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Training a Simple Neural Network, with PyTorch Data Loading¶

Dougal Maclaurin, Peter Hawkins, Matthew Johnson, Roy Frostig, Alex Wiltschko, Chris Leary

JAX

Let's combine everything we showed in the quickstart notebook to train a simple neural network. We will first specify and train a simple MLP on MNIST using JAX for the computation. We will use PyTorch's data loading API to load images and labels (because it's pretty great, and the world doesn't need yet another data loading library).

Of course, you can use JAX with any API that is compatible with NumPy to make specifying the model a bit more plug-and-play. Here, just for explanatory purposes, we won't use any neural network libraries or special APIs for builidng our model.

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!pip install --upgrade -q https://storage.googleapis.com/jax-wheels/cuda$(echo $CUDA_VERSION | sed -e 's/\.//' -e 's/\..*//')/jaxlib-0.1.13-cp36-none-linux_x86_64.whl
!pip install --upgrade -q jax

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from __future__ import print_function, division, absolute_import
import jax.numpy as np
from jax import grad, jit, vmap
from jax import random

Hyperparameters¶

Let's get a few bookkeeping items out of the way.

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# A helper function to randomly initialize weights and biases
# for a dense neural network layer
def random_layer_params(m, n, key, scale=1e-2):
  w_key, b_key = random.split(key)
  return scale * random.normal(w_key, (n, m)), scale * random.normal(b_key, (n,))

# Initialize all layers for a fully-connected neural network with sizes "sizes"
def init_network_params(sizes, key):
  keys = random.split(key, len(sizes))
  return [random_layer_params(m, n, k) for m, n, k in zip(sizes[:-1], sizes[1:], keys)]

layer_sizes = [784, 512, 512, 10]
param_scale = 0.1
step_size = 0.0001
num_epochs = 10
batch_size = 128
n_targets = 10
params = init_network_params(layer_sizes, random.PRNGKey(0))

Auto-batching predictions¶

Let us first define our prediction function. Note that we're defining this for a single image example. We're going to use JAX's vmap function to automatically handle mini-batches, with no performance penalty.

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from jax.scipy.misc import logsumexp

def relu(x):
  return np.maximum(0, x)

def predict(params, image):
  # per-example predictions
  activations = image
  for w, b in params[:-1]:
    outputs = np.dot(w, activations) + b
    activations = relu(outputs)
  
  final_w, final_b = params[-1]
  logits = np.dot(final_w, activations) + final_b
  return logits - logsumexp(logits)

Let's check that our prediction function only works on single images.

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# This works on single examples
random_flattened_image = random.normal(random.PRNGKey(1), (28 * 28,))
preds = predict(params, random_flattened_image)
print(preds.shape)

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# Doesn't work with a batch
random_flattened_images = random.normal(random.PRNGKey(1), (10, 28 * 28))
try:
  preds = predict(params, random_flattened_images)
except TypeError:
  print('Invalid shapes!')

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# Let's upgrade it to handle batches using `vmap`

# Make a batched version of the `predict` function
batched_predict = vmap(predict, in_axes=(None, 0))

# `batched_predict` has the same call signature as `predict`
batched_preds = batched_predict(params, random_flattened_images)
print(batched_preds.shape)

At this point, we have all the ingredients we need to define our neural network and train it. We've built an auto-batched version of predict, which we should be able to use in a loss function. We should be able to use grad to take the derivative of the loss with respect to the neural network parameters. Last, we should be able to use jit to speed up everything.

Utility and loss functions¶

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def one_hot(x, k, dtype=np.float32):
  """Create a one-hot encoding of x of size k."""
  return np.array(x[:, None] == np.arange(k), dtype)
  
def accuracy(params, images, targets):
  target_class = np.argmax(targets, axis=1)
  predicted_class = np.argmax(batched_predict(params, images), axis=1)
  return np.mean(predicted_class == target_class)

def loss(params, images, targets):
  preds = batched_predict(params, images)
  return -np.sum(preds * targets)

@jit
def update(params, x, y):
  grads = grad(loss)(params, x, y)
  return [(w - step_size * dw, b - step_size * db)
          for (w, b), (dw, db) in zip(params, grads)]

Data Loading with PyTorch¶

JAX is laser-focused on program transformations and accelerator-backed NumPy, so we don't include data loading or munging in the JAX library. There are already a lot of great data loaders out there, so let's just use them instead of reinventing anything. We'll grab PyTorch's data loader, and make a tiny shim to make it work with NumPy arrays.

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!pip install torch torchvision

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import numpy as onp
from torch.utils import data
from torchvision.datasets import MNIST

def numpy_collate(batch):
  if isinstance(batch[0], onp.ndarray):
    return onp.stack(batch)
  elif isinstance(batch[0], (tuple,list)):
    transposed = zip(*batch)
    return [numpy_collate(samples) for samples in transposed]
  else:
    return onp.array(batch)

class NumpyLoader(data.DataLoader):
  def __init__(self, dataset, batch_size=1,
                shuffle=False, sampler=None,
                batch_sampler=None, num_workers=0,
                pin_memory=False, drop_last=False,
                timeout=0, worker_init_fn=None):
    super(self.__class__, self).__init__(dataset,
        batch_size=batch_size,
        shuffle=shuffle,
        sampler=sampler,
        batch_sampler=batch_sampler,
        num_workers=num_workers,
        collate_fn=numpy_collate,
        pin_memory=pin_memory,
        drop_last=drop_last,
        timeout=timeout,
        worker_init_fn=worker_init_fn)

class FlattenAndCast(object):
  def __call__(self, pic):
    return onp.ravel(onp.array(pic, dtype=np.float32))

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# Define our dataset, using torch datasets
mnist_dataset = MNIST('/tmp/mnist/', download=True, transform=FlattenAndCast())
training_generator = NumpyLoader(mnist_dataset, batch_size=128, num_workers=0)

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# Get the full train dataset (for checking accuracy while training)
train_images = onp.array(mnist_dataset.train_data).reshape(len(mnist_dataset.train_data), -1)
train_labels = one_hot(onp.array(mnist_dataset.train_labels), n_targets)

# Get full test dataset
mnist_dataset_test = MNIST('/tmp/mnist/', download=True, train=False)
test_images = np.array(mnist_dataset_test.test_data.numpy().reshape(len(mnist_dataset_test.test_data), -1), dtype=np.float32)
test_labels = one_hot(onp.array(mnist_dataset_test.test_labels), n_targets)

Training Loop¶

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import time

for epoch in range(num_epochs):
  start_time = time.time()
  for x, y in training_generator:
    y = one_hot(y, n_targets)
    params = update(params, x, y)
  epoch_time = time.time() - start_time

  train_acc = accuracy(params, train_images, train_labels)
  test_acc = accuracy(params, test_images, test_labels)
  print("Epoch {} in {:0.2f} sec".format(epoch, epoch_time))
  print("Training set accuracy {}".format(train_acc))
  print("Test set accuracy {}".format(test_acc))

We've now used the whole of the JAX API: grad for derivatives, jit for speedups and vmap for auto-vectorization. We used NumPy to specify all of our computation, and borrowed the great data loaders from PyTorch, and ran the whole thing on the GPU.