Tensorflow 卷积的梯度反向传播过程

import tensorflow as tf

# 卷积核
kernel=tf.constant(
  [
    [[[3]],[[4]]],
    [[[5]],[[6]]]
  ]
  ,tf.float32
)

# 某一函数针对sigma的导数
out=tf.constant(
  [
    [
      [[-1],[1]],
      [[2],[-2]]
    ]
  ]
  ,tf.float32
)


# 针对未知变量的导数的方向计算
inputValue=tf.nn.conv2d_backprop_input((1,3,3,1),kernel,out,[1,1,1,1],'VALID')

session=tf.Session()

print(session.run(inputValue))
[[[[ -3.]
  [ -1.]
  [ 4.]]

 [[ 1.]
  [ 1.]
  [ -2.]]

 [[ 10.]
  [ 2.]
  [-12.]]]]

import tensorflow as tf

# 输入张量
x=tf.constant(
  [
    [
      [[1],[2],[3]],
      [[4],[5],[6]],
      [[7],[8],[9]]
    ]
  ]
  ,tf.float32
)

# 某一个函数F对sigma的导数
partial_sigma=tf.constant(
  [
    [
      [[-1],[-2]],
      [[-3],[-4]]
    ]
  ]
  ,tf.float32
)

# 某一个函数F对卷积核k的导数
partial_sigma_k=tf.nn.conv2d_backprop_filter(x,(2,2,1,1),partial_sigma,[1,1,1,1],'VALID')

session=tf.Session()

print(session.run(partial_sigma_k))
[[[[-37.]]

 [[-47.]]]


 [[[-67.]]

 [[-77.]]]]

import tensorflow as tf

# 卷积核
kernel=tf.constant(
  [
    [[[3]],[[4]]],
    [[[5]],[[6]]]
  ]
  ,tf.float32
)

# 某一函数针对sigma的导数
partial_sigma=tf.constant(
  [
    [
      [[-1],[1],[3]],
      [[2],[-2],[-4]],
      [[-3],[4],[1]]
    ]
  ]
  ,tf.float32
)


# 针对未知变量的导数的方向计算
partial_x=tf.nn.conv2d_backprop_input((1,3,3,1),kernel,partial_sigma,[1,1,1,1],'SAME')

session=tf.Session()

print(session.run(inputValue))
[[[[ -3.]
  [ -1.]
  [ 4.]]

 [[ 1.]
  [ 1.]
  [ -2.]]

 [[ 10.]
  [ 2.]
  [-12.]]]]

import tensorflow as tf

# 卷积核
x=tf.constant(
  [
    [
      [[1],[2],[3]],
      [[4],[5],[6]],
      [[7],[8],[9]]
    ]
  ]
  ,tf.float32
)

# 某一函数针对sigma的导数
partial_sigma=tf.constant(
  [
    [
      [[-1],[-2],[1]],
      [[-3],[-4],[2]],
      [[-2],[1],[3]]
    ]
  ]
  ,tf.float32
)


# 针对未知变量的导数的方向计算
partial_sigma_k=tf.nn.conv2d_backprop_filter(x,(2,2,1,1),partial_sigma,[1,1,1,1],'SAME')

session=tf.Session()

print(session.run(partial_sigma_k))
[[[[ -1.]]

 [[-54.]]]


 [[[-43.]]

 [[-77.]]]]