2-3自动微分机制——eat_tensorflow2_in_30_days
作者：互联网
神经网络通常依赖反向传播求梯度来更新网络参数，求梯度过程通常是一件非常复杂而且容易出错的事情
而深度学习框架可以帮助我们自动地完成这种求梯度运算
TensorFlow一般使用梯度磁带tf.GradientTape来记录正向运算过程，然后反播磁带自动得到梯度值
这种利用tf.GradientTape求微分的方法叫作TensorFlow的自动微分机制
利用梯度磁带求导数
import tensorflow as tf
import numpy as np
# 求f(x) = a*x**2 + b*x + c的导数
x = tf.Variable(0.0, name='x', dtype=tf.float32)
a = tf.constant(1.0)
b = tf.constant(-2.0)
c = tf.constant(1.0)
with tf.GradientTape() as tape:
y = a*tf.pow(x, 2) + b*x +c
dy_dx = tape.gradient(y, x)
print(dy_dx)
"""
tf.Tensor(-2.0, shape=(), dtype=float32)
"""
# 对常量张量也可以求导，需要增加watch
with tf.GradientTape() as tape:
tape.watch([a, b, c])
y = a*tf.pow(x, 2) + b*x + c
dy_dx, dy_da, dy_db, dy_dc = tape.gradient(y, [x, a, b, c])
print(dy_dx)
print(dy_da)
print(dy_db)
print(dy_dc)
"""
tf.Tensor(-2.0, shape=(), dtype=float32)
tf.Tensor(0.0, shape=(), dtype=float32)
tf.Tensor(0.0, shape=(), dtype=float32)
tf.Tensor(1.0, shape=(), dtype=float32)
"""
# 可以求二阶导数
with tf.GradientTape() as tape2:
with tf.GradientTape() as tape1:
y = a*tf.pow(x, 2) + b*x + c
dy_dx = tape1.gradient(y, x)
dy2_dx2 = tape2.gradient(dy_dx, x)
print(dy2_dx2)
"""
tf.Tensor(2.0, shape=(), dtype=float32)
"""
# 可以在autograph中使用
@tf.function
def f(x):
a = tf.constant(1.0)
b = tf.constant(-2.0)
c = tf.constant(1.0)
# 自变量转换成tf.float32
x = tf.cast(x, tf.float32)
with tf.GradientTape() as tape:
tape.watch(x)
y = a*tf.pow(x, 2) + b*x + c
dy_dx = tape.gradient(y, x)
return dy_dx, y
tf.print(f(tf.constant(0.0)))
tf.print(f(tf.constant(1.0)))
"""
(-2, 1)
(0, 0)
"""
利用梯度磁带和优化器求最小值
# 求f(x) = a*x**2 + b*x + c的最小值
# 使用optimizer.apply_gradients
x = tf.Variable(0.0, name='x', dtype=tf.float32)
a = tf.constant(1.0)
b = tf.constant(-2.0)
c = tf.constant(1.0)
optimizer = tf.keras.optimizers.SGD(learning_rate=0.01)
for _ in range(1000):
with tf.GradientTape() as tape:
y = a*tf.pow(x, 2) + b*x + c
dy_dx = tape.gradient(y, x)
optimizer.apply_gradients(grads_and_vars=[(dy_dx, x)])
tf.print('y=', y, ";x=", x)
"""
y= 0 ;x= 0.999998569
"""
# 求f(x)=a*x**2 + b*x + c的最小值
# 使用optimizer.minimize
# optimizer.minimize相当于先用tape求gradient，在apply_gradient
x = tf.Variable(0.0, name='x', dtype=tf.float32)
# 注意f()无参数
def f():
a = tf.constant(1.0)
b = tf.constant(-2.0)
c = tf.constant(1.0)
y = a*tf.pow(x, 2) + b*x + c
return y
optimizer = tf.keras.optimizers.SGD(learning_rate=0.01)
for _ in range(1000):
optimizer.minimize(f, [x])
tf.print('y=', f(), ':x=', x)
"""
y = 0 ; x = 0.999998569
"""
# 在autograph中完成最小值求解
# 使用optimizer.apply_gradients
x = tf.Variable(0.0, name='x', dtype=tf.float32)
optimizer = tf.keras.optimizers.SGD(learning_rate=0.01)
@tf.function
def minimizef():
a = tf.constant(1.0)
b = tf.constant(-2.0)
c = tf.constant(1.0)
for _ in tf.range(1000): # 注意autograph时使用tf.range(1000)而不是range(1000)
with tf.GradientTape() as tape:
y = a*tf.pow(x, 2) + b*x + c
dy_dx = tape.gradient(y, x)
optimizer.apply_gradients(grads_and_vars=[(dy_dx, x)])
y = a*tf.pow(x, 2) + b*x + c
return y
tf.print(minimizef())
tf.print(x)
"""
0
0.999998569
"""
# 在autograph中完成最小值求解
# 使用optimizer.minimize
x = tf.Variable(0.0,name = "x",dtype = tf.float32)
optimizer = tf.keras.optimizers.SGD(learning_rate=0.01)
@tf.function
def f():
a = tf.constant(1.0)
b = tf.constant(-2.0)
c = tf.constant(1.0)
y = a*tf.pow(x, 2) + b*x + c
return y
@tf.function
def train(epoch):
for _ in tf.range(epoch):
optimizer.minimize(f, [x])
return f()
tf.print(train(1000))
tf.print(x)
"""
0
0.999998569
"""
标签：tensorflow2,constant,30,days,print,dy,tf,1.0,float32 来源： https://www.cnblogs.com/lotuslaw/p/16098281.html