Tensorflow Depthwise Convolution Understanding

Question

我目前正在尝试了解Tensorflow Depthwise Convolution的工作原理。据我所知，输入图像中的每个通道都与它自己的一组过滤器进行卷积，然后将结果连接起来。为了简化起见，我将坚持使用参数depth_multiplier=1，所以n_inputchannels == n_outputchannels。

所以从理论上讲，我可以将深度卷积分解为N个体，定期Conv2Ds，对吗？为什么下面的代码产生不同的结果然后我想知道 - 这是一个精确的问题吗？我正在关注深度卷积滤镜的排序[filter_height, filter_width, in_channels, 1]和常规卷积的[filter_height, filter_width, in_channels, out_channels]以及NHWC数据格式的文档。

import tensorflow as tf
import numpy as np
import random

width = 128
height = 128
channels = 32
kernel_width = 3
kernel_height = 3

with tf.Session() as sess:

    _input = np.float32(np.random.rand(1, height, width, channels))
    _weights =  np.float32(np.random.rand(kernel_height, kernel_width, channels, 1))

    _input_ph = tf.placeholder(tf.float32, shape=(1, height, width, channels))
    _weights_pc = tf.placeholder(tf.float32, shape=(kernel_height, kernel_width, channels, 1))

    feed = { _input_ph: _input, _weights_pc : _weights }

    result = tf.nn.depthwise_conv2d(_input_ph, _weights_pc, [1,1,1,1], 'SAME')

    individual_results = []
    for i in range(channels):
        individual_results.append(tf.nn.conv2d(tf.expand_dims(_input_ph[:,:,:,i],axis=3), tf.expand_dims(_weights_pc[:,:,i,:],axis=3), [1,1,1,1], 'SAME'))

    depth_result = sess.run(result, feed_dict=feed)
    concat_result = sess.run(tf.concat(individual_results, axis=3), feed_dict=feed)

    channel_diff = 0.0
    for i in range(channels):
        channel_diff += np.sum(depth_result[:,:,:,i]-concat_result[:,:,:,i])

    print(channel_diff)

这里我首先计算正常tf.nn.depthwise_conv2d，然后相应地对输入和权重进行切片并单独执行tf.nn.conv2d。对于这些参数，我得到1e-5差异，但当我增加频道数时，这种情况往往会更高。

如果有人能向我解释发生了什么，我会很高兴:) 谢谢！