std</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__lt__.html">mxnet.np.ndarray.__lt__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__le__.html">mxnet.np.ndarray.__le__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__gt__.html">mxnet.np.ndarray.__gt__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__ge__.html">mxnet.np.ndarray.__ge__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__eq__.html">mxnet.np.ndarray.__eq__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__ne__.html">mxnet.np.ndarray.__ne__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__bool__.html">mxnet.np.ndarray.__bool__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__neg__.html">mxnet.np.ndarray.__neg__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__add__.html">mxnet.np.ndarray.__add__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__sub__.html">mxnet.np.ndarray.__sub__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__mul__.html">mxnet.np.ndarray.__mul__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__truediv__.html">mxnet.np.ndarray.__truediv__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__mod__.html">mxnet.np.ndarray.__mod__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__pow__.html">mxnet.np.ndarray.__pow__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__iadd__.html">mxnet.np.ndarray.__iadd__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__isub__.html">mxnet.np.ndarray.__isub__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__imul__.html">mxnet.np.ndarray.__imul__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__itruediv__.html">mxnet.np.ndarray.__itruediv__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__imod__.html">mxnet.np.ndarray.__imod__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__reduce__.html">mxnet.np.ndarray.__reduce__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__setstate__.html">mxnet.np.ndarray.__setstate__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__len__.html">mxnet.np.ndarray.__len__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__getitem__.html">mxnet.np.ndarray.__getitem__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__setitem__.html">mxnet.np.ndarray.__setitem__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__int__.html">mxnet.np.ndarray.__int__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__float__.html">mxnet.np.ndarray.__float__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__str__.html">mxnet.np.ndarray.__str__</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.__repr__.html">mxnet.np.ndarray.__repr__</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/arrays.indexing.html">Indexing</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/np/routines.html">Routines</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.array-creation.html">Array creation routines</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.eye.html">mxnet.np.eye</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.empty.html">mxnet.np.empty</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.full.html">mxnet.np.full</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.identity.html">mxnet.np.identity</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ones.html">mxnet.np.ones</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ones_like.html">mxnet.np.ones_like</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.zeros.html">mxnet.np.zeros</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.zeros_like.html">mxnet.np.zeros_like</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.array.html">mxnet.np.array</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.copy.html">mxnet.np.copy</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arange.html">mxnet.np.arange</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.linspace.html">mxnet.np.linspace</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.logspace.html">mxnet.np.logspace</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.meshgrid.html">mxnet.np.meshgrid</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.tril.html">mxnet.np.tril</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.array-manipulation.html">Array manipulation routines</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.reshape.html">mxnet.np.reshape</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ravel.html">mxnet.np.ravel</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.flatten.html">mxnet.np.ndarray.flatten</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.swapaxes.html">mxnet.np.swapaxes</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.T.html">mxnet.np.ndarray.T</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.transpose.html">mxnet.np.transpose</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.moveaxis.html">mxnet.np.moveaxis</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.expand_dims.html">mxnet.np.expand_dims</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.squeeze.html">mxnet.np.squeeze</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.broadcast_to.html">mxnet.np.broadcast_to</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.broadcast_arrays.html">mxnet.np.broadcast_arrays</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.concatenate.html">mxnet.np.concatenate</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.stack.html">mxnet.np.stack</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.dstack.html">mxnet.np.dstack</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.vstack.html">mxnet.np.vstack</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.split.html">mxnet.np.split</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.hsplit.html">mxnet.np.hsplit</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.vsplit.html">mxnet.np.vsplit</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.tile.html">mxnet.np.tile</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.repeat.html">mxnet.np.repeat</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.unique.html">mxnet.np.unique</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.reshape.html">mxnet.np.reshape</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.flip.html">mxnet.np.flip</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.roll.html">mxnet.np.roll</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.rot90.html">mxnet.np.rot90</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.io.html">Input