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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>
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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="../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-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-l3"><a class="reference internal" href="../../autograd/index.html">Automatic Differentiation</a></li>
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<li class="toctree-l4 current"><a class="reference internal" href="index.html">Blocks</a><ul class="current">
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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="Layers-and-Blocks">
<h1>Layers and Blocks<a class="headerlink" href="#Layers-and-Blocks" title="Permalink to this headline"></a></h1>
<!-- adapted from diveintodeeplearning --><p>As network complexity increases, we move from designing single to entire layers of neurons.</p>
<p>Neural network designs like <a class="reference external" href="https://www.cv-foundation.org/openaccess/content_cvpr_2016/papers/He_Deep_Residual_Learning_CVPR_2016_paper.pdf">ResNet-152</a> have a fair degree of regularity. They consist of <em>blocks</em> of repeated (or at least similarly designed) layers; these blocks then form the basis of more complex network designs.</p>
<p>In this section, we’ll talk about how to write code that makes such blocks on demand, just like a Lego factory generates blocks which can be combined to produce terrific artifacts.</p>
<p>We start with a very simple block, namely the block for a multilayer perceptron. A common strategy would be to construct a two-layer network as follows:</p>
<div class="nbinput nblast docutils container">
<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[1]:
</pre></div>
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<div class="input_area highlight-python notranslate"><div class="highlight"><pre>
<span></span><span class="kn">from</span> <span class="nn">mxnet</span> <span class="kn">import</span> <span class="n">nd</span>
<span class="kn">from</span> <span class="nn">mxnet.gluon</span> <span class="kn">import</span> <span class="n">nn</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">uniform</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">20</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">Sequential</span><span class="p">()</span>
<span class="n">net</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">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">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">10</span><span class="p">))</span>
<span class="n">net</span><span class="o">.</span><span class="n">initialize</span><span class="p">()</span>
<span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>This generates a network with a hidden layer of <span class="math notranslate nohighlight">\(256\)</span> units, followed by a ReLU activation and another <span class="math notranslate nohighlight">\(10\)</span> units governing the output. In particular, we used the <a class="reference external" href="/api/python/docs/api/gluon/nn/index.html#mxnet.gluon.nn.Sequential">nn.Sequential</a> constructor to generate an empty network into which we then inserted both layers. What exactly happens inside <code class="docutils literal notranslate"><span class="pre">nn.Sequential</span></code> has remained rather mysterious so far. In the following we will see that this really just constructs a block
that is a container for other blocks. These blocks can be combined into larger artifacts, often recursively. The diagram below shows how:</p>
<img alt="Blocks can be used recursively to form larger artifacts" src="tutorials/packages/gluon/blocks/blocks.svg" /><p>In the following we will explain the various steps needed to go from defining layers to defining blocks (of one or more layers):</p>
<ol class="arabic simple">
<li><p>Blocks take data as input.</p></li>
<li><p>Blocks store state in the form of parameters that are inherent to the block. For instance, the block above contains two hidden layers, and we need a place to store parameters for it.</p></li>
<li><p>Blocks produce meaningful output. This is typically encoded in what we will call the <code class="docutils literal notranslate"><span class="pre">forward</span></code> function. It allows us to invoke a block via <code class="docutils literal notranslate"><span class="pre">net(X)</span></code> to obtain the desired output. What happens behind the scenes is that it invokes <code class="docutils literal notranslate"><span class="pre">forward</span></code> to perform forward propagation (also called forward computation).</p></li>
<li><p>Blocks initialize the parameters in a lazy fashion as part of the first <code class="docutils literal notranslate"><span class="pre">forward</span></code> call.</p></li>
<li><p>Blocks calculate a gradient with regard to their input when invoking <code class="docutils literal notranslate"><span class="pre">backward</span></code>. Typically this is automatic.</p></li>
</ol>
<div class="section" id="A-Sequential-Block">
<h2>A Sequential Block<a class="headerlink" href="#A-Sequential-Block" title="Permalink to this headline"></a></h2>
<p>The <a class="reference external" href="/api/python/docs/api/gluon/nn/index.html#mxnet.gluon.nn.Block">Block</a> class is a generic component describing data flow. When the data flows through a sequence of blocks, each block applied to the output of the one before with the first block being applied on the input data itself, we have a special kind of block, namely the <code class="docutils literal notranslate"><span class="pre">Sequential</span></code> block.</p>
<p><code class="docutils literal notranslate"><span class="pre">Sequential</span></code> has helper methods to manage the sequence, with <code class="docutils literal notranslate"><span class="pre">add</span></code> being the main one of interest allowing you to append blocks in sequence. Once the operations have been added, the forward computation of the model applies the blocks on the input data in the order they were added. Below, we implement a <code class="docutils literal notranslate"><span class="pre">MySequential</span></code> class that has the same functionality as the <code class="docutils literal notranslate"><span class="pre">Sequential</span></code> class. This may help you understand more clearly how the <code class="docutils literal notranslate"><span class="pre">Sequential</span></code> class works.</p>
