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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-l4"><a class="reference internal" href="../../../getting-started/crash-course/1-ndarray.html">Manipulate data with <code class="docutils literal notranslate"><span class="pre">ndarray</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/2-nn.html">Create a neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/3-autograd.html">Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/4-train.html">Train the neural network</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 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/logistic_regression_explained.html">Logistic regression explained</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../ndarray/sparse/index.html">Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../ndarray/sparse/train.html">Train a Linear Regression Model with Sparse Symbols</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../ndarray/sparse/train_gluon.html">Sparse NDArrays with Gluon</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../onnx/inference_on_onnx_model.html">Running inference on MXNet/Gluon from an ONNX model</a></li>
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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/1-ndarray.html">Manipulate data with <code class="docutils literal notranslate"><span class="pre">ndarray</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/2-nn.html">Create a neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/3-autograd.html">Automatic differentiation with <code class="docutils literal notranslate"><span class="pre">autograd</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/4-train.html">Train the neural network</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/5-predict.html">Predict with a pre-trained model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../../getting-started/crash-course/6-use_gpus.html">Use GPUs</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 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/logistic_regression_explained.html">Logistic regression explained</a></li>
<li class="toctree-l3"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/packages/gluon/image/mnist.html">MNIST</a></li>
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<li class="toctree-l4 current"><a class="reference internal" href="index.html">Blocks</a><ul class="current">
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<li class="toctree-l5 current"><a class="current reference internal" href="#">Hybridize</a></li>
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<li class="toctree-l5"><a class="reference internal" href="save_load_params.html">Saving and Loading Gluon Models</a></li>
<li class="toctree-l5"><a class="reference internal" href="activations/activations.html">Activation Blocks</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../data/data_augmentation.html">Image Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../data/data_augmentation.html#Spatial-Augmentation">Spatial Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../data/data_augmentation.html#Color-Augmentation">Color Augmentation</a></li>
<li class="toctree-l5"><a class="reference internal" href="../data/data_augmentation.html#Composed-Augmentations">Composed Augmentations</a></li>
<li class="toctree-l5"><a class="reference internal" href="../data/datasets.html">Gluon <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s and <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
<li class="toctree-l5"><a class="reference internal" href="../data/datasets.html#Using-own-data-with-included-Datasets">Using own data with included <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../data/datasets.html#Using-own-data-with-custom-Datasets">Using own data with custom <code class="docutils literal notranslate"><span class="pre">Dataset</span></code>s</a></li>
<li class="toctree-l5"><a class="reference internal" href="../data/datasets.html#Appendix:-Upgrading-from-Module-DataIter-to-Gluon-DataLoader">Appendix: Upgrading from Module <code class="docutils literal notranslate"><span class="pre">DataIter</span></code> to Gluon <code class="docutils literal notranslate"><span class="pre">DataLoader</span></code></a></li>
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<li class="toctree-l5"><a class="reference internal" href="../image/mnist.html">Handwritten Digit Recognition</a></li>
<li class="toctree-l5"><a class="reference internal" href="../image/pretrained_models.html">Using pre-trained models in MXNet</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../loss/kl_divergence.html">Kullback-Leibler (KL) Divergence</a></li>
<li class="toctree-l5"><a class="reference internal" href="../loss/loss.html">Loss functions</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../text/transformer.html">Machine Translation with Transformer</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../training/fit_api_tutorial.html">MXNet Gluon Fit API</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../training/learning_rates/index.html">Learning Rates</a><ul>
<li class="toctree-l6"><a class="reference internal" href="../training/learning_rates/learning_rate_finder.html">Learning Rate Finder</a></li>
<li class="toctree-l6"><a class="reference internal" href="../training/learning_rates/learning_rate_schedules.html">Learning Rate Schedules</a></li>