and output</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.genfromtxt.html">mxnet.np.genfromtxt</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.linalg.html">Linear algebra (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.linalg</span></code>)</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.dot.html">mxnet.np.dot</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.vdot.html">mxnet.np.vdot</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.inner.html">mxnet.np.inner</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.outer.html">mxnet.np.outer</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.tensordot.html">mxnet.np.tensordot</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.einsum.html">mxnet.np.einsum</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.linalg.svd.html">mxnet.np.linalg.svd</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.linalg.norm.html">mxnet.np.linalg.norm</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.trace.html">mxnet.np.trace</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.math.html">Mathematical functions</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.sin.html">mxnet.np.sin</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.cos.html">mxnet.np.cos</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.tan.html">mxnet.np.tan</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arcsin.html">mxnet.np.arcsin</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arccos.html">mxnet.np.arccos</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arctan.html">mxnet.np.arctan</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.degrees.html">mxnet.np.degrees</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.radians.html">mxnet.np.radians</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.hypot.html">mxnet.np.hypot</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arctan2.html">mxnet.np.arctan2</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.deg2rad.html">mxnet.np.deg2rad</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.rad2deg.html">mxnet.np.rad2deg</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.sinh.html">mxnet.np.sinh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.cosh.html">mxnet.np.cosh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.tanh.html">mxnet.np.tanh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arcsinh.html">mxnet.np.arcsinh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arccosh.html">mxnet.np.arccosh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arctanh.html">mxnet.np.arctanh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.rint.html">mxnet.np.rint</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.fix.html">mxnet.np.fix</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.floor.html">mxnet.np.floor</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ceil.html">mxnet.np.ceil</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.trunc.html">mxnet.np.trunc</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.around.html">mxnet.np.around</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.sum.html">mxnet.np.sum</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.prod.html">mxnet.np.prod</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.cumsum.html">mxnet.np.cumsum</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.exp.html">mxnet.np.exp</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.expm1.html">mxnet.np.expm1</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.log.html">mxnet.np.log</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.log10.html">mxnet.np.log10</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.log2.html">mxnet.np.log2</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.log1p.html">mxnet.np.log1p</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ldexp.html">mxnet.np.ldexp</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.lcm.html">mxnet.np.lcm</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.add.html">mxnet.np.add</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../../api/npx/index.html">NPX: NumPy Neural Network Extension</a><ul>
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<span class="mdl-layout-title toc">Table Of Contents</span>
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<ul class="current">
<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">Getting started with NP on MXNet</a><ul class="current">
<li class="toctree-l4"><a class="reference internal" href="1-ndarray.html">Step 1: Manipulate data with NP on MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="2-nn.html">Step 2: Create a neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="3-autograd.html">Step 3: Automatic differentiation with autograd</a></li>
<li class="toctree-l4 current"><a class="current reference internal" href="#">Step 4: Train the neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="5-predict.html">Step 5: Predict with a pretrained model</a></li>
<li class="toctree-l4"><a class="reference internal" href="6-use_gpus.html">Step 6: Use GPUs to increase efficiency</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>
</li>
<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>
</ul>
</li>
<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>
</ul>
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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>
</ul>
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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-l5"><a class="reference internal" href="../../packages/gluon/text/transformer.html">Machine Translation with Transformer</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>
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<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-l3"><a class="reference internal" href="../../packages/legacy/index.html">Legacy</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/legacy/ndarray/index.html">NDArray</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../packages/legacy/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../packages/legacy/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
