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| <p><a id='Digit-Recognition-on-MNIST-1'></a></p> |
| <h1 id="digit-recognition-on-mnist">Digit Recognition on MNIST</h1> |
| <p>In this tutorial, we will work through examples of training a simple multi-layer perceptron and then a convolutional neural network (the LeNet architecture) on the <a href="http://yann.lecun.com/exdb/mnist/">MNIST handwritten digit dataset</a>. The code for this tutorial could be found in <a href="https://github.com/apache/incubator-mxnet/tree/master/julia/examples/mnist">examples/mnist</a>. There are also two Jupyter notebooks that expand a little more on the <a href="https://github.com/ultradian/julia_notebooks/blob/master/mxnet/mnistMLP.ipynb">MLP</a> and the <a href="https://github.com/ultradian/julia_notebooks/blob/master/mxnet/mnistLenet.ipynb">LeNet</a>, using the more general <code>ArrayDataProvider</code>. </p> |
| <p><a id='Simple-3-layer-MLP-1'></a></p> |
| <h2 id="simple-3-layer-mlp">Simple 3-layer MLP</h2> |
| <p>This is a tiny 3-layer MLP that could be easily trained on CPU. The script starts with</p> |
| <pre><code class="julia">using MXNet |
| </code></pre> |
| |
| <p>to load the <code>MXNet</code> module. Then we are ready to define the network architecture via the <a href="/api/julia/docs/api/user-guide/overview/">symbolic API</a>. We start with a placeholder <code>data</code> symbol,</p> |
| <pre><code class="julia">data = mx.Variable(:data) |
| </code></pre> |
| |
| <p>and then cascading fully-connected layers and activation functions:</p> |
| <pre><code class="julia">fc1 = mx.FullyConnected(data, name=:fc1, num_hidden=128) |
| act1 = mx.Activation(fc1, name=:relu1, act_type=:relu) |
| fc2 = mx.FullyConnected(act1, name=:fc2, num_hidden=64) |
| act2 = mx.Activation(fc2, name=:relu2, act_type=:relu) |
| fc3 = mx.FullyConnected(act2, name=:fc3, num_hidden=10) |
| </code></pre> |
| |
| <p>Note each composition we take the previous symbol as the first argument, forming a feedforward chain. The architecture looks like</p> |
| <pre><code>Input --> 128 units (ReLU) --> 64 units (ReLU) --> 10 units |
| </code></pre> |
| |
| <p>where the last 10 units correspond to the 10 output classes (digits 0,...,9). We then add a final <code>SoftmaxOutput</code> operation to turn the 10-dimensional prediction to proper probability values for the 10 classes:</p> |
| <pre><code class="julia">mlp = mx.SoftmaxOutput(fc3, name=:softmax) |
| </code></pre> |
| |
| <p>As we can see, the MLP is just a chain of layers. For this case, we can also use the <code>mx.chain</code> macro. The same architecture above can be defined as</p> |
| <pre><code class="julia">mlp = @mx.chain mx.Variable(:data) => |
| mx.FullyConnected(name=:fc1, num_hidden=128) => |
| mx.Activation(name=:relu1, act_type=:relu) => |
| mx.FullyConnected(name=:fc2, num_hidden=64) => |
| mx.Activation(name=:relu2, act_type=:relu) => |
| mx.FullyConnected(name=:fc3, num_hidden=10) => |
| mx.SoftmaxOutput(name=:softmax) |
| </code></pre> |
| |
| <p>After defining the architecture, we are ready to load the MNIST data. MXNet.jl provide built-in data providers for the MNIST dataset, which could automatically download the dataset into <code>Pkg.dir("MXNet")/data/mnist</code> if necessary. We wrap the code to construct the data provider into <code>mnist-data.jl</code> so that it could be shared by both the MLP example and the LeNet ConvNets example.</p> |
| <pre><code class="julia">batch_size = 100 |
| include("mnist-data.jl") |
| train_provider, eval_provider = get_mnist_providers(batch_size) |
| </code></pre> |
| |
| <p>If you need to write your own data providers for customized data format, please refer to <a href="../../api/io/#MXNet.mx.AbstractDataProvider"><code>mx.AbstractDataProvider</code></a>.</p> |
| <p>Given the architecture and data, we can instantiate an <em>model</em> to do the actual training. <code>mx.FeedForward</code> is the built-in model that is suitable for most feed-forward architectures. When constructing the model, we also specify the <em>context</em> on which the computation should be carried out. Because this is a really tiny MLP, we will just run on a single CPU device.</p> |
| <pre><code class="julia">model = mx.FeedForward(mlp, context=mx.cpu()) |
| </code></pre> |
| |
| <p>You can use a <code>mx.gpu()</code> or if a list of devices (e.g. <code>[mx.gpu(0), mx.gpu(1)]</code>) is provided, data-parallelization will be used automatically. But for this tiny example, using a GPU device might not help.</p> |
| <p>The last thing we need to specify is the optimization algorithm (a.k.a. <em>optimizer</em>) to use. We use the basic SGD with a fixed learning rate 0.1 , momentum 0.9 and weight decay 0.00001:</p> |
| <pre><code class="julia">optimizer = mx.SGD(η=0.1, μ=0.9, λ=0.00001) |
| </code></pre> |
| |
| <p>Now we can do the training. Here the <code>n_epoch</code> parameter specifies that we want to train for 20 epochs. We also supply a <code>eval_data</code> to monitor validation accuracy on the validation set.</p> |
| <pre><code class="julia">mx.fit(model, optimizer, train_provider, n_epoch=20, eval_data=eval_provider) |
| </code></pre> |
| |
| <p>Here is a sample output</p> |
| <pre><code>INFO: Start training on [CPU0] |
