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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"> |
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| <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> |
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| <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> |
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| <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-l5"><a class="reference internal" href="../../../packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/text/transformer.html">Machine Translation with Transformer</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../packages/gluon/training/index.html">Training</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/training/trainer.html">Trainer</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul> |
| <li class="toctree-l6"><a class="reference internal" href="../../../packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/training/normalization/index.html">Normalization Blocks</a></li> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../packages/kvstore/index.html">KVStore</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../packages/legacy/index.html">Legacy</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../packages/legacy/ndarray/index.html">NDArray</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/legacy/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/legacy/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li> |
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| <li class="toctree-l6"><a class="reference internal" href="../../../packages/legacy/ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../packages/legacy/ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../packages/np/index.html">What is NP on MXNet</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../packages/np/cheat-sheet.html">The NP on MXNet cheat sheet</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../packages/np/np-vs-numpy.html">Differences between NP on MXNet and NumPy</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../packages/onnx/fine_tuning_gluon.html">Fine-tuning an ONNX model</a></li> |
| <li class="toctree-l4"><a class="reference internal" href="../../../packages/onnx/inference_on_onnx_model.html">Running inference on MXNet/Gluon from an ONNX model</a></li> |
| <li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/deploy/export/onnx.html">Export ONNX Models</a></li> |
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| <li class="toctree-l4"><a class="reference 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.matrix_power.html">mxnet.np.linalg.matrix_power</a></li> |
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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.eig.html">mxnet.np.linalg.eig</a></li> |
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| <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> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.linalg.solve.html">mxnet.np.linalg.solve</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.arcsin.html">mxnet.np.arcsin</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> |
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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.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.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> |
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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.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> |
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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> |
| <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> |
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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> |
| <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> |
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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> |
| <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> |
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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.nanargmax.html">mxnet.np.nanargmax</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.percentile.html">mxnet.np.percentile</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> |
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| <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.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.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"> |
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| <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"><a class="reference internal" href="../../../packages/index.html">Packages</a><ul> |
| <li class="toctree-l3"><a class="reference internal" href="../../../packages/autograd/index.html">Automatic Differentiation</a></li> |
| <li class="toctree-l3"><a class="reference internal" href="../../../packages/gluon/index.html">Gluon</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../packages/gluon/blocks/index.html">Blocks</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/blocks/custom-layer.html">Custom Layers</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/blocks/hybridize.html">Hybridize</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/blocks/init.html">Initialization</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/blocks/naming.html">Parameter and Block Naming</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/blocks/nn.html">Layers and Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/blocks/parameters.html">Parameter Management</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/blocks/save_load_params.html">Saving and Loading Gluon Models</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/blocks/activations/activations.html">Activation Blocks</a></li> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../packages/gluon/data/index.html">Data Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/data/data_augmentation.html">Image Augmentation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../packages/gluon/image/index.html">Image Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/image/info_gan.html">Image similarity search with InfoGAN</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/image/mnist.html">Handwritten Digit Recognition</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../packages/gluon/loss/index.html">Losses</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/loss/custom-loss.html">Custom Loss Blocks</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/loss/loss.html">Loss functions</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../packages/gluon/text/index.html">Text Tutorials</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/text/gnmt.html">Google Neural Machine Translation</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/text/transformer.html">Machine Translation with Transformer</a></li> |
