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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"><a class="reference internal" href="../../../getting-started/index.html">Getting Started</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/crash-course/index.html">Crash Course</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/0-introduction.html">Introduction</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/1-nparray.html">Step 1: Manipulate data with NP on MXNet</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/2-create-nn.html">Step 2: Create a neural network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/3-autograd.html">Step 3: Automatic differentiation with autograd</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/4-components.html">Step 4: Necessary components that are not in the network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/5-datasets.html">Step 5: <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-l4"><a class="reference internal" href="../../../getting-started/crash-course/5-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-l4"><a class="reference internal" href="../../../getting-started/crash-course/5-datasets.html#Using-your-own-data-with-custom-Datasets">Using your own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/5-datasets.html#New-in-MXNet-2.0:-faster-C++-backend-dataloaders">New in MXNet 2.0: faster C++ backend dataloaders</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/6-train-nn.html">Step 6: Train a Neural Network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/7-use-gpus.html">Step 7: Load and Run a NN using GPU</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/gluon_migration_guide.html">Gluon2.0: Migration Guide</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/logistic_regression_explained.html">Logistic regression explained</a></li> |
| <li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li> |
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| <li class="toctree-l2 current"><a class="reference internal" href="../../index.html">Packages</a><ul class="current"> |
| <li class="toctree-l3"><a class="reference internal" href="../../autograd/index.html">Automatic Differentiation</a></li> |
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| <li class="toctree-l4 current"><a class="reference internal" href="index.html">Blocks</a><ul class="current"> |
| <li class="toctree-l5"><a class="reference internal" href="custom-layer.html">Custom Layers</a></li> |
| <li class="toctree-l5 current"><a class="current reference internal" href="#">Hybridize</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../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> |
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| <li class="toctree-l5"><a class="reference internal" href="../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="../image/info_gan.html">Image similarity search with InfoGAN</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../image/mnist.html">Handwritten Digit Recognition</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../loss/index.html">Losses</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../loss/custom-loss.html">Custom Loss Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../loss/loss.html">Loss functions</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../text/gnmt.html">Google Neural Machine Translation</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../training/learning_rates/index.html">Learning Rates</a><ul> |
| <li class="toctree-l6"><a class="reference internal" href="../training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l5"><a class="reference internal" href="../training/normalization/index.html">Normalization Blocks</a></li> |
| </ul> |
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| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../kvstore/index.html">KVStore</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../kvstore/kvstore.html">Distributed Key-Value Store</a></li> |
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| <li class="toctree-l3"><a class="reference internal" href="../../legacy/index.html">Legacy</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../legacy/ndarray/index.html">NDArray</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../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="../../legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../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="../../legacy/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../legacy/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li> |
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| <li class="toctree-l3"><a class="reference internal" href="../../np/index.html">What is NP on MXNet</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../np/cheat-sheet.html">The NP on MXNet cheat sheet</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../np/np-vs-numpy.html">Differences between NP on MXNet and NumPy</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../onnx/fine_tuning_gluon.html">Fine-tuning an ONNX model</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../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-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 internal" href="../../../../api/np/routines.io.html">Input and output</a><ul> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.ndarray.tolist.html">mxnet.np.ndarray.tolist</a></li> |
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| </ul> |
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| <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> |
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| <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.multi_dot.html">mxnet.np.linalg.multi_dot</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.matmul.html">mxnet.np.matmul</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.matrix_power.html">mxnet.np.linalg.matrix_power</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.kron.html">mxnet.np.kron</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.cholesky.html">mxnet.np.linalg.cholesky</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.qr.html">mxnet.np.linalg.qr</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.eig.html">mxnet.np.linalg.eig</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.eigh.html">mxnet.np.linalg.eigh</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.eigvals.html">mxnet.np.linalg.eigvals</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.eigvalsh.html">mxnet.np.linalg.eigvalsh</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> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.cond.html">mxnet.np.linalg.cond</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.det.html">mxnet.np.linalg.det</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.matrix_rank.html">mxnet.np.linalg.matrix_rank</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.slogdet.html">mxnet.np.linalg.slogdet</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.solve.html">mxnet.np.linalg.solve</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.tensorsolve.html">mxnet.np.linalg.tensorsolve</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.lstsq.html">mxnet.np.linalg.lstsq</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.inv.html">mxnet.np.linalg.inv</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.pinv.html">mxnet.np.linalg.pinv</a></li> |