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<span></span><span class="k">class</span> <span class="nc">MySequential</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Block</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">MySequential</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="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">block</span><span class="p">):</span>
<span class="c1"># Here, block is an instance of a Block subclass, and we assume it has a unique name. We save it in the</span>
<span class="c1"># member variable _children of the Block class, and its type is OrderedDict. When the MySequential instance</span>
<span class="c1"># calls the initialize function, the system automatically initializes all members of _children.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_children</span><span class="p">[</span><span class="n">block</span><span class="o">.</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">block</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="c1"># OrderedDict guarantees that members will be traversed in the order they were added.</span>
<span class="k">for</span> <span class="n">block</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_children</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">block</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="k">return</span> <span class="n">x</span>
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</div>
</div>
<p>At its core is the <code class="docutils literal notranslate"><span class="pre">add</span></code> method. It adds any block to the ordered dictionary of children. These are then executed in sequence when forward propagation is invoked. Let’s see what the MLP looks like now.</p>
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<span></span><span class="n">net</span> <span class="o">=</span> <span class="n">MySequential</span><span class="p">()</span>
<span class="n">net</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">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">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">10</span><span class="p">))</span>
<span class="n">net</span><span class="o">.</span><span class="n">initialize</span><span class="p">()</span>
<span class="n">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>Indeed, it is no different than It can observed here that the use of the <code class="docutils literal notranslate"><span class="pre">MySequential</span></code> class is no different from the use of the Sequential class.</p>
</div>
<div class="section" id="A-Custom-Block">
<h2>A Custom Block<a class="headerlink" href="#A-Custom-Block" title="Permalink to this headline"></a></h2>
<p>It is easy to go beyond simple concatenation with <code class="docutils literal notranslate"><span class="pre">Sequential</span></code>. The <code class="docutils literal notranslate"><span class="pre">Block</span></code> class provides the functionality required to make such customizations. <code class="docutils literal notranslate"><span class="pre">Block</span></code> has a model constructor provided in the <code class="docutils literal notranslate"><span class="pre">nn</span></code> module, which we can inherit to define the model we want. The following inherits the <code class="docutils literal notranslate"><span class="pre">Block</span></code> class to construct the multilayer perceptron mentioned at the beginning of this section. The <code class="docutils literal notranslate"><span class="pre">MLP</span></code> class defined here overrides the <code class="docutils literal notranslate"><span class="pre">__init__</span></code> and <code class="docutils literal notranslate"><span class="pre">forward</span></code> functions of the Block class. They
are used to create model parameters and define forward computations, respectively. Forward computation is also forward propagation.</p>
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<span></span><span class="k">class</span> <span class="nc">MLP</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Block</span><span class="p">):</span>
<span class="c1"># Declare a layer with model parameters. Here, we declare two fully</span>
<span class="c1"># connected layers.</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="c1"># Call the constructor of the MLP parent class Block to perform the</span>
<span class="c1"># necessary initialization. In this way, other function parameters can</span>
<span class="c1"># also be specified when constructing an instance, such as the model</span>
<span class="c1"># parameter, params, described in the following sections.</span>
<span class="nb">super</span><span class="p">(</span><span class="n">MLP</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">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="c1"># Hidden layer</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">10</span><span class="p">)</span> <span class="c1"># Output layer</span>
<span class="c1"># Define the forward computation of the model, that is, how to return the</span>
<span class="c1"># required model output based on the input x.</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">hidden_out</span> <span class="o">=</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="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">output</span><span class="p">(</span><span class="n">hidden_out</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>Let’s look at it a bit more closely. The <code class="docutils literal notranslate"><span class="pre">forward</span></code> method invokes a network simply by evaluating the hidden layer <code class="docutils literal notranslate"><span class="pre">self.hidden(x)</span></code> and subsequently by evaluating the output layer <code class="docutils literal notranslate"><span class="pre">self.output(</span> <span class="pre">...</span> <span class="pre">)</span></code>. This is what we expect in the forward pass of this block.</p>