| </ul> |
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| <li class="toctree-l4"><a class="reference internal" href="../../../packages/gluon/training/index.html">Training</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/training/trainer.html">Trainer</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/training/learning_rates/index.html">Learning Rates</a><ul> |
| <li class="toctree-l6"><a class="reference internal" href="../../../packages/gluon/training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../packages/gluon/training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li> |
| <li class="toctree-l6"><a class="reference internal" href="../../../packages/gluon/training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li> |
| </ul> |
| </li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/gluon/training/normalization/index.html">Normalization Blocks</a></li> |
| </ul> |
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| </ul> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../packages/kvstore/index.html">KVStore</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../packages/kvstore/kvstore.html">Distributed Key-Value Store</a></li> |
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| <li class="toctree-l3"><a class="reference internal" href="../../../packages/legacy/index.html">Legacy</a><ul> |
| <li class="toctree-l4"><a class="reference internal" href="../../../packages/legacy/ndarray/index.html">NDArray</a><ul> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/legacy/ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/legacy/ndarray/02-ndarray-operations.html">NDArray Operations</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/legacy/ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../packages/legacy/ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li> |
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| <li class="toctree-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.matrix_power.html">mxnet.np.linalg.matrix_power</a></li> |
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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.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> |
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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.deg2rad.html">mxnet.np.deg2rad</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.rad2deg.html">mxnet.np.rad2deg</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.unwrap.html">mxnet.np.unwrap</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.sinh.html">mxnet.np.sinh</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.cosh.html">mxnet.np.cosh</a></li> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.arctanh.html">mxnet.np.arctanh</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.rint.html">mxnet.np.rint</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.fix.html">mxnet.np.fix</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.floor.html">mxnet.np.floor</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.ceil.html">mxnet.np.ceil</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.trunc.html">mxnet.np.trunc</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.around.html">mxnet.np.around</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.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> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.prod.html">mxnet.np.prod</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.cumsum.html">mxnet.np.cumsum</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.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> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.reciprocal.html">mxnet.np.reciprocal</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.negative.html">mxnet.np.negative</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.divide.html">mxnet.np.divide</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.power.html">mxnet.np.power</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.subtract.html">mxnet.np.subtract</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.mod.html">mxnet.np.mod</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.multiply.html">mxnet.np.multiply</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.true_divide.html">mxnet.np.true_divide</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.remainder.html">mxnet.np.remainder</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/generated/mxnet.np.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> |
| </ul> |
| </li> |
| <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> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.beta.html">mxnet.np.random.beta</a></li> |
| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.chisquare.html">mxnet.np.random.chisquare</a></li> |
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| <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> |
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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> |
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| <li class="toctree-l5"><a class="reference internal" href="../../../../api/np/random/generated/mxnet.np.random.multinomial.html">mxnet.np.random.multinomial</a></li> |
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| </ul> |
| </li> |
| <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.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> |
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| <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> |
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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> |
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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> |
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| </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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| |
| <!--- 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="oneDNN-Quantization"> |
| <h1>oneDNN Quantization<a class="headerlink" href="#oneDNN-Quantization" title="Permalink to this headline">¶</a></h1> |
| <div class="section" id="Introduction"> |
| <h2>Introduction<a class="headerlink" href="#Introduction" title="Permalink to this headline">¶</a></h2> |