<li class="toctree-l6"><a class="reference internal" href="../training/learning_rates/learning_rate_schedules_advanced.html">Advanced Learning Rate Schedules</a></li>
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<li class="toctree-l5"><a class="reference internal" href="../training/normalization/index.html">Normalization Blocks</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../kvstore/kvstore.html">Distributed Key-Value Store</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../ndarray/01-ndarray-intro.html">An Intro: Manipulate Data the MXNet Way with NDArray</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../ndarray/02-ndarray-operations.html">NDArray Operations</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../ndarray/03-ndarray-contexts.html">NDArray Contexts</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../ndarray/gotchas_numpy_in_mxnet.html">Gotchas using NumPy in Apache MXNet</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../ndarray/sparse/index.html">Tutorials</a><ul>
<li class="toctree-l5"><a class="reference internal" href="../../ndarray/sparse/csr.html">CSRNDArray - NDArray in Compressed Sparse Row Storage Format</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../ndarray/sparse/row_sparse.html">RowSparseNDArray - NDArray for Sparse Gradient Updates</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../ndarray/sparse/train.html">Train a Linear Regression Model with Sparse Symbols</a></li>
<li class="toctree-l5"><a class="reference internal" href="../../ndarray/sparse/train_gluon.html">Sparse NDArrays with Gluon</a></li>
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<li class="toctree-l4"><a class="reference internal" href="../../onnx/fine_tuning_gluon.html">Fine-tuning an ONNX model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../onnx/inference_on_onnx_model.html">Running inference on MXNet/Gluon from an ONNX model</a></li>
<li class="toctree-l4"><a class="reference internal" href="../../onnx/super_resolution.html">Importing an ONNX model into MXNet</a></li>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/python/docs/tutorials/deploy/export/onnx.html">Export ONNX Models</a></li>
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<li class="toctree-l3"><a class="reference internal" href="../../viz/index.html">Visualization</a><ul>
<li class="toctree-l4"><a class="reference external" href="https://mxnet.apache.org/api/faq/visualize_graph">Visualize networks</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../../performance/index.html">Performance</a><ul>
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<li class="toctree-l4"><a class="reference internal" href="../../../performance/compression/int8.html">Deploy with int-8</a></li>
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<!--- Licensed to the Apache Software Foundation (ASF) under one --><!--- or more contributor license agreements. See the NOTICE file --><!--- distributed with this work for additional information --><!--- regarding copyright ownership. The ASF licenses this file --><!--- to you under the Apache License, Version 2.0 (the --><!--- "License"); you may not use this file except in compliance --><!--- with the License. You may obtain a copy of the License at --><!--- http://www.apache.org/licenses/LICENSE-2.0 --><!--- Unless required by applicable law or agreed to in writing, --><!--- software distributed under the License is distributed on an --><!--- "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY --><!--- KIND, either express or implied. See the License for the --><!--- specific language governing permissions and limitations --><!--- under the License. --><div class="section" id="Hybridize">
<h1>Hybridize<a class="headerlink" href="#Hybridize" title="Permalink to this headline"></a></h1>
<!-- adapted from diveintodeeplearning --><div class="section" id="A-Hybrid-of-Imperative-and-Symbolic-Programming">
<h2>A Hybrid of Imperative and Symbolic Programming<a class="headerlink" href="#A-Hybrid-of-Imperative-and-Symbolic-Programming" title="Permalink to this headline"></a></h2>
<p>Imperative programming makes use of programming statements to change a program’s state. Consider the following example of simple imperative programming code.</p>
<div class="nbinput nblast docutils container">
<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[ ]:
</pre></div>
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<div class="input_area highlight-python notranslate"><div class="highlight"><pre>
<span></span><span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
<span class="k">return</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span>
<span class="k">def</span> <span class="nf">fancy_func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
<span class="n">e</span> <span class="o">=</span> <span class="n">add</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">add</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
<span class="n">g</span> <span class="o">=</span> <span class="n">add</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
<span class="k">return</span> <span class="n">g</span>
<span class="n">fancy_func</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
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</div>
</div>