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<li class="toctree-l6"><a class="reference internal" href="../../packages/legacy/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../packages/legacy/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
<li class="toctree-l6"><a class="reference internal" href="../../packages/legacy/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/np/index.html">What is NP on MXNet</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../packages/np/cheat-sheet.html">The NP on MXNet cheat sheet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../packages/np/np-vs-numpy.html">Differences between NP on MXNet and NumPy</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 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>
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<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://gluon-cv.mxnet.io/build/examples_deployment/int8_inference.html">GluonCV with Quantized Models</a></li>
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<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/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-l4"><a class="reference external" href="https://gluon-cv.mxnet.io/build/examples_deployment/export_network.html">Export Gluon CV Models</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../extend/index.html">Extend</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../extend/customop.html">Custom Numpy Operators</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.array-manipulation.html">Array manipulation routines</a><ul>
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<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.swapaxes.html">mxnet.np.swapaxes</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ndarray.T.html">mxnet.np.ndarray.T</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.transpose.html">mxnet.np.transpose</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.moveaxis.html">mxnet.np.moveaxis</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.expand_dims.html">mxnet.np.expand_dims</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.squeeze.html">mxnet.np.squeeze</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.broadcast_to.html">mxnet.np.broadcast_to</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.broadcast_arrays.html">mxnet.np.broadcast_arrays</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.concatenate.html">mxnet.np.concatenate</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.stack.html">mxnet.np.stack</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.dstack.html">mxnet.np.dstack</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.vstack.html">mxnet.np.vstack</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.split.html">mxnet.np.split</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.hsplit.html">mxnet.np.hsplit</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.vsplit.html">mxnet.np.vsplit</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.tile.html">mxnet.np.tile</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.repeat.html">mxnet.np.repeat</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.unique.html">mxnet.np.unique</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.reshape.html">mxnet.np.reshape</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.flip.html">mxnet.np.flip</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.roll.html">mxnet.np.roll</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.rot90.html">mxnet.np.rot90</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.io.html">Input and output</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.genfromtxt.html">mxnet.np.genfromtxt</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.linalg.html">Linear algebra (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.linalg</span></code>)</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.dot.html">mxnet.np.dot</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.vdot.html">mxnet.np.vdot</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.inner.html">mxnet.np.inner</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.outer.html">mxnet.np.outer</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.tensordot.html">mxnet.np.tensordot</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.einsum.html">mxnet.np.einsum</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.linalg.svd.html">mxnet.np.linalg.svd</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.linalg.norm.html">mxnet.np.linalg.norm</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.trace.html">mxnet.np.trace</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.math.html">Mathematical functions</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.sin.html">mxnet.np.sin</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.cos.html">mxnet.np.cos</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.tan.html">mxnet.np.tan</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arcsin.html">mxnet.np.arcsin</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arccos.html">mxnet.np.arccos</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arctan.html">mxnet.np.arctan</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.degrees.html">mxnet.np.degrees</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.radians.html">mxnet.np.radians</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.hypot.html">mxnet.np.hypot</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arctan2.html">mxnet.np.arctan2</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.deg2rad.html">mxnet.np.deg2rad</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.rad2deg.html">mxnet.np.rad2deg</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.sinh.html">mxnet.np.sinh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.cosh.html">mxnet.np.cosh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.tanh.html">mxnet.np.tanh