卷积
卷积概念
- 卷积原属于信号处理中的一种运算，引入CNN中，作为从输入中提取特征的基本操作
- 补零：在输入端外侧填补0值使得卷积输出结果满足某种大小，在外侧的每一边都添加0值，使得输出可以达到某种预定形状
- 跨步：卷积核在输入上滑动时每次移动到下一步的距离
使用张量实现卷积
import torch
a = torch.arange(16).view(4,4)
a
tensor([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
b = a.unfold(0,3,1) #按照第0维度，以每3个元素，跨度为1进行展开
b
tensor([[[ 0, 4, 8],
[ 1, 5, 9],
[ 2, 6, 10],
[ 3, 7, 11]],
[[ 4, 8, 12],
[ 5, 9, 13],
[ 6, 10, 14],
[ 7, 11, 15]]])
torch.tensor.unfold可以按照指定的维度，以一定的间隔对原始张量进行分片，然后返回重整后的张量。
c = b.unfold(1,3,1)
c
tensor([[[[ 0, 1, 2],
[ 4, 5, 6],
[ 8, 9, 10]],
[[ 1, 2, 3],
[ 5, 6, 7],
[ 9, 10, 11]]],
[[[ 4, 5, 6],
[ 8, 9, 10],
[12, 13, 14]],
[[ 5, 6, 7],
[ 9, 10, 11],
[13, 14, 15]]]])
c.shape
torch.Size([2, 2, 3, 3])
上述张量c已经实现了按照3*3滑动窗大小，跨步为1将张量a展开为4为张量。
带补零和跨步设置的4维卷积层操作：
import torch
def conv2d(x,weight,bias,stride,pad):
n,c,h_in,w_in = x.shape
d,c,k,j = weight.shape
x_pad = torch.zeros(n,c,h_in+2*pad,w_in+2*pad).to(x.device)
x_pad[:,:,pad:-pad,pad:-pad] = x #对输入进行补零操作
x_pad = x_pad.unfold(2,k,stride)
x_pad = x_pad.unfold(3,j,stride) #按照滑动窗展开
out = torch.einsum(
'nchwkj,dckj->ndhw',
x_pad,weight)#按照滑动窗相乘，并将所有输入通道上卷积结果累加
out = out + bias.view(1,-1,1,1) #添加偏置
return out
import torch.nn.functional as F
x = torch.randn(2,3,5,5,requires_grad=True)
w = torch.randn(4,3,3,3,requires_grad=True)
b = torch.randn(4,requires_grad=True)
stride = 2
pad = 2
torch_out = F.conv2d(x,w,b,stride,pad)
my_out = conv2d(x,w,b,stride,pad)
torch_out
my_out
tensor([[[[ 0.7389, 2.6153, 1.6206, 0.7432],
[ 3.3159, -1.5308, 9.9275, -1.2443],
[ 3.0869, -6.5276, 5.8508, -2.7660],
[-1.9878, -6.0596, -0.6992, -3.3871]],
[[-0.5907, 1.0378, -2.1682, -1.2919],
[-0.5426, -0.7781, 4.4606, 2.6235],
[-4.9208, 2.5762, -0.1033, -2.2686],
[ 0.8438, -2.4514, 2.3441, -1.5637]],
[[ 1.6342, 1.5391, 4.0431, 4.2984],
[-1.9671, 1.6227, -3.0477, 1.4082],
[ 2.1579, 0.1513, 0.3556, -1.5150],
[ 1.8514, 2.6099, 3.6082, 0.9121]],
[[ 0.3274, -0.2762, 0.1335, 0.9362],
[ 1.9674, -9.8901, 4.4833, -4.0852],
[-4.3262, 0.1775, -0.3596, 1.7832],
[ 3.7039, -2.4898, 5.7371, -1.6463]]],
[[[-0.6281, 2.5599, -1.1673, -0.2803],
[ 0.3624, -3.0622, 0.9032, -2.2624],
[ 5.2199, 10.0974, -6.2536, 3.3783],
[ 0.7550, 6.5702, 1.6907, 0.4545]],
...
[[ 0.3033, -4.3135, 3.3039, -0.7272],
[ 5.8496, -4.2414, -9.7936, -3.2630],
[-5.2852, -5.4366, 8.8947, -1.0325],
[-0.5529, 2.5634, -3.4046, 0.8185]]]], grad_fn=<AddBackward0>)