<p>As expected, Python will perform an addition when running the statement <code class="docutils literal notranslate"><span class="pre">e</span> <span class="pre">=</span> <span class="pre">add(a,</span> <span class="pre">b)</span></code>, and will store the result as the variable <code class="docutils literal notranslate"><span class="pre">e</span></code>, thereby changing the program’s state. The next two statements <code class="docutils literal notranslate"><span class="pre">f</span> <span class="pre">=</span> <span class="pre">add(c,</span> <span class="pre">d)</span></code> and <code class="docutils literal notranslate"><span class="pre">g</span> <span class="pre">=</span> <span class="pre">add(e,</span> <span class="pre">f)</span></code> will similarly perform additions and store the results as variables.</p>
<p>Although imperative programming is convenient, it may be inefficient. On the one hand, even if the <code class="docutils literal notranslate"><span class="pre">add</span></code> function is repeatedly called throughout the <code class="docutils literal notranslate"><span class="pre">fancy_func</span></code> function, Python will execute the three function calling statements individually, one after the other. On the other hand, we need to save the variable values of <code class="docutils literal notranslate"><span class="pre">e</span></code> and <code class="docutils literal notranslate"><span class="pre">f</span></code> until all the statements in <code class="docutils literal notranslate"><span class="pre">fancy_func</span></code> have been executed. This is because we do not know whether the variables <code class="docutils literal notranslate"><span class="pre">e</span></code> and <code class="docutils literal notranslate"><span class="pre">f</span></code> will be used by other
parts of the program after the statements <code class="docutils literal notranslate"><span class="pre">e</span> <span class="pre">=</span> <span class="pre">add(a,</span> <span class="pre">b)</span></code> and <code class="docutils literal notranslate"><span class="pre">f</span> <span class="pre">=</span> <span class="pre">add(c,</span> <span class="pre">d)</span></code> have been executed.</p>
<p>Contrary to imperative programming, symbolic programming is usually performed after the computational process has been fully defined. Symbolic programming is used by multiple deep learning frameworks, including Theano and TensorFlow. The process of symbolic programming generally requires the following three steps:</p>
<ol class="arabic simple">
<li><p>Define the computation process.</p></li>
<li><p>Compile the computation process into an executable program.</p></li>
<li><p>Provide the required inputs and call on the compiled program for execution.</p></li>
</ol>
<p>In the example below, we utilize symbolic programming to re-implement the imperative programming code provided at the beginning of this section.</p>
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<span></span><span class="k">def</span> <span class="nf">add_str</span><span class="p">():</span>
<span class="k">return</span> <span class="s1">&#39;&#39;&#39;</span>
<span class="s1">def add(a, b):</span>
<span class="s1"> return a + b</span>
<span class="s1">&#39;&#39;&#39;</span>
<span class="k">def</span> <span class="nf">fancy_func_str</span><span class="p">():</span>
<span class="k">return</span> <span class="s1">&#39;&#39;&#39;</span>
<span class="s1">def fancy_func(a, b, c, d):</span>
<span class="s1"> e = add(a, b)</span>
<span class="s1"> f = add(c, d)</span>
<span class="s1"> g = add(e, f)</span>
<span class="s1"> return g</span>
<span class="s1">&#39;&#39;&#39;</span>
<span class="k">def</span> <span class="nf">evoke_str</span><span class="p">():</span>
<span class="k">return</span> <span class="n">add_str</span><span class="p">()</span> <span class="o">+</span> <span class="n">fancy_func_str</span><span class="p">()</span> <span class="o">+</span> <span class="s1">&#39;&#39;&#39;</span>
<span class="s1">print(fancy_func(1, 2, 3, 4))</span>
<span class="s1">&#39;&#39;&#39;</span>
<span class="n">prog</span> <span class="o">=</span> <span class="n">evoke_str</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">prog</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="nb">compile</span><span class="p">(</span><span class="n">prog</span><span class="p">,</span> <span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="s1">&#39;exec&#39;</span><span class="p">)</span>
<span class="n">exec</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
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</div>
</div>
<p>The three functions defined above will only return the results of the computation process as a string. Finally, the complete computation process is compiled and run using the <code class="docutils literal notranslate"><span class="pre">compile</span></code> function. This leaves more room to optimize computation, since the system is able to view the entire program during its compilation. For example, during compilation, the program can be rewritten as <code class="docutils literal notranslate"><span class="pre">print((1</span> <span class="pre">+</span> <span class="pre">2)</span> <span class="pre">+</span> <span class="pre">(3</span> <span class="pre">+</span> <span class="pre">4))</span></code> or even directly rewritten as <code class="docutils literal notranslate"><span class="pre">print(10)</span></code>. Apart from reducing the amount of
function calls, this process also saves memory.</p>
<p>A comparison of these two programming methods shows that</p>
<ul class="simple">
