前向传播

前向传播

procedure

• create tensor
• indexing and slices
• reshape and broadcasting
• math operations

Recap

• \(𝑜𝑢𝑡 = 𝑟𝑒𝑙𝑢\{𝑟𝑒𝑙𝑢\{𝑟𝑒𝑙𝑢[𝑋@𝑊_1 + 𝑏1]@𝑊_2 + 𝑏2\}@𝑊_3 + 𝑏3\}\)
• \(𝑝𝑟𝑒𝑑 = 𝑎𝑟𝑔𝑚𝑎𝑥(𝑜𝑢𝑡)\)
• \(𝑙𝑜𝑠𝑠 = 𝑀𝑆𝐸(𝑜𝑢𝑡, 𝑙𝑎𝑏𝑒𝑙)\)
• \(minimize 𝑙𝑜𝑠𝑠 ： [𝑊1′, 𝑏1′, 𝑊2′, 𝑏2′, 𝑊3′ , 𝑏3′]\)

激活函数Relu(非线性激活)

• \(𝑟𝑒𝑙𝑢[𝑋@𝑊_1 + 𝑏_1]\)
• \(𝑟𝑒𝑙𝑢\{𝑟𝑒𝑙𝑢[𝑋@𝑊_1+𝑏_1]@𝑊_2+𝑏_2\}\)
• \(𝑜𝑢𝑡=𝑟𝑒𝑙𝑢\{𝑟𝑒𝑙𝑢\{𝑟𝑒𝑙𝑢[𝑋@𝑊_1+𝑏_1]@𝑊_2+𝑏_2\}@𝑊_3+𝑏_3\}\)

Compute loss(计算LOSS）

loss = tf.square(y_onehot - out)
loss = tf.reduce_mean(loss，axis=1)
loss = tf.reduce_mean(loss)

Compute gradient and update w（计算梯度）

 grads = tape.gradient(loss, [w1, b1, w2, b2, w3, b3])
optimizer.apply_ gradients(zip(grads, [w1, b1, w2，b2, w3, b3]))

Test

import  tensorflow as tf
from    tensorflow import keras
from    tensorflow.keras import datasets
import  os

os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'

# x: [60k, 28, 28],
# y: [60k]
(x, y), _ = datasets.mnist.load_data()
# x: [0~255] => [0~1.]
x = tf.convert_to_tensor(x, dtype=tf.float32) / 255.
y = tf.convert_to_tensor(y, dtype=tf.int32)
print(x.shape, y.shape, x.dtype, y.dtype)
print(tf.reduce_min(x), tf.reduce_max(x))
print(tf.reduce_min(y), tf.reduce_max(y))
train_db = tf.data.Dataset.from_tensor_slices((x,y)).batch(128)
train_iter = iter(train_db)
sample = next(train_iter)
print('batch:', sample[0].shape, sample[1].shape)
# [b, 784] => [b, 256] => [b, 128] => [b, 10]
# [dim_in, dim_out], [dim_out]
w1 = tf.Variable(tf.random.truncated_normal([784, 256], stddev=0.1))
b1 = tf.Variable(tf.zeros([256]))
w2 = tf.Variable(tf.random.truncated_normal([256, 128], stddev=0.1))
b2 = tf.Variable(tf.zeros([128]))
w3 = tf.Variable(tf.random.truncated_normal([128, 10], stddev=0.1))
b3 = tf.Variable(tf.zeros([10]))

lr = 1e-3

for epoch in range(10): # iterate db for 10
    for step, (x, y) in enumerate(train_db): # for every batch
        # x:[128, 28, 28]
        # y: [128]

        # [b, 28, 28] => [b, 28*28]
        x = tf.reshape(x, [-1, 28*28])

        with tf.GradientTape() as tape: # tf.Variable
            # x: [b, 28*28]
            # h1 = x@w1 + b1
            # [b, 784]@[784, 256] + [256] => [b, 256] + [256] => [b, 256] + [b, 256]
            h1 = x@w1 + tf.broadcast_to(b1, [x.shape[0], 256])
            h1 = tf.nn.relu(h1)
            # [b, 256] => [b, 128]
            h2 = h1@w2 + b2
            h2 = tf.nn.relu(h2)
            # [b, 128] => [b, 10]
            out = h2@w3 + b3

            # compute loss
            # out: [b, 10]
            # y: [b] => [b, 10]
            y_onehot = tf.one_hot(y, depth=10)

            # mse = mean(sum(y-out)^2)
            # [b, 10]
            loss = tf.square(y_onehot - out)
            # mean: scalar
            loss = tf.reduce_mean(loss)

        # compute gradients
        grads = tape.gradient(loss, [w1, b1, w2, b2, w3, b3])
        # print(grads)
        # w1 = w1 - lr * w1_grad
        w1.assign_sub(lr * grads[0])
        b1.assign_sub(lr * grads[1])
        w2.assign_sub(lr * grads[2])
        b2.assign_sub(lr * grads[3])
        w3.assign_sub(lr * grads[4])
        b3.assign_sub(lr * grads[5])


        if step % 100 == 0:
            print(epoch, step, 'loss:', float(loss))