| <p>After successful model building and achieving desired accuracy on the test data, often the next step is to optimize inference to deploy the model to production. One of the key features of usable model is to have as small latency as possible to be able to provide services to large number of customers simultaneously. In addition to customer satisfaction, with well optimized model, hardware load is reduced which also reduces energy costs needed to perform inference.</p> |
| <p>Two main types of software optimizations can be characterized as: - memory-bound optimizations - main objective of these optimizations is to reduce the amount of memory operations (reads and writes) - it is done by e.g. chaining operations which can be performed one after another immediately, where input of every subsequent operation is the output of the previous one (example: ReLU activation after convolution), - compute-bound optimizations - these optimizations are mainly made on operations |
| which require large number of CPU cycles to complete, like FullyConnected and Convolution. One of the methods to speedup compute-bound operations is to lower computation precision - this type of optimization is called quantization.</p> |
| <p>In version 2.0 of the Apache MXNet (incubating) GluonAPI2.0 replaced Symbolic API known from versions 1.x, thus there are some differences between API to perform graph fusion and quantization.</p> |
| </div> |
| <div class="section" id="Operator-Fusion"> |
| <h2>Operator Fusion<a class="headerlink" href="#Operator-Fusion" title="Permalink to this headline">¶</a></h2> |
| <p>Models are often represented as a directed graph of operations (represented by nodes) and data flow (represented as edges). This way of visualizing helps a lot when searching for common patterns in whole model which can be optimized by fusion. Example: <img alt="base_model" src="https://github.com/dmlc/web-data/blob/main/mxnet/tutorials/onednn/quantization_2_0/sample_net.png?raw=true" /></p> |
| <p>The simplest way to explain what fusion is and how it works is to present an example. Image above depicts a sequence of popular operations taken from ResNet architecture. This type of architecture is built with many similar blocks called residual blocks. Some possible fusion patterns are:</p> |
| <ul class="simple"> |
| <li><p>Conv2D + BatchNorm => Fusing BatchNorm with Convolution can be performed by modifing weights and bias of Convolution - this way BatchNorm is completely contained within Convolution which makes BatchNorm zero time operation. Only cost of fusing is time needed to prepare weights and bias in Convolution based on BatchNorm parameters.</p></li> |
| <li><p>Conv2D + ReLU => this type of fusion is very popular also with other layers (e.g. FullyConnected + Activation). It is very simple idea where before writing data to output, activation is performed on that data. Main benefit of this fusion is that, there is no need to read and write back data in other layer only to perform simple activation function.</p></li> |
| <li><p>Conv2D + Add => even simpler idea than the previous ones - instead of overwriting the output memory, results are added to it. In the simplest terms: <code class="docutils literal notranslate"><span class="pre">out_mem</span> <span class="pre">=</span> <span class="pre">conv_result</span></code> is replaced by <code class="docutils literal notranslate"><span class="pre">out_mem</span> <span class="pre">+=</span> <span class="pre">conv_result</span></code>.</p></li> |
| </ul> |
| <p>Above examples are presented as atomic ones, but often they can be combined together, thus two patterns that can be fused in above example are: - Conv2D + BatchNorm + ReLU - Conv2D + BatchNorm + Add + ReLU</p> |
| <p>After fusing all patterns, computational graph will be changed to the following one: <img alt="fused_fp32_model" src="https://github.com/dmlc/web-data/blob/main/mxnet/tutorials/onednn/quantization_2_0/fused_f32.png?raw=true" /></p> |
| <div class="section" id="Operator-fusion-in-MXNet"> |
| <h3>Operator fusion in MXNet<a class="headerlink" href="#Operator-fusion-in-MXNet" title="Permalink to this headline">¶</a></h3> |
| <p>Since the version 1.6 of MXNet built with oneDNN support, operator fusion had been enabled by default for executing model with Module API, however in version 2.0 it has been decided to remove setting this feature by environment flag and replace it by aware user API call.</p> |
| <p>To fuse model in MXNet 2.0 there are two requirements: - the model must be defined as a subclass of HybridBlock or Symbol, - the model must have specific operator patterns which can be fused.</p> |
| <p>As an example we define sample block taken from ResNet architecture:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">mxnet</span> <span class="k">as</span> <span class="nn">mx</span> |
| <span class="kn">from</span> <span class="nn">mxnet.gluon</span> <span class="kn">import</span> <span class="n">nn</span> |
| |
| <span class="k">class</span> <span class="nc">SampleBlock</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="nb">super</span><span class="p">(</span><span class="n">SampleBlock</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="bp">self</span><span class="o">.</span><span class="n">conv1</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2D</span><span class="p">(</span><span class="n">channels</span><span class="o">=</span><span class="mi">64</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">strides</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> |
| <span class="n">use_bias</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">in_channels</span><span class="o">=</span><span class="mi">64</span><span class="p">)</span> |
| <span class="bp">self</span><span class="o">.</span><span class="n">bn1</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BatchNorm</span><span class="p">()</span> |
| <span class="bp">self</span><span class="o">.</span><span class="n">conv2</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2D</span><span class="p">(</span><span class="n">channels</span><span class="o">=</span><span class="mi">64</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">strides</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> |
| <span class="n">use_bias</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">in_channels</span><span class="o">=</span><span class="mi">64</span><span class="p">)</span> |
| <span class="bp">self</span><span class="o">.</span><span class="n">bn2</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BatchNorm</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="n">out</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">npx</span><span class="o">.</span><span class="n">activation</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bn1</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">conv1</span><span class="p">(</span><span class="n">x</span><span class="p">)),</span> <span class="s1">'relu'</span><span class="p">)</span> |