<li><p>imperative programming is easier. When imperative programming is used in Python, the majority of the code is straightforward and easy to write. At the same time, it is easier to debug imperative programming code. This is because it is easier to obtain and print all relevant intermediate variable values, or make use of Python’s built-in debugging tools.</p></li>
<li><p>Symbolic programming is more efficient and easier to port. Symbolic programming makes it easier to better optimize the system during compilation, while also having the ability to port the program into a format independent of Python. This allows the program to be run in a non-Python environment, thus avoiding any potential performance issues related to the Python interpreter.</p></li>
</ul>
</div>
<div class="section" id="Hybrid-programming-provides-the-best-of-both-worlds.">
<h2>Hybrid programming provides the best of both worlds.<a class="headerlink" href="#Hybrid-programming-provides-the-best-of-both-worlds." title="Permalink to this headline"></a></h2>
<p>Most deep learning frameworks choose either imperative or symbolic programming. For example, both Theano and TensorFlow (inspired by the latter) make use of symbolic programming, while Chainer and its predecessor PyTorch utilize imperative programming. When designing Gluon, developers considered whether it was possible to harness the benefits of both imperative and symbolic programming. The developers believed that users should be able to develop and debug using pure imperative programming,
while having the ability to convert most programs into symbolic programming to be run when product-level computing performance and deployment are required This was achieved by Gluon through the introduction of hybrid programming.</p>
<p>In hybrid programming, we can build models using either the HybridBlock or the HybridSequential classes. By default, they are executed in the same way Block or Sequential classes are executed in imperative programming. When the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function is called, Gluon will convert the program’s execution into the style used in symbolic programming. In fact, most models can make use of hybrid programming’s execution style.</p>
<p>Through the use of experiments, this section will demonstrate the benefits of hybrid programming.</p>
</div>
<div class="section" id="Constructing-Models-Using-the-HybridSequential-Class">
<h2>Constructing Models Using the HybridSequential Class<a class="headerlink" href="#Constructing-Models-Using-the-HybridSequential-Class" title="Permalink to this headline"></a></h2>
<p>Previously, we learned how to use the Sequential class to concatenate multiple layers. Next, we will replace the Sequential class with the HybridSequential class in order to make use of hybrid programming.</p>
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<span></span><span class="kn">from</span> <span class="nn">mxnet</span> <span class="kn">import</span> <span class="n">nd</span><span class="p">,</span> <span class="n">sym</span>
<span class="kn">from</span> <span class="nn">mxnet.gluon</span> <span class="kn">import</span> <span class="n">nn</span>
<span class="kn">import</span> <span class="nn">time</span>
<span class="k">def</span> <span class="nf">get_net</span><span class="p">():</span>
<span class="n">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">HybridSequential</span><span class="p">()</span> <span class="c1"># Here we use the class HybridSequential.</span>
<span class="n">net</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">256</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">),</span>
<span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">128</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">),</span>
<span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">2</span><span class="p">))</span>
<span class="n">net</span><span class="o">.</span><span class="n">initialize</span><span class="p">()</span>
<span class="k">return</span> <span class="n">net</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">nd</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">512</span><span class="p">))</span>
<span class="n">net</span> <span class="o">=</span> <span class="n">get_net</span><span class="p">()</span>
<span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
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</div>
</div>
<p>By calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function, we are able to compile and optimize the computation of the concatenation layer in the HybridSequential instance. The model’s computation result remains unchanged.</p>
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<span></span><span class="n">net</span><span class="o">.</span><span class="n">hybridize</span><span class="p">()</span>
<span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>It should be noted that only the layers inheriting the HybridBlock class will be optimized during computation. For example, the HybridSequential and <code class="docutils literal notranslate"><span class="pre">Dense</span></code> classes provided by Gluon are all subclasses of HybridBlock class, meaning they will both be optimized during computation. A layer will not be optimized if it inherits from the Block class rather than the HybridBlock class.</p>
<div class="section" id="Computing-Performance">
<h3>Computing Performance<a class="headerlink" href="#Computing-Performance" title="Permalink to this headline"></a></h3>