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| <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> |
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| <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.unwrap.html">mxnet.np.unwrap</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.cosh.html">mxnet.np.cosh</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nansum.html">mxnet.np.nansum</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nancumprod.html">mxnet.np.nancumprod</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nancumsum.html">mxnet.np.nancumsum</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.diff.html">mxnet.np.diff</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.ediff1d.html">mxnet.np.ediff1d</a></li> |
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| <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> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.logaddexp.html">mxnet.np.logaddexp</a></li> |
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| <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> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.true_divide.html">mxnet.np.true_divide</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.float_power.html">mxnet.np.float_power</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.modf.html">mxnet.np.modf</a></li> |
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| <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> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.fabs.html">mxnet.np.fabs</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.heaviside.html">mxnet.np.heaviside</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.fmin.html">mxnet.np.fmin</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nan_to_num.html">mxnet.np.nan_to_num</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.interp.html">mxnet.np.interp</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../api/np/random/index.html">np.random</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.choice.html">mxnet.np.random.choice</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.shuffle.html">mxnet.np.random.shuffle</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.gamma.html">mxnet.np.random.gamma</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.gumbel.html">mxnet.np.random.gumbel</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.logistic.html">mxnet.np.random.logistic</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.lognormal.html">mxnet.np.random.lognormal</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.multinomial.html">mxnet.np.random.multinomial</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.multivariate_normal.html">mxnet.np.random.multivariate_normal</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.pareto.html">mxnet.np.random.pareto</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.power.html">mxnet.np.random.power</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.rayleigh.html">mxnet.np.random.rayleigh</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.weibull.html">mxnet.np.random.weibull</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../api/np/routines.sort.html">Sorting, searching, and counting</a><ul> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.lexsort.html">mxnet.np.lexsort</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.partition.html">mxnet.np.partition</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.argpartition.html">mxnet.np.argpartition</a></li> |
| <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> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanargmax.html">mxnet.np.nanargmax</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanargmin.html">mxnet.np.nanargmin</a></li> |
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| <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> |
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| <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> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.median.html">mxnet.np.median</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.average.html">mxnet.np.average</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanmedian.html">mxnet.np.nanmedian</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanstd.html">mxnet.np.nanstd</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.corrcoef.html">mxnet.np.corrcoef</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.correlate.html">mxnet.np.correlate</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.cov.html">mxnet.np.cov</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.histogram.html">mxnet.np.histogram</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.bincount.html">mxnet.np.bincount</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.histogram_bin_edges.html">mxnet.np.histogram_bin_edges</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.digitize.html">mxnet.np.digitize</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> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../../api/npx/generated/mxnet.npx.cpu.html">mxnet.npx.cpu</a></li> |
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| <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> |
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| <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> |
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| <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> |
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| <span class="mdl-layout-title toc">Table Of Contents</span> |
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| <li class="toctree-l1 current"><a class="reference internal" href="../../../index.html">Python Tutorials</a><ul class="current"> |