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arcsinh.html">mxnet.np.arcsinh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arccosh.html">mxnet.np.arccosh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.arctanh.html">mxnet.np.arctanh</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.rint.html">mxnet.np.rint</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.fix.html">mxnet.np.fix</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.floor.html">mxnet.np.floor</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ceil.html">mxnet.np.ceil</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.trunc.html">mxnet.np.trunc</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.around.html">mxnet.np.around</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.sum.html">mxnet.np.sum</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.prod.html">mxnet.np.prod</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.cumsum.html">mxnet.np.cumsum</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.exp.html">mxnet.np.exp</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.expm1.html">mxnet.np.expm1</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.log.html">mxnet.np.log</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.log10.html">mxnet.np.log10</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.log2.html">mxnet.np.log2</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.log1p.html">mxnet.np.log1p</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.ldexp.html">mxnet.np.ldexp</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.lcm.html">mxnet.np.lcm</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.add.html">mxnet.np.add</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.reciprocal.html">mxnet.np.reciprocal</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.negative.html">mxnet.np.negative</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.divide.html">mxnet.np.divide</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.power.html">mxnet.np.power</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.subtract.html">mxnet.np.subtract</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.mod.html">mxnet.np.mod</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.multiply.html">mxnet.np.multiply</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.true_divide.html">mxnet.np.true_divide</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.remainder.html">mxnet.np.remainder</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.clip.html">mxnet.np.clip</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.sqrt.html">mxnet.np.sqrt</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.cbrt.html">mxnet.np.cbrt</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.square.html">mxnet.np.square</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.absolute.html">mxnet.np.absolute</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.sign.html">mxnet.np.sign</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.maximum.html">mxnet.np.maximum</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.minimum.html">mxnet.np.minimum</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/random/index.html">np.random</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.sort.html">Sorting, searching, and counting</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.argmax.html">mxnet.np.argmax</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.argmin.html">mxnet.np.argmin</a></li>
</ul>
</li>
<li class="toctree-l4"><a class="reference internal" href="../../../api/np/routines.statistics.html">Statistics</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.min.html">mxnet.np.min</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.max.html">mxnet.np.max</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.mean.html">mxnet.np.mean</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.std.html">mxnet.np.std</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.var.html">mxnet.np.var</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/np/generated/mxnet.np.histogram.html">mxnet.np.histogram</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../../api/npx/index.html">NPX: NumPy Neural Network Extension</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.set_np.html">mxnet.npx.set_np</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.reset_np.html">mxnet.npx.reset_np</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.cpu.html">mxnet.npx.cpu</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.cpu_pinned.html">mxnet.npx.cpu_pinned</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.gpu.html">mxnet.npx.gpu</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.gpu_memory_info.html">mxnet.npx.gpu_memory_info</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.current_context.html">mxnet.npx.current_context</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.num_gpus.html">mxnet.npx.num_gpus</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.activation.html">mxnet.npx.activation</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.batch_norm.html">mxnet.npx.batch_norm</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.convolution.html">mxnet.npx.convolution</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.dropout.html">mxnet.npx.dropout</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.embedding.html">mxnet.npx.embedding</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.fully_connected.html">mxnet.npx.fully_connected</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.layer_norm.html">mxnet.npx.layer_norm</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.pooling.html">mxnet.npx.pooling</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.rnn.html">mxnet.npx.rnn</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.leaky_relu.html">mxnet.npx.leaky_relu</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.multibox_detection.html">mxnet.npx.multibox_detection</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.multibox_prior.html">mxnet.npx.multibox_prior</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.multibox_target.html">mxnet.npx.multibox_target</