| <span class="n">out</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bn2</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">conv2</span><span class="p">(</span><span class="n">out</span><span class="p">))</span> |
| <span class="n">out</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">npx</span><span class="o">.</span><span class="n">activation</span><span class="p">(</span><span class="n">out</span> <span class="o">+</span> <span class="n">x</span><span class="p">,</span> <span class="s1">'relu'</span><span class="p">)</span> |
| <span class="k">return</span> <span class="n">out</span> |
| |
| <span class="n">net</span> <span class="o">=</span> <span class="n">SampleBlock</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">data</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">64</span><span class="p">,</span><span class="mi">224</span><span class="p">,</span><span class="mi">224</span><span class="p">))</span> |
| <span class="c1"># run fusion</span> |
| <span class="n">net</span><span class="o">.</span><span class="n">optimize_for</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">backend</span><span class="o">=</span><span class="s1">'ONEDNN'</span><span class="p">)</span> |
| |
| <span class="c1"># We can check fusion by plotting current symbol of our optimized network</span> |
| <span class="n">sym</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">net</span><span class="o">.</span><span class="n">export</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span> |
| <span class="n">graph</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">viz</span><span class="o">.</span><span class="n">plot_network</span><span class="p">(</span><span class="n">sym</span><span class="p">,</span> <span class="n">save_format</span><span class="o">=</span><span class="s1">'png'</span><span class="p">)</span> |
| <span class="n">graph</span><span class="o">.</span><span class="n">view</span><span class="p">()</span> |
| </pre></div> |
| </div> |
| <p>Both HybridBlock and Symbol classes provide API to easily run fusion of operators. Single line of code is enabling fusion passes on model:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">net</span><span class="o">.</span><span class="n">optimize_for</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">backend</span><span class="o">=</span><span class="s1">'ONEDNN'</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p><em>optimize_for</em> function is available also as Symbol class method. Example call to this API is shown below. Notice that Symbol’s <em>optimize_for</em> method is not done in-place, so assigning it to a new variable is required:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">optimized_symbol</span> <span class="o">=</span> <span class="n">sym</span><span class="o">.</span><span class="n">optimize_for</span><span class="p">(</span><span class="n">backend</span><span class="o">=</span><span class="s1">'ONEDNN'</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>For the above model definition in a naive benchmark with artificial data, we can gain up to <em>10.8x speedup</em> without any accuracy loss on our testing machine with Intel(R) Xeon(R) Platinum 8375C CPU.</p> |
| </div> |
| </div> |
| <div class="section" id="Quantization"> |
| <h2>Quantization<a class="headerlink" href="#Quantization" title="Permalink to this headline">¶</a></h2> |
| <p>As mentioned in the introduction, precision reduction is another very popular method of improving performance of workloads and, what is important, in most cases is combined together with operator fusion which improves performance even more. In training precision reduction utilizes 16 bit data types like bfloat or float16, but for inference great results can be achieved using int8.</p> |
| <p>Model quantization helps on both memory-bound and compute-bound operations. In quantized model IO operations are reduced as int8 data type is 4x smaller than float32, and also computational throughput is increased as more data can be SIMD’ed. On modern Intel architectures using int8 data type can bring even more speedup by utilizing special VNNI instruction set.</p> |
| <p><img alt="before_quant" src="https://github.com/dmlc/web-data/blob/main/mxnet/tutorials/onednn/quantization_2_0/before_quant.png?raw=true" /></p> |
| <p>Firstly quantization performs operator fusion on floating-point model as mentioned in paragraph earlier. Next, all operators which support int8 data type are marked as quantized and if needed additional operators are injected into graph surrounding quantizable operator - the goal of this additional operators is to quantize, dequantize or requantize data to keep data type between operators compatible.</p> |
| <p><img alt="quant_not_calib" src="https://github.com/dmlc/web-data/blob/main/mxnet/tutorials/onednn/quantization_2_0/quant_not_calib.png?raw=true" /></p> |
| <p>After injection step it is important to perform calibration of the model, however this step is optional. Quantizing without calibration is not recommended in terms of performance. It will result in calculating data minimum and maximum in quantize and requantize nodes during each inference pass. Calibrating a model greatly improves performance as minimum and maximum values are collected offline and are saved inside node - this way there is no need to search for these values during inference pass.</p> |
| <p><img alt="quant_calib" src="https://github.com/dmlc/web-data/blob/main/mxnet/tutorials/onednn/quantization_2_0/quant_calib.png?raw=true" /></p> |
| <p>Currently, there are three supported calibration methods: - naive — min/max values from the calibration run, - entropy — uses KL divergence to determine the best symmetrical quantization thresholds for a given histogram of values, - custom — uses user-defined CalibrationCollector to control the calibration process.</p> |
| <p>Last stage of quantization flow is to perform additional operator fusion. Second fusion is about merging requantize and dequantize operators into preceding node - oneDNN kernels can perform needed scaling before writing result to output which results in model execution speed-up. Notice that last Convolution does not need minimum and maximum values as it is not requantizing int32 to int8, but dequantizing directly to float32 and scale is calculated basing on minimum and maximum of input and |
| weights.</p> |
| <p><img alt="quant_calib_fused" src="https://github.com/dmlc/web-data/blob/main/mxnet/tutorials/onednn/quantization_2_0/quant_calib_fused.png?raw=true" /></p> |