| <li class="toctree-l2"><a class="reference internal" href="../../../getting-started/index.html">Getting Started</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/crash-course/index.html">Crash Course</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/0-introduction.html">Introduction</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/1-nparray.html">Step 1: Manipulate data with NP on MXNet</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/2-create-nn.html">Step 2: Create a neural network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/3-autograd.html">Step 3: Automatic differentiation with autograd</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/4-components.html">Step 4: Necessary components that are not in the network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/5-datasets.html">Step 5: <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-l4"><a class="reference internal" href="../../../getting-started/crash-course/5-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-l4"><a class="reference internal" href="../../../getting-started/crash-course/5-datasets.html#Using-your-own-data-with-custom-Datasets">Using your own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/5-datasets.html#New-in-MXNet-2.0:-faster-C++-backend-dataloaders">New in MXNet 2.0: faster C++ backend dataloaders</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/6-train-nn.html">Step 6: Train a Neural Network</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/7-use-gpus.html">Step 7: Load and Run a NN using GPU</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/to-mxnet/index.html">Moving to MXNet from Other Frameworks</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../getting-started/to-mxnet/pytorch.html">PyTorch vs Apache MXNet</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/gluon_from_experiment_to_deployment.html">Gluon: from experiment to deployment</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/gluon_migration_guide.html">Gluon2.0: Migration Guide</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../getting-started/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 current"><a class="reference internal" href="../../index.html">Packages</a><ul class="current"> |
| <li class="toctree-l3"><a class="reference internal" href="../../autograd/index.html">Automatic Differentiation</a></li> |
| <li class="toctree-l3 current"><a class="reference internal" href="../index.html">Gluon</a><ul class="current"> |
| <li class="toctree-l4 current"><a class="reference internal" href="index.html">Blocks</a><ul class="current"> |
| <li class="toctree-l5"><a class="reference internal" href="custom-layer.html">Custom Layers</a></li> |
| <li class="toctree-l5 current"><a class="current reference internal" href="#">Hybridize</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="init.html">Initialization</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="naming.html">Parameter and Block Naming</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="nn.html">Layers and Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="parameters.html">Parameter Management</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="save_load_params.html">Saving and Loading Gluon Models</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="activations/activations.html">Activation Blocks</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../data/index.html">Data Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../data/data_augmentation.html">Image Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../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="../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="../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="../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-l4"><a class="reference internal" href="../image/index.html">Image Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../image/info_gan.html">Image similarity search with InfoGAN</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../image/mnist.html">Handwritten Digit Recognition</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l4"><a class="reference internal" href="../loss/index.html">Losses</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../loss/custom-loss.html">Custom Loss Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../loss/loss.html">Loss functions</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../text/index.html">Text Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../text/gnmt.html">Google Neural Machine Translation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../text/transformer.html">Machine Translation with Transformer</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../training/index.html">Training</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../training/trainer.html">Trainer</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../training/learning_rates/index.html">Learning Rates</a><ul> |
| <li class="toctree-l6"><a class="reference internal" href="../training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l5"><a class="reference internal" href="../training/normalization/index.html">Normalization Blocks</a></li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../kvstore/index.html">KVStore</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../kvstore/kvstore.html">Distributed Key-Value Store</a></li> |
| </ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../../legacy/index.html">Legacy</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../legacy/ndarray/index.html">NDArray</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../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="../../legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../legacy/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../legacy/ndarray/sparse/index.html">Tutorials</a><ul> |
| <li class="toctree-l6"><a class="reference internal" href="../../legacy/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../legacy/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li> |
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| </li> |
| </ul> |
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| </ul> |
| </li> |
| <li class="toctree-l3"><a class="reference internal" href="../../np/index.html">What is NP on MXNet</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../np/cheat-sheet.html">The NP on MXNet cheat sheet</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../np/np-vs-numpy.html">Differences between NP on MXNet and NumPy</a></li> |
| </ul> |
| </li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../api/np/routines.io.html">Input and output</a><ul> |
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| <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> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.svd.html">mxnet.np.linalg.svd</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.norm.html">mxnet.np.linalg.norm</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.cond.html">mxnet.np.linalg.cond</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../api/np/routines.math.html">Mathematical functions</a><ul> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.cos.html">mxnet.np.cos</a></li> |
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| <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.round_.html">mxnet.np.round_</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.sum.html">mxnet.np.sum</a></li> |