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.roi_pooling.html">mxnet.npx.roi_pooling</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.sigmoid.html">mxnet.npx.sigmoid</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.smooth_l1.html">mxnet.npx.smooth_l1</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.softmax.html">mxnet.npx.softmax</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.topk.html">mxnet.npx.topk</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.waitall.html">mxnet.npx.waitall</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.load.html">mxnet.npx.load</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.save.html">mxnet.npx.save</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.one_hot.html">mxnet.npx.one_hot</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.pick.html">mxnet.npx.pick</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.reshape_like.html">mxnet.npx.reshape_like</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.batch_flatten.html">mxnet.npx.batch_flatten</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.batch_dot.html">mxnet.npx.batch_dot</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.gamma.html">mxnet.npx.gamma</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/npx/generated/mxnet.npx.sequence_mask.html">mxnet.npx.sequence_mask</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../../api/gluon/index.html">mxnet.gluon</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/block.html">gluon.Block</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/hybrid_block.html">gluon.HybridBlock</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/symbol_block.html">gluon.SymbolBlock</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/constant.html">gluon.Constant</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/parameter.html">gluon.Parameter</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/parameter_dict.html">gluon.ParameterDict</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/trainer.html">gluon.Trainer</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/contrib/index.html">gluon.contrib</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/data/index.html">gluon.data</a><ul>
<li class="toctree-l4"><a class="reference internal" href="../../../api/gluon/data/vision/index.html">data.vision</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../../api/gluon/data/vision/datasets/index.html">vision.datasets</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../../api/gluon/data/vision/transforms/index.html">vision.transforms</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/loss/index.html">gluon.loss</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/metric/index.html">gluon.metric</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/model_zoo/index.html">gluon.model_zoo.vision</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/nn/index.html">gluon.nn</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/rnn/index.html">gluon.rnn</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../../api/gluon/utils/index.html">gluon.utils</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../../api/autograd/index.html">mxnet.autograd</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../api/initializer/index.html">mxnet.initializer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../api/optimizer/index.html">mxnet.optimizer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../api/lr_scheduler/index.html">mxnet.lr_scheduler</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../api/kvstore/index.html">mxnet.kvstore</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../api/module/index.html">mxnet.module</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../../api/contrib/index.html">mxnet.contrib</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../../api/contrib/autograd/index.html">contrib.autograd</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="Step-4:-Train-the-neural-network">
<h1>Step 4: Train the neural network<a class="headerlink" href="#Step-4:-Train-the-neural-network" title="Permalink to this headline"></a></h1>
<p>In this step, you learn how to train the previously defined network with data. First, import the libraries. The new ones are <code class="docutils literal notranslate"><span class="pre">mxnet.init</span></code> for more weight initialization methods. Import the <code class="docutils literal notranslate"><span class="pre">datasets</span></code> and <code class="docutils literal notranslate"><span class="pre">transforms</span></code> to load and transform computer vision datasets. Import <code class="docutils literal notranslate"><span class="pre">matplotlib</span></code> for drawing, and <code class="docutils literal notranslate"><span class="pre">time</span></code> for benchmarking. The example command here shows this.</p>
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<span></span><span class="c1"># Uncomment the following line if matplotlib is not installed.</span>
<span class="c1"># !pip install matplotlib</span>
<span class="kn">from</span> <span class="nn">mxnet</span> <span class="kn">import</span> <span class="n">np</span><span class="p">,</span> <span class="n">npx</span><span class="p">,</span> <span class="n">gluon</span><span class="p">,</span> <span class="n">init</span><span class="p">,</span> <span class="n">autograd</span>
<span class="kn">from</span> <span class="nn">mxnet.gluon</span> <span class="kn">import</span> <span class="n">nn</span>
<span class="kn">from</span> <span class="nn">IPython</span> <span class="kn">import</span> <span class="n">display</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">time</span>
<span class="n">npx</span><span class="o">.</span><span class="n">set_np</span><span class="p">()</span>
</pre></div>
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</div>
<div class="section" id="Get-data">
<h2>Get data<a class="headerlink" href="#Get-data" title="Permalink to this headline"></a></h2>
<p>The handwritten digit, MNIST dataset is one of the most commonly used datasets in deep learning. However, it’s too simple to get 99 percent accuracy. For this tutorial, you use a similar but slightly more complicated dataset called FashionMNIST. The end-goal is to classify clothing types.</p>