<p>To demonstrate the performance improvement gained by the use of symbolic programming, we will compare the computation time before and after calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function. Here we time 1000 <code class="docutils literal notranslate"><span class="pre">net</span></code> model computations. The model computations are based on imperative and symbolic programming, respectively, before and after <code class="docutils literal notranslate"><span class="pre">net</span></code> has called the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function.</p>
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<span></span><span class="k">def</span> <span class="nf">benchmark</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000</span><span class="p">):</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">nd</span><span class="o">.</span><span class="n">waitall</span><span class="p">()</span> <span class="c1"># To facilitate timing, we wait for all computations to be completed.</span>
<span class="k">return</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start</span>
<span class="n">net</span> <span class="o">=</span> <span class="n">get_net</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;before hybridizing: </span><span class="si">%.4f</span><span class="s1"> sec&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">benchmark</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">x</span><span class="p">)))</span>
<span class="n">net</span><span class="o">.</span><span class="n">hybridize</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;after hybridizing: </span><span class="si">%.4f</span><span class="s1"> sec&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">benchmark</span><span class="p">(</span><span class="n">net</span><span class="p">,</span> <span class="n">x</span><span class="p">)))</span>
</pre></div>
</div>
</div>
<p>As is observed in the above results, after a HybridSequential instance calls the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function, computing performance is improved through the use of symbolic programming.</p>
</div>
<div class="section" id="Achieving-Symbolic-Programming">
<h3>Achieving Symbolic Programming<a class="headerlink" href="#Achieving-Symbolic-Programming" title="Permalink to this headline"></a></h3>
<p>We can save the symbolic program and model parameters to the hard disk through the use of the <code class="docutils literal notranslate"><span class="pre">export</span></code> function after the <code class="docutils literal notranslate"><span class="pre">net</span></code> model has finished computing the output based on the input, such as in the case of <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> in the <code class="docutils literal notranslate"><span class="pre">benchmark</span></code> function.</p>
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<span></span><span class="n">net</span><span class="o">.</span><span class="n">export</span><span class="p">(</span><span class="s1">&#39;my_mlp&#39;</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>The .json and .params files generated during this process are a symbolic program and a model parameter, respectively. They can be read by other front-end languages supported by Python or MXNet, such as C++, R, Scala, and Perl. This allows us to deploy trained models to other devices and easily use other front-end programming languages. At the same time, because symbolic programming was used during deployment, the computing performance is often superior to that based on imperative programming.</p>
<p>In MXNet, a symbolic program refers to a program that makes use of the Symbol type. We know that, when the NDArray input <code class="docutils literal notranslate"><span class="pre">x</span></code> is provided to <code class="docutils literal notranslate"><span class="pre">net</span></code>, <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> will directly calculate the model output and return a result based on <code class="docutils literal notranslate"><span class="pre">x</span></code>. For models that have called the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function, we can also provide a Symbol-type input variable, and <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> will return Symbol type results.</p>
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<span></span><span class="n">x</span> <span class="o">=</span> <span class="n">sym</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="s1">&#39;data&#39;</span><span class="p">)</span>
<span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="section" id="Constructing-Models-Using-the-HybridBlock-Class">
<h2>Constructing Models Using the HybridBlock Class<a class="headerlink" href="#Constructing-Models-Using-the-HybridBlock-Class" title="Permalink to this headline"></a></h2>
<p>Similar to the correlation between the Sequential Block classes, the HybridSequential class is a HybridBlock subclass. Contrary to the Block instance, which needs to use the <code class="docutils literal notranslate"><span class="pre">forward</span></code> function, for a HybridBlock instance we need to use the <code class="docutils literal notranslate"><span class="pre">hybrid_forward</span></code> function.</p>
<p>Earlier, we demonstrated that, after calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function, the model is able to achieve superior computing performance and portability. In addition, model flexibility can be affected after calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function. We will demonstrate this by constructing a model using the HybridBlock class.</p>