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| <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.nanprod.html">mxnet.np.nanprod</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nansum.html">mxnet.np.nansum</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.cumprod.html">mxnet.np.cumprod</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nancumprod.html">mxnet.np.nancumprod</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nancumsum.html">mxnet.np.nancumsum</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.diff.html">mxnet.np.diff</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.ediff1d.html">mxnet.np.ediff1d</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.cross.html">mxnet.np.cross</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.trapz.html">mxnet.np.trapz</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.logaddexp.html">mxnet.np.logaddexp</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.i0.html">mxnet.np.i0</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.signbit.html">mxnet.np.signbit</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.copysign.html">mxnet.np.copysign</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.frexp.html">mxnet.np.frexp</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.spacing.html">mxnet.np.spacing</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.gcd.html">mxnet.np.gcd</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-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.positive.html">mxnet.np.positive</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.float_power.html">mxnet.np.float_power</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.fmod.html">mxnet.np.fmod</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.modf.html">mxnet.np.modf</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.divmod.html">mxnet.np.divmod</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.floor_divide.html">mxnet.np.floor_divide</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> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.fabs.html">mxnet.np.fabs</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.heaviside.html">mxnet.np.heaviside</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.fmax.html">mxnet.np.fmax</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.fmin.html">mxnet.np.fmin</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nan_to_num.html">mxnet.np.nan_to_num</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.interp.html">mxnet.np.interp</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../../api/np/random/index.html">np.random</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.choice.html">mxnet.np.random.choice</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.shuffle.html">mxnet.np.random.shuffle</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.normal.html">mxnet.np.random.normal</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.uniform.html">mxnet.np.random.uniform</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.rand.html">mxnet.np.random.rand</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.randint.html">mxnet.np.random.randint</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.chisquare.html">mxnet.np.random.chisquare</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.exponential.html">mxnet.np.random.exponential</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.f.html">mxnet.np.random.f</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.gamma.html">mxnet.np.random.gamma</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.gumbel.html">mxnet.np.random.gumbel</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.laplace.html">mxnet.np.random.laplace</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.logistic.html">mxnet.np.random.logistic</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.lognormal.html">mxnet.np.random.lognormal</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.multinomial.html">mxnet.np.random.multinomial</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.multivariate_normal.html">mxnet.np.random.multivariate_normal</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.pareto.html">mxnet.np.random.pareto</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.power.html">mxnet.np.random.power</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.rayleigh.html">mxnet.np.random.rayleigh</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.weibull.html">mxnet.np.random.weibull</a></li> |
| </ul> |
| </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.ndarray.sort.html">mxnet.np.ndarray.sort</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.lexsort.html">mxnet.np.lexsort</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.argsort.html">mxnet.np.argsort</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.flatnonzero.html">mxnet.np.flatnonzero</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.where.html">mxnet.np.where</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.extract.html">mxnet.np.extract</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.count_nonzero.html">mxnet.np.count_nonzero</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> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanmax.html">mxnet.np.nanmax</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.ptp.html">mxnet.np.ptp</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.percentile.html">mxnet.np.percentile</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanpercentile.html">mxnet.np.nanpercentile</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.quantile.html">mxnet.np.quantile</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanquantile.html">mxnet.np.nanquantile</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.median.html">mxnet.np.median</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.average.html">mxnet.np.average</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanmedian.html">mxnet.np.nanmedian</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanstd.html">mxnet.np.nanstd</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.nanvar.html">mxnet.np.nanvar</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.corrcoef.html">mxnet.np.corrcoef</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.correlate.html">mxnet.np.correlate</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.cov.html">mxnet.np.cov</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.histogram.html">mxnet.np.histogram</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.histogram2d.html">mxnet.np.histogram2d</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.histogramdd.html">mxnet.np.histogramdd</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.bincount.html">mxnet.np.bincount</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.histogram_bin_edges.html">mxnet.np.histogram_bin_edges</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.digitize.html">mxnet.np.digitize</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> |
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| <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_device.html">mxnet.npx.current_device</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> |
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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="Hybridize"> |
| <h1>Hybridize<a class="headerlink" href="#Hybridize" title="Permalink to this headline">¶</a></h1> |
| <!-- adapted from diveintodeeplearning --><div class="section" id="A-Hybrid-of-Imperative-and-Symbolic-Programming"> |