<p>The dataset can be automatically downloaded through Gluon’s <code class="docutils literal notranslate"><span class="pre">data.vision.datasets</span></code> module. The following code downloads the training dataset and shows the first example.</p>
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<span></span><span class="n">mnist_train</span> <span class="o">=</span> <span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">vision</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">FashionMNIST</span><span class="p">(</span><span class="n">train</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">mnist_train</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="p">(</span><span class="s1">&#39;X shape: &#39;</span><span class="p">,</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="s1">&#39;X dtype&#39;</span><span class="p">,</span> <span class="n">X</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="s1">&#39;y:&#39;</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
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<p>Each example in this dataset is a <span class="math notranslate nohighlight">\(28\times 28\)</span> size grey image, which is presented as ndarray with the shape format of <code class="docutils literal notranslate"><span class="pre">(height,</span> <span class="pre">width,</span> <span class="pre">channel)</span></code>. The label is a <code class="docutils literal notranslate"><span class="pre">numpy</span></code> scalar.</p>
<p>Next, visualize the first six examples.</p>
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<span></span><span class="n">text_labels</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;t-shirt&#39;</span><span class="p">,</span> <span class="s1">&#39;trouser&#39;</span><span class="p">,</span> <span class="s1">&#39;pullover&#39;</span><span class="p">,</span> <span class="s1">&#39;dress&#39;</span><span class="p">,</span> <span class="s1">&#39;coat&#39;</span><span class="p">,</span>
<span class="s1">&#39;sandal&#39;</span><span class="p">,</span> <span class="s1">&#39;shirt&#39;</span><span class="p">,</span> <span class="s1">&#39;sneaker&#39;</span><span class="p">,</span> <span class="s1">&#39;bag&#39;</span><span class="p">,</span> <span class="s1">&#39;ankle boot&#39;</span><span class="p">]</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">mnist_train</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">10</span><span class="p">]</span>
<span class="c1"># plot images</span>
<span class="n">display</span><span class="o">.</span><span class="n">set_matplotlib_formats</span><span class="p">(</span><span class="s1">&#39;svg&#39;</span><span class="p">)</span>
<span class="n">_</span><span class="p">,</span> <span class="n">figs</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">15</span><span class="p">))</span>
<span class="k">for</span> <span class="n">f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">yi</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">figs</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="c1"># 3D-&gt;2D by removing the last channel dim</span>
<span class="n">f</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">28</span><span class="p">,</span><span class="mi">28</span><span class="p">))</span><span class="o">.</span><span class="n">asnumpy</span><span class="p">())</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">f</span><span class="o">.</span><span class="n">axes</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">text_labels</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">yi</span><span class="p">)])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">title</span><span class="o">.</span><span class="n">set_fontsize</span><span class="p">(</span><span class="mi">14</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">get_xaxis</span><span class="p">()</span><span class="o">.</span><span class="n">set_visible</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">get_yaxis</span><span class="p">()</span><span class="o">.</span><span class="n">set_visible</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<p>In order to feed data into a Gluon model, convert the images to the <code class="docutils literal notranslate"><span class="pre">(channel,</span> <span class="pre">height,</span> <span class="pre">width)</span></code> format with a floating point data type. It can be done by <code class="docutils literal notranslate"><span class="pre">transforms.ToTensor</span></code>. In addition, normalize all pixel values with <code class="docutils literal notranslate"><span class="pre">transforms.Normalize</span></code> with the real mean 0.13 and standard deviation 0.31. You can chain these two transforms together and apply it to the first element of the data pair, namely the images.</p>
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<span></span><span class="n">transformer</span> <span class="o">=</span> <span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">vision</span><span class="o">.</span><span class="n">transforms</span><span class="o">.</span><span class="n">Compose</span><span class="p">([</span>
<span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">vision</span><span class="o">.</span><span class="n">transforms</span><span class="o">.</span><span class="n">ToTensor</span><span class="p">(),</span>
<span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">vision</span><span class="o">.</span><span class="n">transforms</span><span class="o">.</span><span class="n">Normalize</span><span class="p">(</span><span class="mf">0.13</span><span class="p">,</span> <span class="mf">0.31</span><span class="p">)])</span>
<span class="n">mnist_train</span> <span class="o">=</span> <span class="n">mnist_train</span><span class="o">.</span><span class="n">transform_first</span><span class="p">(</span><span class="n">transformer</span><span class="p">)</span>