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<span></span><span class="k">class</span> <span class="nc">HybridNet</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">HybridBlock</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="nb">super</span><span class="p">(</span><span class="n">HybridNet</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">hidden</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">output</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">hybrid_forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;F: &#39;</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;x: &#39;</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">F</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">hidden</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;hidden: &#39;</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">output</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
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</div>
</div>
<p>We need to add the additional input <code class="docutils literal notranslate"><span class="pre">F</span></code> to the <code class="docutils literal notranslate"><span class="pre">hybrid_forward</span></code> function when inheriting the HybridBlock class. We already know that MXNet uses both an NDArray class and a Symbol class, which are based on imperative programming and symbolic programming, respectively. Since these two classes perform very similar functions, MXNet will determine whether <code class="docutils literal notranslate"><span class="pre">F</span></code> will call NDArray or Symbol based on the input provided.</p>
<p>The following creates a HybridBlock instance. As we can see, by default, <code class="docutils literal notranslate"><span class="pre">F</span></code> uses NDArray. We also printed out the <code class="docutils literal notranslate"><span class="pre">x</span></code> input as well as the hidden layer’s output using the ReLU activation function.</p>
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<span></span><span class="n">net</span> <span class="o">=</span> <span class="n">HybridNet</span><span class="p">()</span>
<span class="n">net</span><span class="o">.</span><span class="n">initialize</span><span class="p">()</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">nd</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
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</div>
</div>
<p>Repeating the forward computation will achieve the same results.</p>
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<span></span><span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
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<p>Next, we will see what happens after we call the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function.</p>
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<span></span><span class="n">net</span><span class="o">.</span><span class="n">hybridize</span><span class="p">()</span>
<span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>We can see that <code class="docutils literal notranslate"><span class="pre">F</span></code> turns into a Symbol. Moreover, even though the input data is still NDArray, the same input and intermediate output will all be converted to Symbol type in the <code class="docutils literal notranslate"><span class="pre">hybrid_forward</span></code> function.</p>
<p>Now, we repeat the forward computation.</p>
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<div class="input_area highlight-python notranslate"><div class="highlight"><pre>
<span></span><span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>We can see that the three lines of print statements defined in the <code class="docutils literal notranslate"><span class="pre">hybrid_forward</span></code> function will not print anything. This is because a symbolic program has been produced since the last time <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> was run by calling the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function. Afterwards, when we run <code class="docutils literal notranslate"><span class="pre">net(x)</span></code> again, MXNet will no longer need to access Python code, but can directly perform symbolic programming at the C++ backend. This is another reason why model computing performance will be improve after the
<code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function is called. However, there is always the potential that any programs we write will suffer a loss in flexibility. If we want to use the three lines of print statements to debug the code in the above example, they will be skipped over and we would not be able to print when the symbolic program is executed. Additionally, in the case of a few functions not supported by Symbol (like <code class="docutils literal notranslate"><span class="pre">asnumpy</span></code>), and operations in-place like <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">+=</span> <span class="pre">b</span></code> and <code class="docutils literal notranslate"><span class="pre">a[:]</span> <span class="pre">=</span> <span class="pre">a</span> <span class="pre">+</span> <span class="pre">b</span></code> (must be rewritten as