| <h2>A Hybrid of Imperative and Symbolic Programming<a class="headerlink" href="#A-Hybrid-of-Imperative-and-Symbolic-Programming" title="Permalink to this headline">¶</a></h2> |
| <p>Imperative programming makes use of programming statements to change a program’s state. Consider the following example of simple imperative programming code.</p> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[1]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span> |
| <span class="k">return</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span> |
| |
| <span class="k">def</span> <span class="nf">fancy_func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span> |
| <span class="n">e</span> <span class="o">=</span> <span class="n">add</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> |
| <span class="n">f</span> <span class="o">=</span> <span class="n">add</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span> |
| <span class="n">g</span> <span class="o">=</span> <span class="n">add</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span> |
| <span class="k">return</span> <span class="n">g</span> |
| |
| <span class="n">fancy_func</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[1]: |
| </pre></div> |
| </div> |
| <div class="output_area highlight-none notranslate"><div class="highlight"><pre> |
| <span></span>10 |
| </pre></div> |
| </div> |
| </div> |
| <p>As expected, Python will perform an addition when running the statement <code class="docutils literal notranslate"><span class="pre">e</span> <span class="pre">=</span> <span class="pre">add(a,</span> <span class="pre">b)</span></code>, and will store the result as the variable <code class="docutils literal notranslate"><span class="pre">e</span></code>, thereby changing the program’s state. The next two statements <code class="docutils literal notranslate"><span class="pre">f</span> <span class="pre">=</span> <span class="pre">add(c,</span> <span class="pre">d)</span></code> and <code class="docutils literal notranslate"><span class="pre">g</span> <span class="pre">=</span> <span class="pre">add(e,</span> <span class="pre">f)</span></code> will similarly perform additions and store the results as variables.</p> |
| <p>Although imperative programming is convenient, it may be inefficient. On the one hand, even if the <code class="docutils literal notranslate"><span class="pre">add</span></code> function is repeatedly called throughout the <code class="docutils literal notranslate"><span class="pre">fancy_func</span></code> function, Python will execute the three function calling statements individually, one after the other. On the other hand, we need to save the variable values of <code class="docutils literal notranslate"><span class="pre">e</span></code> and <code class="docutils literal notranslate"><span class="pre">f</span></code> until all the statements in <code class="docutils literal notranslate"><span class="pre">fancy_func</span></code> have been executed. This is because we do not know whether the variables <code class="docutils literal notranslate"><span class="pre">e</span></code> and <code class="docutils literal notranslate"><span class="pre">f</span></code> will be used by other |
| parts of the program after the statements <code class="docutils literal notranslate"><span class="pre">e</span> <span class="pre">=</span> <span class="pre">add(a,</span> <span class="pre">b)</span></code> and <code class="docutils literal notranslate"><span class="pre">f</span> <span class="pre">=</span> <span class="pre">add(c,</span> <span class="pre">d)</span></code> have been executed.</p> |
| <p>Contrary to imperative programming, symbolic programming is usually performed after the computational process has been fully defined. Symbolic programming is used by multiple deep learning frameworks, including Theano and TensorFlow. The process of symbolic programming generally requires the following three steps:</p> |
| <ol class="arabic simple"> |
| <li><p>Define the computation process.</p></li> |
| <li><p>Compile the computation process into an executable program.</p></li> |
| <li><p>Provide the required inputs and call on the compiled program for execution.</p></li> |
| </ol> |
| <p>In the example below, we utilize symbolic programming to re-implement the imperative programming code provided at the beginning of this section.</p> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[2]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="k">def</span> <span class="nf">add_str</span><span class="p">():</span> |
| <span class="k">return</span> <span class="s1">'''</span> |
| <span class="s1">def add(a, b):</span> |
| <span class="s1"> return a + b</span> |
| <span class="s1">'''</span> |
| |
| <span class="k">def</span> <span class="nf">fancy_func_str</span><span class="p">():</span> |
| <span class="k">return</span> <span class="s1">'''</span> |
| <span class="s1">def fancy_func(a, b, c, d):</span> |
| <span class="s1"> e = add(a, b)</span> |
| <span class="s1"> f = add(c, d)</span> |
| <span class="s1"> g = add(e, f)</span> |
| <span class="s1"> return g</span> |
| <span class="s1">'''</span> |
| |
| <span class="k">def</span> <span class="nf">evoke_str</span><span class="p">():</span> |
| <span class="k">return</span> <span class="n">add_str</span><span class="p">()</span> <span class="o">+</span> <span class="n">fancy_func_str</span><span class="p">()</span> <span class="o">+</span> <span class="s1">'''</span> |
| <span class="s1">print(fancy_func(1, 2, 3, 4))</span> |
| <span class="s1">'''</span> |
| |
| <span class="n">prog</span> <span class="o">=</span> <span class="n">evoke_str</span><span class="p">()</span> |
| <span class="nb">print</span><span class="p">(</span><span class="n">prog</span><span class="p">)</span> |
| <span class="n">y</span> <span class="o">=</span> <span class="nb">compile</span><span class="p">(</span><span class="n">prog</span><span class="p">,</span> <span class="s1">''</span><span class="p">,</span> <span class="s1">'exec'</span><span class="p">)</span> |
| <span class="n">exec</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt empty docutils container"> |
| </div> |
| <div class="output_area docutils container"> |
| <div class="highlight"><pre> |
| |
| def add(a, b): |
| return a + b |
| |
| def fancy_func(a, b, c, d): |
| e = add(a, b) |
| f = add(c, d) |
| g = add(e, f) |
| return g |
| |
| print(fancy_func(1, 2, 3, 4)) |
| |
| 10 |
| </pre></div></div> |
| </div> |
| <p>The three functions defined above will only return the results of the computation process as a string. Finally, the complete computation process is compiled and run using the <code class="docutils literal notranslate"><span class="pre">compile</span></code> function. This leaves more room to optimize computation, since the system is able to view the entire program during its compilation. For example, during compilation, the program can be rewritten as <code class="docutils literal notranslate"><span class="pre">print((1</span> <span class="pre">+</span> <span class="pre">2)</span> <span class="pre">+</span> <span class="pre">(3</span> <span class="pre">+</span> <span class="pre">4))</span></code> or even directly rewritten as <code class="docutils literal notranslate"><span class="pre">print(10)</span></code>. Apart from reducing the amount of |