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<p><code class="docutils literal notranslate"><span class="pre">FashionMNIST</span></code> is a subclass of <code class="docutils literal notranslate"><span class="pre">gluon.data.Dataset</span></code>, which defines how to get the <code class="docutils literal notranslate"><span class="pre">i</span></code>-th example. In order to use it in training, you need to get a (randomized) batch of examples. Do this by using <code class="docutils literal notranslate"><span class="pre">gluon.data.DataLoader</span></code>. The example here uses four works to process data in parallel, which is often necessary especially for complex data transforms.</p>
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<span></span><span class="n">batch_size</span> <span class="o">=</span> <span class="mi">256</span>
<span class="n">train_data</span> <span class="o">=</span> <span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">DataLoader</span><span class="p">(</span>
<span class="n">mnist_train</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">shuffle</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">num_workers</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
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<p>The returned <code class="docutils literal notranslate"><span class="pre">train_data</span></code> is an iterable object that yields batches of images and labels pairs.</p>
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<span></span><span class="k">for</span> <span class="n">data</span><span class="p">,</span> <span class="n">label</span> <span class="ow">in</span> <span class="n">train_data</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">label</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="k">break</span>
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</div>
</div>
<p>Finally, create a validation dataset and data loader.</p>
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<span></span><span class="n">mnist_valid</span> <span class="o">=</span> <span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">vision</span><span class="o">.</span><span class="n">FashionMNIST</span><span class="p">(</span><span class="n">train</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">valid_data</span> <span class="o">=</span> <span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">DataLoader</span><span class="p">(</span>
<span class="n">mnist_valid</span><span class="o">.</span><span class="n">transform_first</span><span class="p">(</span><span class="n">transformer</span><span class="p">),</span>
<span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span> <span class="n">num_workers</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="Define-the-model">
<h2>Define the model<a class="headerlink" href="#Define-the-model" title="Permalink to this headline"></a></h2>
<p>Implement the network called <a class="reference external" href="http://yann.lecun.com/exdb/lenet/">LeNet</a>. One difference here is that you change the weight initialization method to <code class="docutils literal notranslate"><span class="pre">Xavier</span></code>, which is a popular choice for deep convolutional neural networks.</p>
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<span></span><span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">()</span>
<span class="n">net</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Conv2D</span><span class="p">(</span><span class="n">channels</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">),</span>
<span class="n">nn</span><span class="o">.</span><span class="n">MaxPool2D</span><span class="p">(</span><span class="n">pool_size</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">strides</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
<span class="n">nn</span><span class="o">.</span><span class="n">Conv2D</span><span class="p">(</span><span class="n">channels</span><span class="o">=</span><span class="mi">16</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">),</span>
<span class="n">nn</span><span class="o">.</span><span class="n">MaxPool2D</span><span class="p">(</span><span class="n">pool_size</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">strides</span><span class="o">=</span><span class="mi">2</span><span class="p">),</span>
<span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">120</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s2">&quot;relu&quot;</span><span class="p">),</span>
<span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">84</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s2">&quot;relu&quot;</span><span class="p">),</span>
<span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">10</span><span class="p">))</span>
<span class="n">net</span><span class="o">.</span><span class="n">initialize</span><span class="p">(</span><span class="n">init</span><span class="o">=</span><span class="n">init</span><span class="o">.</span><span class="n">Xavier</span><span class="p">())</span>
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</div>
<p>In addition to the neural network, define the loss function and optimization method for training. Use standard softmax cross entropy loss for classification problems. It first performs softmax on the output to obtain the predicted probability, and then compares the label with the cross entropy.</p>
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<span></span><span class="n">softmax_cross_entropy</span> <span class="o">=</span> <span class="n">gluon</span><span class="o">.</span><span class="n">loss</span><span class="o">.</span><span class="n">SoftmaxCrossEntropyLoss</span><span class="p">()</span>
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<p>The optimization method you pick is the standard stochastic gradient descent with constant learning rate of 0.1.</p>
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<span></span><span class="n">trainer</span> <span class="o">=</span> <span class="n">gluon</span><span class="o">.</span><span class="n">Trainer</span><span class="p">(</span><span class="n">net</span><span class="o">.</span><span class="n">collect_params</span><span class="p">(),</span> <span class="s1">&#39;sgd&#39;</span><span class="p">,</span> <span class="p">{</span><span class="s1">&#39;learning_rate&#39;</span><span class="p">:</span> <span class="mf">0.1</span><span class="p">})</span>