<code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">=</span> <span class="pre">a</span> <span class="pre">+</span> <span class="pre">b</span></code>). Therefore, we will not be able to use the <code class="docutils literal notranslate"><span class="pre">hybrid_forward</span></code> function or perform forward computation after the <code class="docutils literal notranslate"><span class="pre">hybridize</span></code> function has been called.</p>
</div>
<div class="section" id="Key-differences-and-limitations-of-hybridization">
<h2>Key differences and limitations of hybridization<a class="headerlink" href="#Key-differences-and-limitations-of-hybridization" title="Permalink to this headline"></a></h2>
<p>The difference between a purely imperative <code class="docutils literal notranslate"><span class="pre">Block</span></code> and hybridizable <code class="docutils literal notranslate"><span class="pre">HybridBlock</span></code> can superficially appear to be simply the injection of the <code class="docutils literal notranslate"><span class="pre">F</span></code> function space (resolving to <a class="reference external" href="/api/python/docs/api/ndarray/index.html">mx.nd</a> or <a class="reference external" href="/api/python/docs/api/symbol/index.html">mx.sym</a>) in the forward function that is renamed from <code class="docutils literal notranslate"><span class="pre">forward</span></code> to <code class="docutils literal notranslate"><span class="pre">hybrid_forward</span></code>. However there are some limitations that apply when using hybrid blocks. In the following section we will review the main
differences, giving example of code snippets that generate errors when such blocks get hybridized.</p>
<div class="section" id="Indexing">
<h3>Indexing<a class="headerlink" href="#Indexing" title="Permalink to this headline"></a></h3>
<p>When trying to access specific elements in a tensor like this:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hybrid_forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span>
</pre></div>
</div>
<p>Would generate the following error:</p>
<p><code class="docutils literal notranslate"><span class="pre">TypeError:</span> <span class="pre">Symbol</span> <span class="pre">only</span> <span class="pre">support</span> <span class="pre">integer</span> <span class="pre">index</span> <span class="pre">to</span> <span class="pre">fetch</span> <span class="pre">i-th</span> <span class="pre">output</span></code></p>
<p>There are however several operators that can help you with array manipulations like: <a class="reference external" href="/api/python/docs/api/ndarray/ndarray.html#mxnet.ndarray.split">F.split</a>, <a class="reference external" href="/api/python/docs/api/ndarray/ndarray.html#mxnet.ndarray.slice">F.slice</a>, <a class="reference external" href="/api/python/docs/api/ndarray/ndarray.html#mxnet.ndarray.take">F.take</a>,<a class="reference external" href="/api/python/docs/api/ndarray/ndarray.html#mxnet.ndarray.pick">F.pick</a>, <a class="reference external" href="/api/python/docs/api/ndarray/ndarray.html#mxnet.ndarray.where">F.where</a>,
<a class="reference external" href="/api/python/docs/api/ndarray/ndarray.html#mxnet.ndarray.reshape">F.reshape</a> or <a class="reference external" href="/api/python/docs/api/ndarray/ndarray.html#mxnet.ndarray.reshape_like">F.reshape_like</a>.</p>
</div>
<div class="section" id="Data-Type">
<h3>Data Type<a class="headerlink" href="#Data-Type" title="Permalink to this headline"></a></h3>
<p>Sometimes one can be tempted to use conditional logic on the type of the input tensors however the following block:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hybrid_forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">dtype</span> <span class="o">==</span><span class="s1">&#39;float16&#39;</span><span class="p">:</span>
<span class="k">return</span> <span class="n">x</span>
<span class="k">return</span> <span class="n">x</span><span class="o">*</span><span class="mi">2</span>
</pre></div>
</div>
<p>Would generate a <code class="docutils literal notranslate"><span class="pre">AttributeError:</span> <span class="pre">'Symbol'</span> <span class="pre">object</span> <span class="pre">has</span> <span class="pre">no</span> <span class="pre">attribute</span> <span class="pre">'dtype'</span></code></p>
<p>You cannot use the <code class="docutils literal notranslate"><span class="pre">dtype</span></code> of the symbol at runtime. Symbols only describe operations and not the underlying data they operate on. One workaround is to pass the type as a constructor argument of your network and hence build the appropriate compute graph for each situation.</p>
</div>
<div class="section" id="Compute-Context">
<h3>Compute Context<a class="headerlink" href="#Compute-Context" title="Permalink to this headline"></a></h3>
<p>Similarly you cannot use the compute context of symbol for the same reason that symbols only describe the operations on the data and not the data (or context). You cannot do this:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hybrid_forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">context</span> <span class="o">==</span> <span class="n">mx</span><span class="o">.</span><span class="n">cpu</span><span class="p">():</span>
<span class="k">return</span> <span class="n">x</span>
<span class="k">return</span> <span class="n">x</span><span class="o">*</span><span class="mi">2</span>
</pre></div>
</div>
<p>Without getting a <code class="docutils literal notranslate"><span class="pre">AttributeError:</span> <span class="pre">'Symbol'</span> <span class="pre">object</span> <span class="pre">has</span> <span class="pre">no</span> <span class="pre">attribute</span> <span class="pre">'context'</span></code></p>