| INFO: Initializing parameters... |
| INFO: Creating KVStore... |
| INFO: == Epoch 001 ========== |
| INFO: ## Training summary |
| INFO: :accuracy = 0.7554 |
| INFO: time = 1.3165 seconds |
| INFO: ## Validation summary |
| INFO: :accuracy = 0.9502 |
| ... |
| INFO: == Epoch 020 ========== |
| INFO: ## Training summary |
| INFO: :accuracy = 0.9949 |
| INFO: time = 0.9287 seconds |
| INFO: ## Validation summary |
| INFO: :accuracy = 0.9775 |
| </code></pre> |
| |
| <p><a id='Convolutional-Neural-Networks-1'></a></p> |
| <h2 id="convolutional-neural-networks">Convolutional Neural Networks</h2> |
| <p>In the second example, we show a slightly more complicated architecture that involves convolution and pooling. This architecture for the MNIST is usually called the [LeNet]_. The first part of the architecture is listed below:</p> |
| <pre><code class="julia"># input |
| data = mx.Variable(:data) |
| |
| # first conv |
| conv1 = @mx.chain mx.Convolution(data, kernel=(5,5), num_filter=20) => |
| mx.Activation(act_type=:tanh) => |
| mx.Pooling(pool_type=:max, kernel=(2,2), stride=(2,2)) |
| |
| # second conv |
| conv2 = @mx.chain mx.Convolution(conv1, kernel=(5,5), num_filter=50) => |
| mx.Activation(act_type=:tanh) => |
| mx.Pooling(pool_type=:max, kernel=(2,2), stride=(2,2)) |
| </code></pre> |
| |
| <p>We basically defined two convolution modules. Each convolution module is actually a chain of <code>Convolution</code>, <code>tanh</code> activation and then max <code>Pooling</code> operations.</p> |
| <p>Each sample in the MNIST dataset is a 28x28 single-channel grayscale image. In the tensor format used by <code>NDArray</code>, a batch of 100 samples is a tensor of shape <code>(28,28,1,100)</code>. The convolution and pooling operates in the spatial axis, so <code>kernel=(5,5)</code> indicate a square region of 5-width and 5-height. The rest of the architecture follows as:</p> |
| <pre><code class="julia"># first fully-connected |
| fc1 = @mx.chain mx.Flatten(conv2) => |
| mx.FullyConnected(num_hidden=500) => |
| mx.Activation(act_type=:tanh) |
| |
| # second fully-connected |
| fc2 = mx.FullyConnected(fc1, num_hidden=10) |
| |
| # softmax loss |
| lenet = mx.Softmax(fc2, name=:softmax) |
| </code></pre> |
| |
| <p>Note a fully-connected operator expects the input to be a matrix. However, the results from spatial convolution and pooling are 4D tensors. So we explicitly used a <code>Flatten</code> operator to flat the tensor, before connecting it to the <code>FullyConnected</code> operator.</p> |
| <p>The rest of the network is the same as the previous MLP example. As before, we can now load the MNIST dataset:</p> |
| <pre><code class="julia">batch_size = 100 |
| include("mnist-data.jl") |
| train_provider, eval_provider = get_mnist_providers(batch_size; flat=false) |
| </code></pre> |
| |
| <p>Note we specified <code>flat=false</code> to tell the data provider to provide 4D tensors instead of 2D matrices because the convolution operators needs correct spatial shape information. We then construct a feedforward model on GPU, and train it.</p> |
| <pre><code class="julia"># fit model |
| model = mx.FeedForward(lenet, context=mx.gpu()) |
| |
| # optimizer |
| optimizer = mx.SGD(η=0.05, μ=0.9, λ=0.00001) |
| |
| # fit parameters |
| mx.fit(model, optimizer, train_provider, n_epoch=20, eval_data=eval_provider) |
| </code></pre> |
| |
| <p>And here is a sample of running outputs:</p> |
| <pre><code>INFO: == Epoch 001 ========== |
| INFO: ## Training summary |
| INFO: :accuracy = 0.6750 |
| INFO: time = 4.9814 seconds |
| INFO: ## Validation summary |
| INFO: :accuracy = 0.9712 |
| ... |
| INFO: == Epoch 020 ========== |
| INFO: ## Training summary |
| INFO: :accuracy = 1.0000 |
| INFO: time = 4.0086 seconds |
| INFO: ## Validation summary |
| INFO: :accuracy = 0.9915 |
| </code></pre> |
| |
| <p><a id='Predicting-with-a-trained-model-1'></a></p> |
| <h2 id="predicting-with-a-trained-model">Predicting with a trained model</h2> |
| <p>Predicting with a trained model is very simple. By calling <code>mx.predict</code> with the model and a data provider, we get the model output as a Julia Array:</p> |
| <pre><code class="julia">probs = mx.predict(model, eval_provider) |
| </code></pre> |
| |
| <p>The following code shows a stupid way of getting all the labels from the data provider, and compute the prediction accuracy manually:</p> |
| <pre><code class="julia"># collect all labels from eval data |
| labels = reduce( |
| vcat, |
| copy(mx.get(eval_provider, batch, :softmax_label)) for batch ∈ eval_provider) |
| # labels are 0...9 |
| labels .= labels .+ 1 |
| |
| # Now we use compute the accuracy |
| pred = map(i -> argmax(probs[1:10, i]), 1:size(probs, 2)) |
| correct = sum(pred .== labels) |
| @printf "Accuracy on eval set: %.2f%%\n" 100correct/length(labels) |
| </code></pre> |
| |
| <p>Alternatively, when the dataset is huge, one can provide a callback to <code>mx.predict</code>, then the callback function will be invoked with the outputs of each mini-batch. The callback could, for example, write the data to disk for future inspection. In this case, no value is returned from <code>mx.predict</code>. See also predict.</p> |
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