| function calls, this process also saves memory.</p> |
| <p>A comparison of these two programming methods shows that</p> |
| <ul class="simple"> |
| <li><p>imperative programming is easier. When imperative programming is used in Python, the majority of the code is straightforward and easy to write. At the same time, it is easier to debug imperative programming code. This is because it is easier to obtain and print all relevant intermediate variable values, or make use of Python’s built-in debugging tools.</p></li> |
| <li><p>Symbolic programming is more efficient and easier to port. Symbolic programming makes it easier to better optimize the system during compilation, while also having the ability to port the program into a format independent of Python. This allows the program to be run in a non-Python environment, thus avoiding any potential performance issues related to the Python interpreter.</p></li> |
| </ul> |
| </div> |
| <div class="section" id="Hybrid-programming-provides-the-best-of-both-worlds."> |
| <h2>Hybrid programming provides the best of both worlds.<a class="headerlink" href="#Hybrid-programming-provides-the-best-of-both-worlds." title="Permalink to this headline">¶</a></h2> |
| <p>Most deep learning frameworks choose either imperative or symbolic programming. For example, both Theano and TensorFlow (inspired by the latter) make use of symbolic programming, while Chainer and its predecessor PyTorch utilize imperative programming. When designing Gluon, developers considered whether it was possible to harness the benefits of both imperative and symbolic programming. The developers believed that users should be able to develop and debug using pure imperative programming, |
| while having the ability to convert most programs into symbolic programming to be run when product-level computing performance and deployment are required This was achieved by Gluon through the introduction of hybrid programming.</p> |
| <p>In hybrid programming, we can build models using either the HybridBlock or the HybridSequential classes. By default, they are executed in the same way Block or Sequential classes are executed in imperative programming. When the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function is called, Gluon will convert the program’s execution into the style used in symbolic programming. In fact, most models can make use of hybrid programming’s execution style.</p> |
| <p>Through the use of experiments, this section will demonstrate the benefits of hybrid programming.</p> |
| </div> |
| <div class="section" id="Constructing-Models-Using-the-HybridSequential-Class"> |
| <h2>Constructing Models Using the HybridSequential Class<a class="headerlink" href="#Constructing-Models-Using-the-HybridSequential-Class" title="Permalink to this headline">¶</a></h2> |
| <p>Previously, we learned how to use the Sequential class to concatenate multiple layers. Next, we will replace the Sequential class with the HybridSequential class in order to make use of hybrid programming.</p> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[3]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></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">sym</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">import</span> <span class="nn">time</span> |
| |
| <span class="k">def</span> <span class="nf">get_net</span><span class="p">():</span> |
| <span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">HybridSequential</span><span class="p">()</span> <span class="c1"># Here we use the class HybridSequential.</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">Dense</span><span class="p">(</span><span class="mi">256</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">'relu'</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">128</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">'relu'</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">2</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="k">return</span> <span class="n">net</span> |
| |
| <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">512</span><span class="p">))</span> |
| <span class="n">net</span> <span class="o">=</span> <span class="n">get_net</span><span class="p">()</span> |
| <span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput docutils container"> |
| <div class="prompt empty docutils container"> |
| </div> |
| <div class="output_area stderr docutils container"> |
| <div class="highlight"><pre> |
| [04:45:52] /work/mxnet/src/storage/storage.cc:202: Using Pooled (Naive) StorageManager for CPU |
| </pre></div></div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[3]: |
| </pre></div> |
| </div> |
| <div class="output_area highlight-none notranslate"><div class="highlight"><pre> |
| <span></span>array([[-0.00306124, -0.19131702]]) |
| </pre></div> |
| </div> |
| </div> |
| <p>By calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function, we are able to compile and optimize the computation of the concatenation layer in the HybridSequential instance. The model’s computation result remains unchanged.</p> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[4]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="n">net</span><span class="o">.</span><span class="n">hybridize</span><span class="p">()</span> |
| <span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[4]: |
| </pre></div> |
| </div> |
| <div class="output_area highlight-none notranslate"><div class="highlight"><pre> |
| <span></span>array([[-0.00306124, -0.19131702]]) |
| </pre></div> |
| </div> |
| </div> |
| <p>It should be noted that only the layers inheriting the HybridBlock class will be optimized during computation. For example, the HybridSequential and <code class="docutils literal notranslate"><span class="pre">Dense</span></code> classes provided by Gluon are all subclasses of HybridBlock class, meaning they will both be optimized during computation. A layer will not be optimized if it inherits from the Block class rather than the HybridBlock class.</p> |
| <div class="section" id="Computing-Performance"> |
| <h3>Computing Performance<a class="headerlink" href="#Computing-Performance" title="Permalink to this headline">¶</a></h3> |
| <p>To demonstrate the performance improvement gained by the use of symbolic programming, we will compare the computation time before and after calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function. Here we time 1000 <code class="docutils literal notranslate"><span class="pre">net</span></code> model computations. The model computations are based on imperative and symbolic programming, respectively, before and after <code class="docutils literal notranslate"><span class="pre">net</span></code> has called the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function.</p> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[5]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="k">def</span> <span class="nf">benchmark</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