| <p>In MXNet 2.0, the quantization procedure has been adjusted to work well with Gluon models since it is the main API now. The goal was to allow the user to quantize fp32 HybridBlock model in just a few lines of code.</p> |
| <div class="section" id="Quantization-in-MXNet"> |
| <h3>Quantization in MXNet<a class="headerlink" href="#Quantization-in-MXNet" title="Permalink to this headline">¶</a></h3> |
| <p>As an example of a quantization procedure, pretrained <em>resnet50_v1</em> from <em>model_zoo.vision</em> package can be used. To get it simply run the following code:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">mxnet</span> <span class="k">as</span> <span class="nn">mx</span> |
| <span class="kn">from</span> <span class="nn">mxnet.gluon.model_zoo.vision</span> <span class="kn">import</span> <span class="n">resnet50_v1</span> |
| |
| <span class="n">net</span> <span class="o">=</span> <span class="n">resnet50_v1</span><span class="p">(</span><span class="n">pretrained</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>Now, to get a ready-to-deploy quantized model two steps are required:</p> |
| <ol class="arabic simple"> |
| <li><p>Prepare data loader with calibration data - this data will be used as input to the network. All necessary layers will be observed with layer collector to calculate minimum and maximum value of that layer. This flow is internal mechanism and all what user needs to do is to provide data loader.</p></li> |
| <li><p>Call <code class="docutils literal notranslate"><span class="pre">quantize_net</span></code> function from <code class="docutils literal notranslate"><span class="pre">contrib.quantize</span></code> package - both operator fusion calls will be called inside this API.</p></li> |
| </ol> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">calib_data_loader</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">DataLoader</span><span class="p">(</span><span class="n">dummy_data</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">)</span> |
| <span class="n">qnet</span> <span class="o">=</span> <span class="n">quantize_net</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">calib_mode</span><span class="o">=</span><span class="s1">'naive'</span><span class="p">,</span> <span class="n">calib_data</span><span class="o">=</span><span class="n">calib_data_loader</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <p>Following function, which calculates total inference time on the model with an artificial data, can be used to compare the performance:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">benchmark_net</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="mi">32</span><span class="p">,</span> <span class="n">batches</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">warmup_batches</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span> |
| <span class="kn">import</span> <span class="nn">time</span> |
| <span class="n">data</span> <span class="o">=</span> <span class="n">mx</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">uniform</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="p">(</span><span class="n">batch_size</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">224</span><span class="p">,</span> <span class="mi">224</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="n">batches</span> <span class="o">+</span> <span class="n">warmup_batches</span><span class="p">):</span> |
| <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="n">warmup_batches</span><span class="p">:</span> |
| <span class="n">tic</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> |
| <span class="n">out</span> <span class="o">=</span> <span class="n">net</span><span class="p">(</span><span class="n">data</span><span class="p">)</span> |
| <span class="n">out</span><span class="o">.</span><span class="n">wait_to_read</span><span class="p">()</span> |
| |
| <span class="n">total_time</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="o">-</span> <span class="n">tic</span> |
| <span class="k">return</span> <span class="n">total_time</span> |
| </pre></div> |
| </div> |
| <p>Comparing fused float32 network to quantized network on Intel(R) Xeon(R) Platinum 8375C CPU shows <em>4.2x speedup</em> - measurment was done on 32 cores and this machine utilizes VNNI instruction set.</p> |
| <p>The other aspect of lowering the precision of a model is a difference in its accuracy. We will check that on previously tested resnet50_v1 with ImageNet dataset. To run this example you will need ImageNet dataset prepared with this tutorial and stored in path_to_imagenet. Let’s compare top1 and top5 accuracy of standard fp32 model with quantized int8 model calibrated using naive and entropy calibration mode. We will use only 10 batches of the validation dataset to calibrate quantized model.</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">mxnet</span> <span class="k">as</span> <span class="nn">mx</span> |
| <span class="kn">from</span> <span class="nn">mxnet.gluon.model_zoo.vision</span> <span class="kn">import</span> <span class="n">resnet50_v1</span> |
| <span class="kn">from</span> <span class="nn">mxnet.gluon.data.vision</span> <span class="kn">import</span> <span class="n">transforms</span> |
| <span class="kn">from</span> <span class="nn">mxnet.contrib.quantization</span> <span class="kn">import</span> <span class="n">quantize_net</span> |
| |
| <span class="k">def</span> <span class="nf">test_accuracy</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">data_loader</span><span class="p">,</span> <span class="n">description</span><span class="p">):</span> |
| <span class="n">acc_top1</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">gluon</span><span class="o">.</span><span class="n">metric</span><span class="o">.</span><span class="n">Accuracy</span><span class="p">()</span> |
| <span class="n">acc_top5</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">gluon</span><span class="o">.</span><span class="n">metric</span><span class="o">.</span><span class="n">TopKAccuracy</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span> |
| <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span> |
| <span class="n">tic</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> |
| <span class="k">for</span> <span class="n">x</span><span class="p">,</span> <span class="n">label</span> <span class="ow">in</span> <span class="n">data_loader</span><span class="p">:</span> |
| <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span> |
| <span class="n">output</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">acc_top1</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">label</span><span class="p">,</span> <span class="n">output</span><span class="p">)</span> |