<p>Accessing the current compute context is not possible with symbols. Consider passing this information in the constructor if you require it to create the appropriate compute graph.</p>
</div>
<div class="section" id="Shape">
<h3>Shape<a class="headerlink" href="#Shape" title="Permalink to this headline"></a></h3>
<p>Accessing shape information of tensors is very often used for example when trying to flatten a tensor and then reshape it back to its original shape.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hybrid_forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
</pre></div>
</div>
<p>Trying to access the shape of a tensor in a hybridized block would result in this error: <code class="docutils literal notranslate"><span class="pre">AttributeError:</span> <span class="pre">'Symbol'</span> <span class="pre">object</span> <span class="pre">has</span> <span class="pre">no</span> <span class="pre">attribute</span> <span class="pre">'shape'</span></code>.</p>
<p>Again, you cannot use the shape of the symbol at runtime as symbols only describe operations and not the underlying data they operate on. Note: This will change in the future as Apache MXNet will support <a class="reference external" href="https://cwiki.apache.org/confluence/display/MXNET/Dynamic+shape">dynamic shape inference</a>, and the shapes of symbols will be symbols themselves</p>
<p>There are also a lot of operators that support special indices to help with most of the use-cases where you would want to access the shape information. For example, <code class="docutils literal notranslate"><span class="pre">F.reshape(x,</span> <span class="pre">(0,0,-1))</span></code> will keep the first two dimensions unchanged and collapse all further dimensions into the third dimension. See the documentation of the <a class="reference external" href="/api/python/docs/api/ndarray/ndarray.html#mxnet.ndarray.reshape">F.reshape</a> for more details.</p>
</div>
<div class="section" id="Item-assignment">
<h3>Item assignment<a class="headerlink" href="#Item-assignment" title="Permalink to this headline"></a></h3>
<p>Last but not least, you cannot directly assign values in tensor in a symbolic graph, the resulting tensors always needs to be the results of operations performed on the inputs of the computational graph. The following code:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hybrid_forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">2</span>
<span class="k">return</span> <span class="n">x</span>
</pre></div>
</div>
<p>Would get you this error <code class="docutils literal notranslate"><span class="pre">TypeError:</span> <span class="pre">'Symbol'</span> <span class="pre">object</span> <span class="pre">does</span> <span class="pre">not</span> <span class="pre">support</span> <span class="pre">item</span> <span class="pre">assignment</span></code>.</p>
<p>Direct item assignment is not possible in symbolic graph since it needs to be part of a computational graph. One way is to use add more inputs to your graph and use masking or the <a class="reference external" href="/api/python/docs/api/ndarray/ndarray.html#mxnet.ndarray.where">F.where</a> operator.</p>
<p>e.g to set the first element to 2 you can do:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
<span class="n">value</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">*</span><span class="mi">2</span>
<span class="n">condition</span> <span class="o">=</span> <span class="n">mx</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
<span class="n">mx</span><span class="o">.</span><span class="n">nd</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">condition</span><span class="o">=</span><span class="n">condition</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="n">value</span><span class="p">)</span>
</pre></div>
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<span class="caption-text">Table Of Contents</span>
</p>
<ul>
<li><a class="reference internal" href="#">Hybridize</a><ul>
<li><a class="reference internal" href="#A-Hybrid-of-Imperative-and-Symbolic-Programming">A Hybrid of Imperative and Symbolic Programming</a></li>
<li><a class="reference internal" href="#Hybrid-programming-provides-the-best-of-both-worlds.">Hybrid programming provides the best of both worlds.</a></li>
<li><a class="reference internal" href="#Constructing-Models-Using-the-HybridSequential-Class">Constructing Models Using the HybridSequential Class</a><ul>
<li><a class="reference internal" href="#Computing-Performance">Computing Performance</a></li>
<li><a class="reference internal" href="#Achieving-Symbolic-Programming">Achieving Symbolic Programming</a></li>
</ul>
</li>
<li><a class="reference internal" href="#Constructing-Models-Using-the-HybridBlock-Class">Constructing Models Using the HybridBlock Class</a></li>
<li><a class="reference internal" href="#Key-differences-and-limitations-of-hybridization">Key differences and limitations of hybridization</a><ul>
<li><a class="reference internal" href="#Indexing">Indexing</a></li>
<li><a class="reference internal" href="#Data-Type">Data Type</a></li>
<li><a class="reference internal" href="#Compute-Context">Compute Context</a></li>
<li><a class="reference internal" href="#Shape">Shape</a></li>
<li><a class="reference internal" href="#Item-assignment">Item assignment</a></li>
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