| <span class="n">start</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">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000</span><span class="p">):</span> |
| <span class="n">_</span> <span class="o">=</span> <span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
| <span class="n">npx</span><span class="o">.</span><span class="n">waitall</span><span class="p">()</span> <span class="c1"># To facilitate timing, we wait for all computations to be completed.</span> |
| <span class="k">return</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">start</span> |
| |
| <span class="n">net</span> <span class="o">=</span> <span class="n">get_net</span><span class="p">()</span> |
| <span class="nb">print</span><span class="p">(</span><span class="s1">'before hybridizing: </span><span class="si">%.4f</span><span class="s1"> sec'</span> <span class="o">%</span> <span class="p">(</span><span class="n">benchmark</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">x</span><span class="p">)))</span> |
| <span class="n">net</span><span class="o">.</span><span class="n">hybridize</span><span class="p">()</span> |
| <span class="nb">print</span><span class="p">(</span><span class="s1">'after hybridizing: </span><span class="si">%.4f</span><span class="s1"> sec'</span> <span class="o">%</span> <span class="p">(</span><span class="n">benchmark</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">x</span><span class="p">)))</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt empty docutils container"> |
| </div> |
| <div class="output_area docutils container"> |
| <div class="highlight"><pre> |
| before hybridizing: 0.4131 sec |
| after hybridizing: 0.2037 sec |
| </pre></div></div> |
| </div> |
| <p>As is observed in the above results, after a HybridSequential instance calls the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function, computing performance is improved through the use of symbolic programming.</p> |
| </div> |
| <div class="section" id="Achieving-Symbolic-Programming"> |
| <h3>Achieving Symbolic Programming<a class="headerlink" href="#Achieving-Symbolic-Programming" title="Permalink to this headline">¶</a></h3> |
| <p>We can save the symbolic program and model parameters to the hard disk through the use of the <code class="docutils literal notranslate"><span class="pre">export</span></code> function after the <code class="docutils literal notranslate"><span class="pre">net</span></code> model has finished computing the output based on the input, such as in the case of <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> in the <code class="docutils literal notranslate"><span class="pre">benchmark</span></code> function.</p> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[6]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="n">net</span><span class="o">.</span><span class="n">export</span><span class="p">(</span><span class="s1">'my_mlp'</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[6]: |
| </pre></div> |
| </div> |
| <div class="output_area highlight-none notranslate"><div class="highlight"><pre> |
| <span></span>('my_mlp-symbol.json', 'my_mlp-0000.params') |
| </pre></div> |
| </div> |
| </div> |
| <p>The .json and .params files generated during this process are a symbolic program and a model parameter, respectively. They can be read by other front-end languages supported by Python or MXNet, such as C++, R, Scala, and Perl. This allows us to deploy trained models to other devices and easily use other front-end programming languages. At the same time, because symbolic programming was used during deployment, the computing performance is often superior to that based on imperative programming.</p> |
| <p>In MXNet, a symbolic program refers to a program that makes use of the Symbol type. We know that, when the NDArray input <code class="docutils literal notranslate"><span class="pre">x</span></code> is provided to <code class="docutils literal notranslate"><span class="pre">net</span></code>, <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> will directly calculate the model output and return a result based on <code class="docutils literal notranslate"><span class="pre">x</span></code>. For models that have called the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function, we can also provide a Symbol-type input variable, and <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> will return Symbol type results.</p> |
| <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">sym</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="s1">'data'</span><span class="p">)</span> |
| <span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| </div> |
| <div class="section" id="Constructing-Models-Using-the-HybridBlock-Class"> |
| <h2>Constructing Models Using the HybridBlock Class<a class="headerlink" href="#Constructing-Models-Using-the-HybridBlock-Class" title="Permalink to this headline">¶</a></h2> |
| <p>Similar to the correlation between the Sequential Block classes, the HybridSequential class is a HybridBlock subclass.</p> |
| <p>Earlier, we demonstrated that, after calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function, the model is able to achieve superior computing performance and portability. In addition, model flexibility can be affected after calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function. We will demonstrate this by constructing a model using the HybridBlock class.</p> |
| <div class="nbinput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[7]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="k">class</span> <span class="nc">HybridNet</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">HybridBlock</span><span class="p">):</span> |
| <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span> |
| <span class="nb">super</span><span class="p">(</span><span class="n">HybridNet</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> |
| <span class="bp">self</span><span class="o">.</span><span class="n">hidden</span> <span class="o">=</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="bp">self</span><span class="o">.</span><span class="n">output</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> |
| |
| <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
| <span class="nb">print</span><span class="p">(</span><span class="s1">'x: '</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> |
| <span class="n">x</span> <span class="o">=</span> <span class="n">npx</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">hidden</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> |
| <span class="nb">print</span><span class="p">(</span><span class="s1">'hidden: '</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> |