</pre></div>
</div>
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<p>The <code class="docutils literal notranslate"><span class="pre">trainer</span></code> is created with all parameters (both weights and gradients) in <code class="docutils literal notranslate"><span class="pre">net</span></code>. Later on, you only need to call the <code class="docutils literal notranslate"><span class="pre">step</span></code> method to update its weights.</p>
</div>
<div class="section" id="Train-the-model">
<h2>Train the model<a class="headerlink" href="#Train-the-model" title="Permalink to this headline"></a></h2>
<p>Create an auxiliary function to calculate the model accuracy.</p>
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<span></span><span class="k">def</span> <span class="nf">acc</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">label</span><span class="p">):</span>
<span class="c1"># output: (batch, num_output) float32 ndarray</span>
<span class="c1"># label: (batch, ) int32 ndarray</span>
<span class="k">return</span> <span class="p">(</span><span class="n">output</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> <span class="o">==</span> <span class="n">label</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="s1">&#39;float32&#39;</span><span class="p">))</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
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</div>
<p>Implement the complete training loop.</p>
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<span></span><span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">):</span>
<span class="n">train_loss</span><span class="p">,</span> <span class="n">train_acc</span><span class="p">,</span> <span class="n">valid_acc</span> <span class="o">=</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="n">tic</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="k">for</span> <span class="n">data</span><span class="p">,</span> <span class="n">label</span> <span class="ow">in</span> <span class="n">train_data</span><span class="p">:</span>
<span class="c1"># forward + backward</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">output</span> <span class="o">=</span> <span class="n">net</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">softmax_cross_entropy</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">label</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="c1"># update parameters</span>
<span class="n">trainer</span><span class="o">.</span><span class="n">step</span><span class="p">(</span><span class="n">batch_size</span><span class="p">)</span>
<span class="c1"># calculate training metrics</span>
<span class="n">train_loss</span> <span class="o">+=</span> <span class="n">loss</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
<span class="n">train_acc</span> <span class="o">+=</span> <span class="n">acc</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">label</span><span class="p">)</span>
<span class="c1"># calculate validation accuracy</span>
<span class="k">for</span> <span class="n">data</span><span class="p">,</span> <span class="n">label</span> <span class="ow">in</span> <span class="n">valid_data</span><span class="p">:</span>
<span class="n">valid_acc</span> <span class="o">+=</span> <span class="n">acc</span><span class="p">(</span><span class="n">net</span><span class="p">(</span><span class="n">data</span><span class="p">),</span> <span class="n">label</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Epoch </span><span class="si">%d</span><span class="s2">: loss </span><span class="si">%.3f</span><span class="s2">, train acc </span><span class="si">%.3f</span><span class="s2">, test acc </span><span class="si">%.3f</span><span class="s2">, in </span><span class="si">%.1f</span><span class="s2"> sec&quot;</span> <span class="o">%</span> <span class="p">(</span>
<span class="n">epoch</span><span class="p">,</span> <span class="n">train_loss</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">train_data</span><span class="p">),</span> <span class="n">train_acc</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">train_data</span><span class="p">),</span>
<span class="n">valid_acc</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">valid_data</span><span class="p">),</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="o">-</span><span class="n">tic</span><span class="p">))</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="Save-the-model">
<h2>Save the model<a class="headerlink" href="#Save-the-model" title="Permalink to this headline"></a></h2>
<p>Finally, save the trained parameters onto disk, so that you can use them later.</p>
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<span></span><span class="n">net</span><span class="o">.</span><span class="n">save_parameters</span><span class="p">(</span><span class="s1">&#39;net.params&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="Next-Steps">
<h2>Next Steps<a class="headerlink" href="#Next-Steps" title="Permalink to this headline"></a></h2>
<p>After the model is trained and saved, learn how to use it to predict new examples: <a class="reference internal" href="5-predict.html"><span class="doc">Step 5: Predict with a pretrained model</span></a>.</p>
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<span class="caption-text">Table Of Contents</span>
</p>
<ul>
<li><a class="reference internal" href="#">Step 4: Train the neural network</a><ul>
<li><a class="reference internal" href="#Get-data">Get data</a></li>
<li><a class="reference internal" href="#Define-the-model">Define the model</a></li>
<li><a class="reference internal" href="#Train-the-model">Train the model</a></li>
<li><a class="reference internal" href="#Save-the-model">Save the model</a></li>
<li><a class="reference internal" href="#Next-Steps">Next Steps</a></li>
</ul>
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<div>Step 3: Automatic differentiation with autograd</div>
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<div>Step 5: Predict with a pretrained model</div>
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