用JAX訓練神經網絡

Google JAX是一種用於轉換數值函數的機器學習框架。

它被描述為匯集了autograd（通過函數微分自動獲得梯度函數）和TensorFlow的XLA（加速線性代數）的修改版本。

JAX 的主要功能是:

1. grad: 自動微分/求導數
2. jit：編譯/加速
3. vmap：自動矢量化/批次處理(batch)
4. pmap：SPMD編程

首先導入必要的庫

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

再來定義一個函數random_layer_params

輸入為(m,n,key,scale)分別對應輸入神經元數量,輸出神經元數量

隨機key,和一個scale控制數值大小,主要功能是返回一個隨機初始化的層

下面那個函數init_network_params則是給定layer_sizes和隨機key

返回整個神經網路架構,這裡要提的key有點像其他框架的random_seed

目的是讓程式有可再現性.

# 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]
step_size = 0.01
num_epochs = 10
batch_size = 128
n_targets = 10
params = init_network_params(layer_sizes, random.PRNGKey(0))

自動批處理預測

讓我們首先定義我們的預測函數。

請注意，我們正在為單個輸入範例定義這函數。

我們將使用 JAX 的 vmap 函數來自動處理batch(批量)，而不會降低性能。

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)

讓我們檢查一下我們的預測函數是否僅適用於單個輸入。

# 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)

至此，我們擁有了定義神經網絡並對其進行訓練所需的所有要素。我們已經構建了一個自動批處理版本的預測，我們應該能夠在損失函數中使用它

我們應該能夠使用 grad 對神經網絡參數求損失的導數。最後，我們應該能夠使用 jit 來加速一切。

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)]

使用tensorflow/datasets讀取訓練資料

讓我們使用看看 tensorflow/datasets的dataloader

import tensorflow as tf
# Ensure TF does not see GPU and grab all GPU memory.
tf.config.set_visible_devices([], device_type='GPU')

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)

訓練迴圈

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

我們現在已經使用了三個 JAX API：

1. grad 用於求導數(gradient)
2. jit 用於加速
3. vmap 用於自動批量化(batch)

我們使用 NumPy 來指定我們所有的計算，並從 tensorflow/datasets 借用了強大的數據加載器，並在 GPU 上運行了整個過程。