| <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">output</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[8]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="n">net</span> <span class="o">=</span> <span class="n">HybridNet</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">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span> |
| <span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput docutils container"> |
| <div class="prompt empty docutils container"> |
| </div> |
| <div class="output_area docutils container"> |
| <div class="highlight"><pre> |
| x: [[ 2.145466 0.64158314 -0.00491827 0.3836984 ]] |
| hidden: [[0.15626392 0. 0. 0.10257901 0. 0. |
| 0. 0. 0.14553794 0.03259005]] |
| </pre></div></div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[8]: |
| </pre></div> |
| </div> |
| <div class="output_area highlight-none notranslate"><div class="highlight"><pre> |
| <span></span>array([[-0.00194377, 0.00215183]]) |
| </pre></div> |
| </div> |
| </div> |
| <p>Repeating the forward computation will achieve the same results.</p> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[9]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput docutils container"> |
| <div class="prompt empty docutils container"> |
| </div> |
| <div class="output_area docutils container"> |
| <div class="highlight"><pre> |
| x: [[ 2.145466 0.64158314 -0.00491827 0.3836984 ]] |
| hidden: [[0.15626392 0. 0. 0.10257901 0. 0. |
| 0. 0. 0.14553794 0.03259005]] |
| </pre></div></div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[9]: |
| </pre></div> |
| </div> |
| <div class="output_area highlight-none notranslate"><div class="highlight"><pre> |
| <span></span>array([[-0.00194377, 0.00215183]]) |
| </pre></div> |
| </div> |
| </div> |
| <p>Next, we will see what happens after we call the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function.</p> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[10]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="n">net</span><span class="o">.</span><span class="n">hybridize</span><span class="p">()</span> |
| <span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput docutils container"> |
| <div class="prompt empty docutils container"> |
| </div> |
| <div class="output_area docutils container"> |
| <div class="highlight"><pre> |
| x: [[ 2.145466 0.64158314 -0.00491827 0.3836984 ]] |
| hidden: [[0.15626392 0. 0. 0.10257901 0. 0. |
| 0. 0. 0.14553794 0.03259005]] |
| </pre></div></div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[10]: |
| </pre></div> |
| </div> |
| <div class="output_area highlight-none notranslate"><div class="highlight"><pre> |
| <span></span>array([[-0.00194377, 0.00215183]]) |
| </pre></div> |
| </div> |
| </div> |
| <p>Now, we repeat the forward computation.</p> |
| <div class="nbinput docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[11]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
| <div class="nboutput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[11]: |
| </pre></div> |
| </div> |
| <div class="output_area highlight-none notranslate"><div class="highlight"><pre> |
| <span></span>array([[-0.00194377, 0.00215183]]) |
| </pre></div> |
| </div> |
| </div> |
| <p>We can see that the three lines of print statements defined in the <code class="docutils literal notranslate"><span class="pre">forward</span></code> function will not print anything. This is because a symbolic computing graph has been recorded since the last time <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> was run by calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function. Afterwards, when we run <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> again, MXNet will no longer need to access Python code, but can directly perform symbolic programming at the C++ backend. This is another reason why model computing performance will be improve after the |
| <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function is called. However, there is always the potential that any programs we write will suffer a loss in flexibility. If we want to use the three lines of print statements to debug the code in the above example, they will be skipped over and we would not be able to print when the symbolic program is executed. Additionally, in the case of a few functions not supported by Symbol (like <code class="docutils literal notranslate"><span class="pre">asnumpy</span></code>), and operations in-place like <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">+=</span> <span class="pre">b</span></code> and <code class="docutils literal notranslate"><span class="pre">a[:]</span> <span class="pre">=</span> <span class="pre">a</span> <span class="pre">+</span> <span class="pre">b</span></code> (must be rewritten as |
| <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">=</span> <span class="pre">a</span> <span class="pre">+</span> <span class="pre">b</span></code>). Therefore, we will not be able to use the <code class="docutils literal notranslate"><span class="pre">forward</span></code> function or perform forward computation after the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function has been called.</p> |
| </div> |
| <div class="section" id="Disabling-Hybridization"> |
| <h2>Disabling Hybridization<a class="headerlink" href="#Disabling-Hybridization" title="Permalink to this headline">¶</a></h2> |
| <p>If we want to disable the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function, we can do that by using the following code:</p> |
| <div class="nbinput nblast docutils container"> |
| <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[12]: |
| </pre></div> |
| </div> |
| <div class="input_area highlight-python notranslate"><div class="highlight"><pre> |
| <span></span><span class="n">net</span><span class="o">.</span><span class="n">hybridize</span><span class="p">(</span><span class="n">active</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| </div> |
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| </p> |
| <ul> |
| <li><a class="reference internal" href="#">Hybridize</a><ul> |
| <li><a class="reference internal" href="#A-Hybrid-of-Imperative-and-Symbolic-Programming">A Hybrid of Imperative and Symbolic Programming</a></li> |
| <li><a class="reference internal" href="#Hybrid-programming-provides-the-best-of-both-worlds.">Hybrid programming provides the best of both worlds.</a></li> |
| <li><a class="reference internal" href="#Constructing-Models-Using-the-HybridSequential-Class">Constructing Models Using the HybridSequential Class</a><ul> |
| <li><a class="reference internal" href="#Computing-Performance">Computing Performance</a></li> |
| <li><a class="reference internal" href="#Achieving-Symbolic-Programming">Achieving Symbolic Programming</a></li> |
| </ul> |
| </li> |
| <li><a class="reference internal" href="#Constructing-Models-Using-the-HybridBlock-Class">Constructing Models Using the HybridBlock Class</a></li> |
| <li><a class="reference internal" href="#Disabling-Hybridization">Disabling Hybridization</a></li> |
| </ul> |
| </li> |
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