• Plese see this answer for a detailed example of how tf.nn.conv2d_backprop_input and tf.nn.conv2d_backprop_filter in an example.

In tf.nn, there are 4 closely related 2d conv functions:

• tf.nn.conv2d
• tf.nn.conv2d_backprop_filter
• tf.nn.conv2d_backprop_input
• tf.nn.conv2d_transpose

Given out = conv2d(x, w)

• Use tf.nn.conv2d_backprop_filter to compute the filter gradient d_w
• Use tf.nn.conv2d_backprop_input to compute the filter gradient d_x
• tf.nn.conv2d_backprop_input can be implemented by tf.nn.conv2d_transpose
• All 4 functions above can be implemented by tf.nn.conv2d
• Actually, use TF‘s autodiff is the fastest way to compute gradients

Long Answer

Now, let‘s give an actual working code example of how to use the 4 functions above to compute d_x and d_w given d_out. This shows how conv2d, conv2d_backprop_filter, conv2d_backprop_input, and conv2d_transpose are related to each other. Please find the full scripts here.

Computing d_x in 4 different ways:

# Method 1: TF‘s autodiff
d_x = tf.gradients(f, x)[0]

# Method 2: manually using conv2d
d_x_manual = tf.nn.conv2d(input=tf_pad_to_full_conv2d(d_out, w_size),
                          filter=tf_rot180(w),
                          strides=strides,
                          padding=‘VALID‘)

# Method 3: conv2d_backprop_input
d_x_backprop_input = tf.nn.conv2d_backprop_input(input_sizes=x_shape,
                                                 filter=w,
                                                 out_backprop=d_out,
                                                 strides=strides,
                                                 padding=‘VALID‘)

# Method 4: conv2d_transpose
d_x_transpose = tf.nn.conv2d_transpose(value=d_out,
                                       filter=w,
                                       output_shape=x_shape,
                                       strides=strides,
                                       padding=‘VALID‘)

Computing d_w in 3 different ways:

# Method 1: TF‘s autodiff
d_w = tf.gradients(f, w)[0]

# Method 2: manually using conv2d
d_w_manual = tf_NHWC_to_HWIO(tf.nn.conv2d(input=x,
                                          filter=tf_NHWC_to_HWIO(d_out),
                                          strides=strides,
                                          padding=‘VALID‘))

# Method 3: conv2d_backprop_filter
d_w_backprop_filter = tf.nn.conv2d_backprop_filter(input=x,
                                                   filter_sizes=w_shape,
                                                   out_backprop=d_out,
                                                   strides=strides,
                                                   padding=‘VALID‘)

Please see the full scripts for the implementation of tf_rot180, tf_pad_to_full_conv2d, tf_NHWC_to_HWIO. In the scripts, we check that the final output values of different methods are the same; a numpy implementation is also available.

• 第十四節，TensorFlow中的反卷積，反池化操作以及gradients的使用
• http://www.cnblogs.com/pinard/p/6494810.html ：卷積神經網絡(CNN)反向傳播算法
• http://blog.csdn.net/yunpiao123456/article/details/52437794

tensorflow 卷積/反卷積-池化/反池化操作詳解