Digit Recognition on MNIST
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 MNIST handwritten digit dataset. The code for this tutorial could be found in examples/mnist. There are also two Jupyter notebooks that expand a little more on the MLP and the LeNet, using the more general
Simple 3-layer MLP
This is a tiny 3-layer MLP that could be easily trained on CPU. The script starts with
to load the
MXNet module. Then we are ready to define the network architecture via the symbolic API. We start with a placeholder
data = mx.Variable(:data)
and then cascading fully-connected layers and activation functions:
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)
Note each composition we take the previous symbol as the first argument, forming a feedforward chain. The architecture looks like
Input --> 128 units (ReLU) --> 64 units (ReLU) --> 10 units
where the last 10 units correspond to the 10 output classes (digits 0,...,9). We then add a final
SoftmaxOutput operation to turn the 10-dimensional prediction to proper probability values for the 10 classes:
mlp = mx.SoftmaxOutput(fc3, name=:softmax)
As we can see, the MLP is just a chain of layers. For this case, we can also use the
mx.chain macro. The same architecture above can be defined as
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)
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
Pkg.dir("MXNet")/data/mnist if necessary. We wrap the code to construct the data provider into
mnist-data.jl so that it could be shared by both the MLP example and the LeNet ConvNets example.
batch_size = 100 include("mnist-data.jl") train_provider, eval_provider = get_mnist_providers(batch_size)
If you need to write your own data providers for customized data format, please refer to
Given the architecture and data, we can instantiate an model to do the actual training.
mx.FeedForward is the built-in model that is suitable for most feed-forward architectures. When constructing the model, we also specify the context on which the computation should be carried out. Because this is a really tiny MLP, we will just run on a single CPU device.
model = mx.FeedForward(mlp, context=mx.cpu())
You can use a
mx.gpu() or if a list of devices (e.g.
[mx.gpu(0), mx.gpu(1)]) is provided, data-parallelization will be used automatically. But for this tiny example, using a GPU device might not help.
The last thing we need to specify is the optimization algorithm (a.k.a. optimizer) to use. We use the basic SGD with a fixed learning rate 0.1 , momentum 0.9 and weight decay 0.00001:
optimizer = mx.SGD(η=0.1, μ=0.9, λ=0.00001)
Now we can do the training. Here the
n_epoch parameter specifies that we want to train for 20 epochs. We also supply a
eval_data to monitor validation accuracy on the validation set.
mx.fit(model, optimizer, train_provider, n_epoch=20, eval_data=eval_provider)
Here is a sample output
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
Convolutional Neural Networks
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:
# 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))
We basically defined two convolution modules. Each convolution module is actually a chain of
tanh activation and then max
Each sample in the MNIST dataset is a 28x28 single-channel grayscale image. In the tensor format used by
NDArray, a batch of 100 samples is a tensor of shape
(28,28,1,100). The convolution and pooling operates in the spatial axis, so
kernel=(5,5) indicate a square region of 5-width and 5-height. The rest of the architecture follows as:
# 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)
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
Flatten operator to flat the tensor, before connecting it to the
The rest of the network is the same as the previous MLP example. As before, we can now load the MNIST dataset:
batch_size = 100 include("mnist-data.jl") train_provider, eval_provider = get_mnist_providers(batch_size; flat=false)
Note we specified
flat=false 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.
# 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)
And here is a sample of running outputs:
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
Predicting with a trained model
Predicting with a trained model is very simple. By calling
mx.predict with the model and a data provider, we get the model output as a Julia Array:
probs = mx.predict(model, eval_provider)
The following code shows a stupid way of getting all the labels from the data provider, and compute the prediction accuracy manually:
# 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 -> indmax(probs[1:10, i]), 1:size(probs, 2)) correct = sum(pred .== labels) @printf "Accuracy on eval set: %.2f%%\n" 100correct/length(labels)
Alternatively, when the dataset is huge, one can provide a callback to
mx.predict, 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
mx.predict. See also predict.