<p>In order for the block to know what it needs to evaluate, we first need to define the layers. This is what the <code class="docutils literal notranslate"><span class="pre">__init__</span></code> method does. It first initializes all of the Block-related parameters and then constructs the requisite layers. This attaches the coresponding layers and the required parameters to the class. Note that there is no need to define a backpropagation method in the class. The system automatically generates the <code class="docutils literal notranslate"><span class="pre">backward</span></code> method needed for back propagation by automatically
finding the gradient (see the tutorial on <a class="reference external" href="/api/python/docs/tutorials/packages/autograd/index.html">autograd</a>). The same applies to the <a class="reference external" href="/api/python/docs/api/gluon/nn/index.html#mxnet.gluon.nn.Block.initialize">initialize</a> method, which is generated automatically. Let’s try this out:</p>
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<span></span><span class="n">net</span> <span class="o">=</span> <span class="n">MLP</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">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>As explained above, the <code class="docutils literal notranslate"><span class="pre">Block</span></code> class can be quite versatile in terms of what it does. For instance, its subclass can be a layer (such as the <code class="docutils literal notranslate"><span class="pre">Dense</span></code> class provided by Gluon), it can be a model (such as the <code class="docutils literal notranslate"><span class="pre">MLP</span></code> class we just derived), or it can be a part of a model (this is what typically happens when designing very deep networks). Throughout this chapter we will see how to use this with great flexibility.</p>
</div>
<div class="section" id="Coding-with-Blocks">
<h2>Coding with <code class="docutils literal notranslate"><span class="pre">Blocks</span></code><a class="headerlink" href="#Coding-with-Blocks" title="Permalink to this headline"></a></h2>
<div class="section" id="Blocks">
<h3>Blocks<a class="headerlink" href="#Blocks" title="Permalink to this headline"></a></h3>
<p>The <a class="reference external" href="/api/python/docs/api/gluon/nn/index.html#mxnet.gluon.nn.Sequential">Sequential</a> class can make model construction easier and does not require you to define the <code class="docutils literal notranslate"><span class="pre">forward</span></code> method; however, directly inheriting from its parent class, <a class="reference external" href="/api/python/docs/api/gluon/nn/index.html#mxnet.gluon.nn.Block">Block</a>, can greatly expand the flexibility of model construction. For example, implementing the <code class="docutils literal notranslate"><span class="pre">forward</span></code> method means you can introduce control flow in the network.</p>
</div>
<div class="section" id="Constant-parameters">
<h3>Constant parameters<a class="headerlink" href="#Constant-parameters" title="Permalink to this headline"></a></h3>
<p>Now we’d like to introduce the notation of a <em>constant</em> parameter. These are parameters that are not used when invoking backpropagation. This sounds very abstract but here’s what’s really going on. Assume that we have some function</p>
<div class="math notranslate nohighlight">
\[f(\mathbf{x},\mathbf{w}) = 3 \cdot \mathbf{w}^\top \mathbf{x}.\]</div>
<p>In this case <span class="math notranslate nohighlight">\(3\)</span> is a constant parameter. We could change <span class="math notranslate nohighlight">\(3\)</span> to something else, say <span class="math notranslate nohighlight">\(c\)</span> via</p>
<div class="math notranslate nohighlight">
\[f(\mathbf{x},\mathbf{w}) = c \cdot \mathbf{w}^\top \mathbf{x}.\]</div>
<p>Nothing has really changed, except that we can adjust the value of <span class="math notranslate nohighlight">\(c\)</span>. It is still a constant as far as <span class="math notranslate nohighlight">\(\mathbf{w}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{x}\)</span> are concerned. However, Gluon doesn’t know about this unless we create it with <code class="docutils literal notranslate"><span class="pre">get_constant</span></code> (this makes the code go faster, too, since we’re not sending the Gluon engine on a wild goose chase after a parameter that doesn’t change).</p>
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<span></span><span class="k">class</span> <span class="nc">FancyMLP</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Block</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">FancyMLP</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="c1"># Random weight parameters created with the get_constant are not</span>
<span class="c1"># iterated during training (i.e. constant parameters).</span>
<span class="bp">self</span><span class="o">.</span><span class="n">rand_weight</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="o">.</span><span class="n">get_constant</span><span class="p">(</span>
<span class="s1">&#39;rand_weight&#39;</span><span class="p">,</span> <span class="n">nd</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">20</span><span class="p">)))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">dense</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">20</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="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">x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="c1"># Use the constant parameters created, as well as the ReLU and dot</span>
<span class="c1"># functions of NDArray.</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">nd</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">nd</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">rand_weight</span><span class="o">.</span><span class="n">data</span><span class="p">())</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="c1"># Re-use the fully connected layer. This is equivalent to sharing</span>
