张量流-了解张量形状以进行卷积

目前正在尝试通过用于卷积网络的Tensorflow MNIST教程并且我可以使用一些帮助来了解织补张量的尺寸.

Currently trying to work my way through the Tensorflow MNIST tutorial for convolutional networks and I could use some help with understanding the dimensions of the darn tensors.

所以我们的图像大小为28x28像素.

So we have images of 28x28 pixels in size.

卷积将为每个5x5补丁计算32个特征.

The convolution will compute 32 features for each 5x5 patch.

让我们暂时接受一下，然后再问自己为什么要使用32个功能以及为什么要使用5x5补丁.

Let's just accept this, for now, and ask ourselves later why 32 features and why 5x5 patches.

其重量张量将具有[5, 5, 1, 32]的形状.前两个维是音色大小，下一个是输入通道数，最后一个是输出通道数.

Its weight tensor will have a shape of [5, 5, 1, 32]. The first two dimensions are the patch size, the next is the number of input channels, and the last is the number of output channels.

W_conv1 = weight_variable([5, 5, 1, 32])

b_conv1 = bias_variable([32])

如果你这么说...

要应用该层，我们首先将x重塑为4d张量，其第二和第三个尺寸对应于图像的宽度和高度，最终尺寸对应于颜色通道的数量.

To apply the layer, we first reshape x to a 4d tensor, with the second and third dimensions corresponding to image width and height, and the final dimension corresponding to the number of color channels.

x_image = tf.reshape(x, [-1,28,28,1])

好的，现在我迷路了.

从最后一次重塑来看，我们有 不过" 28x28x1块"是我们的图像像素.

Judging by this last reshape, we have "howevermany" 28x28x1 "blocks" of pixels that are our images.

我想这是有道理的，因为图像是灰度的

I guess this makes sense because the images are in greyscale

但是，如果那是顺序，那么我们的权重张量实际上就是五个5x1x32个块"值的集合.

However, if that is the ordering, then our weight tensor is essentially a collection of five 5x1x32 "blocks" of values.

如果我们想推断每个补丁的32功能，我认为x32很有意义

The x32 makes sense, I guess, if we want to infer 32 features per patch

不过，其余的我并不十分相信.

The rest, though, I'm not terribly convinced by.

为什么重量张量看起来像它的样子?

Why does the weight tensor look the way it apparently does?

(为完整性:我们使用它们

(For completeness: we use them

h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1)
h_pool1 = max_pool_2x2(h_conv1)

其中

def conv2d(x,W):
    '''
    2D convolution, expects 4D input x and filter matrix W
    '''
    return tf.nn.conv2d(x,W,strides=[1,1,1,1],padding ='SAME')

def max_pool_2x2(x):
    '''
    max-pooling, using 2x2 patches
    '''
    return tf.nn.max_pool(x,ksize=[1,2,2,1], strides=[1,2,2,1],padding='SAME')

)