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#@title Licensed under the Apache License, Version 2.0 (the "License");
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# https://www.apache.org/licenses/LICENSE-2.0
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在上一个教程中，我们介绍了 "张量"（Tensor）及其操作。本教程涉及自动微分（automatic differentitation），它是优化机器学习模型的关键技巧之一。
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!pip install tensorflow==2.0.0-beta1
import tensorflow as tf
TensorFlow 为自动微分提供了 tf.GradientTape API ，根据某个函数的输入变量来计算它的导数。Tensorflow 会把 'tf.GradientTape' 上下文中执行的所有操作都记录在一个磁带上 ("tape")。 然后基于这个磁带和每次操作产生的导数，用反向微分法（"reverse mode differentiation"）来计算这些被“记录在案”的函数的导数。
例如：
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x = tf.ones((2, 2))
with tf.GradientTape() as t:
t.watch(x)
y = tf.reduce_sum(x)
z = tf.multiply(y, y)
# Derivative of z with respect to the original input tensor x
dz_dx = t.gradient(z, x)
for i in [0, 1]:
for j in [0, 1]:
assert dz_dx[i][j].numpy() == 8.0
你也可以使用 tf.GradientTape 上下文计算过程产生的中间结果来求取导数。
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x = tf.ones((2, 2))
with tf.GradientTape() as t:
t.watch(x)
y = tf.reduce_sum(x)
z = tf.multiply(y, y)
# Use the tape to compute the derivative of z with respect to the
# intermediate value y.
dz_dy = t.gradient(z, y)
assert dz_dy.numpy() == 8.0
默认情况下，调用 GradientTape.gradient() 方法时， GradientTape 占用的资源会立即得到释放。通过创建一个持久的梯度带，可以计算同个函数的多个导数。这样在磁带对象被垃圾回收时，就可以多次调用 'gradient()' 方法。例如：
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x = tf.constant(3.0)
with tf.GradientTape(persistent=True) as t:
t.watch(x)
y = x * x
z = y * y
dz_dx = t.gradient(z, x) # 108.0 (4*x^3 at x = 3)
dy_dx = t.gradient(y, x) # 6.0
del t # Drop the reference to the tape
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def f(x, y):
output = 1.0
for i in range(y):
if i > 1 and i < 5:
output = tf.multiply(output, x)
return output
def grad(x, y):
with tf.GradientTape() as t:
t.watch(x)
out = f(x, y)
return t.gradient(out, x)
x = tf.convert_to_tensor(2.0)
assert grad(x, 6).numpy() == 12.0
assert grad(x, 5).numpy() == 12.0
assert grad(x, 4).numpy() == 4.0
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x = tf.Variable(1.0) # Create a Tensorflow variable initialized to 1.0
with tf.GradientTape() as t:
with tf.GradientTape() as t2:
y = x * x * x
# Compute the gradient inside the 't' context manager
# which means the gradient computation is differentiable as well.
dy_dx = t2.gradient(y, x)
d2y_dx2 = t.gradient(dy_dx, x)
assert dy_dx.numpy() == 3.0
assert d2y_dx2.numpy() == 6.0