Copyright 2018 Google LLC.

Licensed under the Apache License, Version 2.0 (the “License”);

Licensed 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

https://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.

Training a Simple Neural Network, with tensorflow/datasets Data Loading

Open in Colab

Forked from neural_network_and_data_loading.ipynb

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 tensorflow/datasets data loading API to load images and labels (because it’s pretty great, and the world doesn’t need yet another data loading library :P).

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.

import jax.numpy as jnp
from jax import grad, jit, vmap
from jax import random

Hyperparameters

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

# 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 = 0.01
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.

from jax.scipy.special import logsumexp

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

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

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

# This works on single examples
random_flattened_image = random.normal(random.PRNGKey(1), (28 * 28,))
preds = predict(params, random_flattened_image)
print(preds.shape)
(10,)
# 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!')
Invalid shapes!
# 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)
(10, 10)

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

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

def loss(params, images, targets):
  preds = batched_predict(params, images)
  return -jnp.mean(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 tensorflow/datasets

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 use the tensorflow/datasets data loader.

import tensorflow_datasets as tfds

data_dir = '/tmp/tfds'

# Fetch full datasets for evaluation
# tfds.load returns tf.Tensors (or tf.data.Datasets if batch_size != -1)
# You can convert them to NumPy arrays (or iterables of NumPy arrays) with tfds.dataset_as_numpy
mnist_data, info = tfds.load(name="mnist", batch_size=-1, data_dir=data_dir, with_info=True)
mnist_data = tfds.as_numpy(mnist_data)
train_data, test_data = mnist_data['train'], mnist_data['test']
num_labels = info.features['label'].num_classes
h, w, c = info.features['image'].shape
num_pixels = h * w * c

# Full train set
train_images, train_labels = train_data['image'], train_data['label']
train_images = jnp.reshape(train_images, (len(train_images), num_pixels))
train_labels = one_hot(train_labels, num_labels)

# Full test set
test_images, test_labels = test_data['image'], test_data['label']
test_images = jnp.reshape(test_images, (len(test_images), num_pixels))
test_labels = one_hot(test_labels, num_labels)
print('Train:', train_images.shape, train_labels.shape)
print('Test:', test_images.shape, test_labels.shape)
Train: (60000, 784) (60000, 10)
Test: (10000, 784) (10000, 10)

Training Loop

import time

def get_train_batches():
  # as_supervised=True gives us the (image, label) as a tuple instead of a dict
  ds = tfds.load(name='mnist', split='train', as_supervised=True, data_dir=data_dir)
  # You can build up an arbitrary tf.data input pipeline
  ds = ds.batch(batch_size).prefetch(1)
  # tfds.dataset_as_numpy converts the tf.data.Dataset into an iterable of NumPy arrays
  return tfds.as_numpy(ds)

for epoch in range(num_epochs):
  start_time = time.time()
  for x, y in get_train_batches():
    x = jnp.reshape(x, (len(x), num_pixels))
    y = one_hot(y, num_labels)
    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))
Epoch 0 in 28.30 sec
Training set accuracy 0.8400499820709229
Test set accuracy 0.8469000458717346
Epoch 1 in 14.74 sec
Training set accuracy 0.8743667006492615
Test set accuracy 0.8803000450134277
Epoch 2 in 14.57 sec
Training set accuracy 0.8901500105857849
Test set accuracy 0.8957000374794006
Epoch 3 in 14.36 sec
Training set accuracy 0.8991333246231079
Test set accuracy 0.903700053691864
Epoch 4 in 14.20 sec
Training set accuracy 0.9061833620071411
Test set accuracy 0.9087000489234924
Epoch 5 in 14.89 sec
Training set accuracy 0.9113333225250244
Test set accuracy 0.912600040435791
Epoch 6 in 13.95 sec
Training set accuracy 0.9156833291053772
Test set accuracy 0.9176000356674194
Epoch 7 in 13.32 sec
Training set accuracy 0.9192000031471252
Test set accuracy 0.9214000701904297
Epoch 8 in 13.55 sec
Training set accuracy 0.9222500324249268
Test set accuracy 0.9241000413894653
Epoch 9 in 13.40 sec
Training set accuracy 0.9253666996955872
Test set accuracy 0.9269000291824341

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 tensorflow/datasets, and ran the whole thing on the GPU.