<span class="c1"># parameters with two fully connected layers.</span>
<span class="n">x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="c1"># Here in the control flow, we need to call `asscalar` to return the</span>
<span class="c1"># scalar for comparison.</span>
<span class="k">while</span> <span class="n">x</span><span class="o">.</span><span class="n">norm</span><span class="p">()</span><span class="o">.</span><span class="n">asscalar</span><span class="p">()</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">x</span> <span class="o">/=</span> <span class="mi">2</span>
<span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">norm</span><span class="p">()</span><span class="o">.</span><span class="n">asscalar</span><span class="p">()</span> <span class="o">&lt;</span> <span class="mf">0.8</span><span class="p">:</span>
<span class="n">x</span> <span class="o">*=</span> <span class="mi">10</span>
<span class="k">return</span> <span class="n">x</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
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</div>
</div>
<p>In this <code class="docutils literal notranslate"><span class="pre">FancyMLP</span></code> model, we used constant weight <code class="docutils literal notranslate"><span class="pre">rand_weight</span></code> (note that it is not a model parameter), performed a matrix multiplication operation (<code class="docutils literal notranslate"><span class="pre">nd.dot</span></code>), and reused the <em>same</em> <code class="docutils literal notranslate"><span class="pre">Dense</span></code> layer. Note that this is very different from using two dense layers with different sets of parameters. Instead, we used the same network twice. Quite often in deep networks one also says that the parameters are <em>tied</em> when one wants to express that multiple parts of a network share the same
parameters. Let’s see what happens if we construct it and feed data through it.</p>
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<span></span><span class="n">net</span> <span class="o">=</span> <span class="n">FancyMLP</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">net</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
<p>There’s no reason why we couldn’t mix and match these ways of building a network. Obviously the example below resembles a <a class="reference external" href="https://en.wikipedia.org/wiki/Rube_Goldberg_machine">Rube Goldberg Machine</a>. That said, it combines examples for building a block from individual blocks, which in turn, may be blocks themselves. Furthermore, we can even combine multiple strategies inside the same forward function. To demonstrate this, here’s the network.</p>
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<span></span><span class="k">class</span> <span class="nc">NestMLP</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Block</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">NestMLP</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">net</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</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">64</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">32</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="bp">self</span><span class="o">.</span><span class="n">dense</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">16</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="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="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="bp">self</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">chimera</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">()</span>
<span class="n">chimera</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">NestMLP</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">20</span><span class="p">),</span> <span class="n">FancyMLP</span><span class="p">())</span>
<span class="n">chimera</span><span class="o">.</span><span class="n">initialize</span><span class="p">()</span>
<span class="n">chimera</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
<div class="section" id="Hybridization">
<h2>Hybridization<a class="headerlink" href="#Hybridization" title="Permalink to this headline"></a></h2>
<p>The reader may be starting to think about the efficiency of this Python code. After all, we have lots of dictionary lookups, code execution, and lots of other Pythonic things going on in what is supposed to be a high performance deep learning library. The problems of Python’s <a class="reference external" href="https://wiki.python.org/moin/GlobalInterpreterLock">Global Interpreter Lock</a> are well known.</p>
<p>In the context of deep learning, we often have highly performant GPUs that depend on CPUs running Python to tell them what to do. This mismatch can manifest in the form of GPU starvation when the CPUs can not provide instruction fast enough. We can improve this situation by deferring to a more performant language instead of Python when possible.</p>
<p>Gluon does this by allowing for <a class="reference external" href="hybridize.html">Hybridization</a>. In it, the Python interpreter executes the block the first time it’s invoked. The Gluon runtime records what is happening and the next time around it short circuits any calls to Python. This can accelerate things considerably in some cases but care needs to be taken with <a class="reference external" href="/api/python/docs/tutorials/packages/autograd/index.html#Advanced:-Using-Python-control-flow">control flow</a>.</p>
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<ul>
<li><a class="reference internal" href="#">Layers and Blocks</a><ul>
<li><a class="reference internal" href="#A-Sequential-Block">A Sequential Block</a></li>
<li><a class="reference internal" href="#A-Custom-Block">A Custom Block</a></li>
<li><a class="reference internal" href="#Coding-with-Blocks">Coding with <code class="docutils literal notranslate"><span class="pre">Blocks</span></code></a><ul>
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<li><a class="reference internal" href="#Constant-parameters">Constant parameters</a></li>
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