| <span class="n">acc_top5</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">label</span><span class="p">,</span> <span class="n">output</span><span class="p">)</span> |
| <span class="n">time_spend</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="o">-</span> <span class="n">tic</span> |
| <span class="n">_</span><span class="p">,</span> <span class="n">top1</span> <span class="o">=</span> <span class="n">acc_top1</span><span class="o">.</span><span class="n">get</span><span class="p">()</span> |
| <span class="n">_</span><span class="p">,</span> <span class="n">top5</span> <span class="o">=</span> <span class="n">acc_top5</span><span class="o">.</span><span class="n">get</span><span class="p">()</span> |
| <span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="si">{:12}</span><span class="s1"> Top1 Accuracy: </span><span class="si">{:.4f}</span><span class="s1"> Top5 Accuracy: </span><span class="si">{:.4f}</span><span class="s1"> from </span><span class="si">{:4}</span><span class="s1"> batches in </span><span class="si">{:8.2f}</span><span class="s1">s'</span> |
| <span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">description</span><span class="p">,</span> <span class="n">top1</span><span class="p">,</span> <span class="n">top5</span><span class="p">,</span> <span class="n">count</span><span class="p">,</span> <span class="n">time_spend</span><span class="p">))</span> |
| |
| <span class="n">rgb_mean</span> <span class="o">=</span> <span class="p">(</span><span class="mf">0.485</span><span class="p">,</span> <span class="mf">0.456</span><span class="p">,</span> <span class="mf">0.406</span><span class="p">)</span> |
| <span class="n">rgb_std</span> <span class="o">=</span> <span class="p">(</span><span class="mf">0.229</span><span class="p">,</span> <span class="mf">0.224</span><span class="p">,</span> <span class="mf">0.225</span><span class="p">)</span> |
| <span class="n">batch_size</span> <span class="o">=</span> <span class="mi">64</span> |
| |
| <span class="n">dataset</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">vision</span><span class="o">.</span><span class="n">ImageRecordDataset</span><span class="p">(</span><span class="s1">'path_to_imagenet/val.rec'</span><span class="p">)</span> |
| <span class="n">transformer</span> <span class="o">=</span> <span class="n">transforms</span><span class="o">.</span><span class="n">Compose</span><span class="p">([</span><span class="n">transforms</span><span class="o">.</span><span class="n">Resize</span><span class="p">(</span><span class="mi">256</span><span class="p">),</span> |
| <span class="n">transforms</span><span class="o">.</span><span class="n">CenterCrop</span><span class="p">(</span><span class="mi">224</span><span class="p">),</span> |
| <span class="n">transforms</span><span class="o">.</span><span class="n">ToTensor</span><span class="p">(),</span> |
| <span class="n">transforms</span><span class="o">.</span><span class="n">Normalize</span><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="n">rgb_mean</span><span class="p">,</span> <span class="n">std</span><span class="o">=</span><span class="n">rgb_std</span><span class="p">)])</span> |
| <span class="n">val_data</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">gluon</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">DataLoader</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">transform_first</span><span class="p">(</span><span class="n">transformer</span><span class="p">),</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">shuffle</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> |
| |
| <span class="n">net</span> <span class="o">=</span> <span class="n">resnet50_v1</span><span class="p">(</span><span class="n">pretrained</span><span class="o">=</span><span class="kc">True</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="n">static_alloc</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">static_shape</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> |
| <span class="n">test_accuracy</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">val_data</span><span class="p">,</span> <span class="s2">"FP32"</span><span class="p">)</span> |
| |
| <span class="n">dummy_data</span> <span class="o">=</span> <span class="n">mx</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">uniform</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="p">(</span><span class="n">batch_size</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">224</span><span class="p">,</span> <span class="mi">224</span><span class="p">))</span> |
| <span class="n">net</span><span class="o">.</span><span class="n">optimize_for</span><span class="p">(</span><span class="n">dummy_data</span><span class="p">,</span> <span class="n">backend</span><span class="o">=</span><span class="s1">'ONEDNN'</span><span class="p">,</span> <span class="n">static_alloc</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">static_shape</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> |
| <span class="n">test_accuracy</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">val_data</span><span class="p">,</span> <span class="s2">"FP32 fused"</span><span class="p">)</span> |
| |
| <span class="n">qnet</span> <span class="o">=</span> <span class="n">quantize_net</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">calib_mode</span><span class="o">=</span><span class="s1">'naive'</span><span class="p">,</span> <span class="n">calib_data</span><span class="o">=</span><span class="n">val_data</span><span class="p">,</span> <span class="n">num_calib_batches</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span> |
| <span class="n">qnet</span><span class="o">.</span><span class="n">hybridize</span><span class="p">(</span><span class="n">static_alloc</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">static_shape</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> |
| <span class="n">test_accuracy</span><span class="p">(</span><span class="n">qnet</span><span class="p">,</span> <span class="n">val_data</span><span class="p">,</span> <span class="s1">'INT8 Naive'</span><span class="p">)</span> |
| |
| <span class="n">qnet</span> <span class="o">=</span> <span class="n">quantize_net</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">calib_mode</span><span class="o">=</span><span class="s1">'entropy'</span><span class="p">,</span> <span class="n">calib_data</span><span class="o">=</span><span class="n">val_data</span><span class="p">,</span> <span class="n">num_calib_batches</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span> |
| <span class="n">qnet</span><span class="o">.</span><span class="n">hybridize</span><span class="p">(</span><span class="n">static_alloc</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">static_shape</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> |
| <span class="n">test_accuracy</span><span class="p">(</span><span class="n">qnet</span><span class="p">,</span> <span class="n">val_data</span><span class="p">,</span> <span class="s1">'INT8 Entropy'</span><span class="p">)</span> |
| </pre></div> |
| </div> |
| <div class="section" id="Output:"> |
| <h4>Output:<a class="headerlink" href="#Output:" title="Permalink to this headline">¶</a></h4> |
| <blockquote> |
| <div><div class="line-block"> |
| <div class="line"><code class="docutils literal notranslate"><span class="pre">FP32</span>         <span class="pre">Top1</span> <span class="pre">Accuracy:</span> <span class="pre">0.7636</span> <span class="pre">Top5</span> <span class="pre">Accuracy:</span> <span class="pre">0.9309</span> <span class="pre">from</span> <span class="pre">782</span> <span class="pre">batches</span> <span class="pre">in</span> <span class="pre">1560.97s</span></code></div> |
| <div class="line"><code class="docutils literal notranslate"><span class="pre">FP32</span> <span class="pre">fused</span>   <span class="pre">Top1</span> <span class="pre">Accuracy:</span> <span class="pre">0.7636</span> <span class="pre">Top5</span> <span class="pre">Accuracy:</span> <span class="pre">0.9309</span> <span class="pre">from</span> <span class="pre">782</span> <span class="pre">batches</span> <span class="pre">in</span>  <span class="pre">281.03s</span></code></div> |
| <div class="line"><code class="docutils literal notranslate"><span class="pre">INT8</span> <span class="pre">Naive</span>   <span class="pre">Top1</span> <span class="pre">Accuracy:</span> <span class="pre">0.7631</span> <span class="pre">Top5</span> <span class="pre">Accuracy:</span> <span class="pre">0.9309</span> <span class="pre">from</span> <span class="pre">782</span> <span class="pre">batches</span> <span class="pre">in</span>  <span class="pre">184.87s</span></code></div> |
| <div class="line"><code class="docutils literal notranslate"><span class="pre">INT8</span> <span class="pre">Entropy</span> <span class="pre">Top1</span> <span class="pre">Accuracy:</span> <span class="pre">0.7617</span> <span class="pre">Top5</span> <span class="pre">Accuracy:</span> <span class="pre">0.9298</span> <span class="pre">from</span> <span class="pre">782</span> <span class="pre">batches</span> <span class="pre">in</span>  <span class="pre">185.23s</span></code></div> |
| </div> |
| </div></blockquote> |
| <p>With quantized model there is a tiny accuracy drop, however this is the cost of great performance optimization and memory footprint reduction. The difference between calibration methods is dependent on the model itself, used activation layers and the size of calibration data.</p> |
| </div> |
| </div> |
| <div class="section" id="Custom-layer-collectors-and-calibrating-the-model"> |
| <h3>Custom layer collectors and calibrating the model<a class="headerlink" href="#Custom-layer-collectors-and-calibrating-the-model" title="Permalink to this headline">¶</a></h3> |
| <p>In MXNet 2.0 new interface for creating custom calibration collector has been added. Main goal of this interface is to give the user as much flexibility as possible in almost every step of quantization. Creating own layer collector is pretty easy, however computing effective min/max values can be not a trivial task.</p> |
| <p>Layer collectors are responsible for collecting statistics of each node in the graph — it means that the input/output data of every operator executed can be observed. Collector utilizes the register_op_hook method of HybridBlock class.</p> |
| <p>Custom layer collector has to inherit from the CalibrationCollector class, which is provided in <code class="docutils literal notranslate"><span class="pre">contrib.quantization</span></code> package. This inheritance allows API to be consistent. Below is an example implementation of CalibrationCollector:</p> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">ExampleNaiveCollector</span><span class="p">(</span><span class="n">CalibrationCollector</span><span class="p">):</span> |
| <span class="w"> </span><span class="sd">"""Saves layer output min and max values in a dict with layer names as keys.</span> |
| <span class="sd"> The collected min and max values will be directly used as thresholds for quantization.</span> |
| <span class="sd"> """</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="n">logger</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span> |
| <span class="c1"># important! initialize base class attributes</span> |
| <span class="nb">super</span><span class="p">(</span><span class="n">ExampleNaiveCollector</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="bp">self</span><span class="o">.</span><span class="n">logger</span> <span class="o">=</span> <span class="n">logger</span> |
| |
| <span class="k">def</span> <span class="nf">collect</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">op_name</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span> |
| <span class="w"> </span><span class="sd">"""Callback function for collecting min and max values from an NDArray."""</span> |
| <span class="k">if</span> <span class="n">name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">include_layers</span><span class="p">:</span> <span class="c1"># include_layers is populated by quantization API</span> |
| <span class="k">return</span> |
| <span class="n">arr</span> <span class="o">=</span> <span class="n">arr</span><span class="o">.</span><span class="n">copyto</span><span class="p">(</span><span class="n">cpu</span><span class="p">())</span><span class="o">.</span><span class="n">asnumpy</span><span class="p">()</span> |
| |
| <span class="n">min_range</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> |
| <span class="n">max_range</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> |
| |
| <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">min_max_dict</span><span class="p">:</span> <span class="c1"># min_max_dict is by default empty dict</span> |
| <span class="n">cur_min_max</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">min_max_dict</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> |
| <span class="bp">self</span><span class="o">.</span><span class="n">min_max_dict</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="nb">min</span><span class="p">(</span><span class="n">cur_min_max</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">min_range</span><span class="p">),</span> |
| <span class="nb">max</span><span class="p">(</span><span class="n">cur_min_max</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">max_range</span><span class="p">))</span> |
| <span class="k">else</span><span class="p">:</span> |
| <span class="bp">self</span><span class="o">.</span><span class="n">min_max_dict</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">min_range</span><span class="p">,</span> <span class="n">max_range</span><span class="p">)</span> |
| |
| <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">logger</span><span class="p">:</span> |
| <span class="bp">self</span><span class="o">.</span><span class="n">logger</span><span class="o">.</span><span class="n">debug</span><span class="p">(</span><span class="s2">"Collecting layer </span><span class="si">%s</span><span class="s2"> min_range=</span><span class="si">%f</span><span class="s2">, max_range=</span><span class="si">%f</span><span class="s2">"</span> |
| <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">min_range</span><span class="p">,</span> <span class="n">max_range</span><span class="p">))</span> |
| |
| <span class="k">def</span> <span class="nf">post_collect</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span> |
| <span class="c1"># we're using min_max_dict and don't process any collected statistics so we don't</span> |
| <span class="c1"># need to override this function, however we are doing this for the sake of this article</span> |
| <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">min_max_dict</span> |
| </pre></div> |
| </div> |
| <p>Quantization API ‘injects’ names of nodes which require calibration into the include_layers attribute of custom collector — list of included layers allows to avoid unnecessary collecting on nodes which are not relevant in terms of quantization. Using this attribute is fully optional and user can implement his own logic.</p> |
| <p>After collecting all statistic data post_collect function is called. In post_collect additional processing logic can be implemented, but it must return dictionary of nodes names as key and tuple of minimum and maximum values which should be used to calculate data scaling factors.</p> |
| </div> |
| <div class="section" id="Example-of-usage-with-quantization-API:"> |
| <h3>Example of usage with quantization API:<a class="headerlink" href="#Example-of-usage-with-quantization-API:" title="Permalink to this headline">¶</a></h3> |
| <div class="highlight-default notranslate"><div class="highlight"><pre><span></span>from mxnet.contrib.quantization import * |
| import logging |
| logging.getLogger().setLevel(logging.DEBUG) |
| |
| #… |
| |
| calib_data_loader = mx.gluon.data.DataLoader(…) |
| my_collector = ExampleNaiveCollector(logger=logging.getLogger()) |
| |
| qnet = quantize_net(net, calib_mode='custom', calib_data=calib_data_loader, LayerOutputCollector=my_collector) |
| </pre></div> |
| </div> |
| </div> |
| </div> |
| <div class="section" id="Performance-and-accuracy-results"> |
| <h2>Performance and accuracy results<a class="headerlink" href="#Performance-and-accuracy-results" title="Permalink to this headline">¶</a></h2> |
| <div class="section" id="Performance"> |
| <h3>Performance<a class="headerlink" href="#Performance" title="Permalink to this headline">¶</a></h3> |
| <p>Performance results of CV models. Chart presents three different runs: base float32 model without optimizations, fused float32 model with optimizations and quantized model. <img alt="performance" src="https://github.com/dmlc/web-data/blob/main/mxnet/tutorials/onednn/quantization_2_0/speedup.png?raw=true" /> <strong>Figure 1.</strong> Relative Inference Performance (img/sec) for Batch Size 128</p> |
| </div> |
| <div class="section" id="Accuracy"> |
| <h3>Accuracy<a class="headerlink" href="#Accuracy" title="Permalink to this headline">¶</a></h3> |
| <p>Accuracy results of CV models. Chart presents three different runs: base float32 model without optimizations, fused float32 model with optimizations and fused quantized model. <img alt="accuracy" src="https://github.com/dmlc/web-data/blob/main/mxnet/tutorials/onednn/quantization_2_0/accuracy.png?raw=true" /> <strong>Figure 2.</strong> ImageNet(ILSVRC2012) TOP1 validation accuracy</p> |
| </div> |
| </div> |
| <div class="section" id="Notes"> |
| <h2>Notes<a class="headerlink" href="#Notes" title="Permalink to this headline">¶</a></h2> |
| <div class="line-block"> |
| <div class="line">Accuracy and speedup tested on:</div> |
| <div class="line">- AWS c6i.16xlarge EC2 instance with Ubuntu 20.04 LTS (ami-0558cee5b20db1f9c)</div> |
| <div class="line">- MXNet SHA: 9fa75b470b8f0238a98635f20f5af941feb60929 / oneDNN v2.6 SHA: 52b5f107dd9cf10910aaa19cb47f3abf9b349815</div> |
| <div class="line">- with following enviroment variables were set: <code class="docutils literal notranslate"><span class="pre">OMP_NUM_THREADS=32</span> <span class="pre">OMP_PROC_BIND=TRUE</span> <span class="pre">OMP_PLACES={0}:32:1</span></code> (by <a class="reference external" href="https://github.com/apache/incubator-mxnet/blob/102388a0557c530741ed8e9b31296416a1c23925/benchmark/python/dnnl/run.sh">benchmark/python/dnnl/run.sh</a>)</div> |
| </div> |
| </div> |
| </div> |
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| <p class="caption"> |
| <span class="caption-text">Table Of Contents</span> |
| </p> |
| <ul> |
| <li><a class="reference internal" href="#">oneDNN Quantization</a><ul> |
| <li><a class="reference internal" href="#Introduction">Introduction</a></li> |
| <li><a class="reference internal" href="#Operator-Fusion">Operator Fusion</a><ul> |
| <li><a class="reference internal" href="#Operator-fusion-in-MXNet">Operator fusion in MXNet</a></li> |
| </ul> |
| </li> |
| <li><a class="reference internal" href="#Quantization">Quantization</a><ul> |
| <li><a class="reference internal" href="#Quantization-in-MXNet">Quantization in MXNet</a><ul> |
| <li><a class="reference internal" href="#Output:">Output:</a></li> |
| </ul> |
| </li> |
| <li><a class="reference internal" href="#Custom-layer-collectors-and-calibrating-the-model">Custom layer collectors and calibrating the model</a></li> |
| <li><a class="reference internal" href="#Example-of-usage-with-quantization-API:">Example of usage with quantization API:</a></li> |
| </ul> |
| </li> |
| <li><a class="reference internal" href="#Performance-and-accuracy-results">Performance and accuracy results</a><ul> |
| <li><a class="reference internal" href="#Performance">Performance</a></li> |
| <li><a class="reference internal" href="#Accuracy">Accuracy</a></li> |
| </ul> |
| </li> |
| <li><a class="reference internal" href="#Notes">Notes</a></li> |
| </ul> |
| </li> |
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