PyTorch - Conv2d 和 MaxPool2d

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参考视频：土堆说 卷积计算
https://www.bilibili.com/video/BV1hE411t7RN

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关于 torch.nn 和 torch.nn.function
torch.nn 是对 torch.nn.function 的封装，前者更方便实用。

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Conv2d

卷积过程可见文末动画

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计算

卷积层输入特征图(input feature map)的尺寸为：H_i × W_i × C_i

• H_i ：输入特征图的高
• W_i ：输入特征图的宽
• C_i ：输入特征图的通道数
  （如果是第一个卷积层则是输入图像的通道数，如果是中间的卷积层，则是上一层的输出通道数

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卷积层的参数如下：

• P：padding，补零的行数和列数
• F：正方形卷积核的边长
• S：stride，步幅
• K：输出通道数

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输出特征图(output feature map)的尺寸为 H_o × W_o × C_o ，其中每一个变量的计算方式如下：

• H_o = (H_i + 2P − F)/S + 1
• W_o = (W_i + 2P − F)/S + 1
• C_o = K

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• 卷积时，超出边界的不计算。

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参数量大小的计算，分为weights和biases：

首先，计算weights的参数量：F × F × C_i × K
接着计算biases的参数量：K
所以总参数量为：F × F × C_i × K + K

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计算示例

输入	卷积核	步长	padding	输出	计算
5x5	2x2	1	0	4x4	4 = (5-2)/1 + 1
5x5	3x3	1	0	3x3	3 = (5-3)/1 + 1
5x5	2x2	2	0	2x2	2 = (5-2)/2 + 1
6x6	2x2	2	0	3x3	3 = (6-2)/2 + 1
5x5	2x2	1	1	6x6	4 = (5 + 1*2 - 2)/1 + 1
5x5	3x3	1	1	5x5	3 = (5 + 1*2 - 3)/1 + 1
5x5	3x3	2	2	4x4	3 = (5 + 2*2 - 3)/2 + 1

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Conv2d 函数解析

• torch.nn.functional.conv2d 官方说明
  https://pytorch.org/docs/stable/generated/torch.nn.functional.conv2d.html#torch.nn.functional.conv2d

torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True, padding_mode=‘zeros’, device=None, dtype=None)

• in_channels
• out_channels
• kernel_size，卷积核大小；可以是一个数（n*n矩阵），也可以是一个元组。这个值在训练过程中，会不断被调整。
• stride=1
• padding=0
• dilation=1，卷积核对应位的距离
• groups=1，分组卷积；一般为1，很少改动。
• bias=True，偏置，一般为True
• padding_mode=‘zeros’，如果设置了 padding，填充模式。默认为 zeros，即填充0。
• device=None
• dtype=None)

一般只设置前五个参数

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代码示例

import torch
import torch.nn.functional as F

t1 = torch.Tensor([[1, 2, 0, 3, 1], 
                   [0, 1, 2, 3, 1],
                   [1, 2, 1, 0, 0],
                   [5, 2, 3, 1, 1],
                   [2, 1, 0, 1, 1], ])

kernel = torch.Tensor([
    [1, 2, 1],
    [0, 1, 0],
    [2, 1, 0]
])
t1.shape, kernel.shape
# (torch.Size([5, 5]), torch.Size([3, 3]))

# channel 和 batch_size 为 1
ip = torch.reshape(t1, (1, 1, 5, 5))
kernel = torch.reshape(kernel, (1, 1, 3, 3))
ip.shape, kernel.shape
# (torch.Size([1, 1, 5, 5]), torch.Size([1, 1, 3, 3]))


op = F.conv2d(ip, kernel, stride=1) 
op, op.shape 
'''
(tensor([[[[10., 12., 12.],
           [18., 16., 16.],
           [13.,  9.,  3.]]]]),
           
 torch.Size([1, 1, 3, 3]))
'''

# 不同 stride
op = F.conv2d(ip, kernel, stride=2) 
op, op.shape 
'''
(tensor([[[[10., 12.],
           [13.,  3.]]]]),
 
torch.Size([1, 1, 2, 2]))
'''

# 增加 padding
op = F.conv2d(ip, kernel, stride=2, padding=1) 
op, op.shape 
'''
(tensor([[[[ 1.,  4.,  8.],
           [ 7., 16.,  8.],
           [14.,  9.,  4.]]]]),
           
 torch.Size([1, 1, 3, 3]))
'''

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MaxPool2d

池化的目的是保留特征，减少数据量；
最大池化也被称为 下采样；
另外池化操作是分别应用到每一个深度切片层。输出深度 与 输入的深度 相同。

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计算

• 输入宽高深：H_i，W_i, D_i
• 滤波器宽高：f_w， f_h
• S: stride，步长

输出为：
H_o = (H_i - f_h)/S + 1
W_o = (W_i - f_w)/S + 1
D_o = D_i

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输入维度是 4x4x5 (HxWxD)
滤波器大小 2x2 (HxW)
stride 的高和宽都是 2 (S)

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函数说明

• 官方说明
  https://pytorch.org/docs/stable/generated/torch.nn.MaxPool2d.html#torch.nn.MaxPool2d

torch.nn.MaxPool2d(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False)

• ceil_mode，超出范围时是否计算

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代码实现

import torch
import torch.nn as nn

# MaxPool2d 函数 input 需要是 4维
ip = torch.reshape(t1, (-1, 1, 5, 5))


class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.maxpool = nn.MaxPool2d(kernel_size=3, ceil_mode=True)
#         self.maxpool = nn.MaxPool2d(kernel_size=3, ceil_mode=False)
        
    def forward(self, input):
        output = self.maxpool(input)
        return output
        
net = Net()
ret = net(ip)
ret

# tensor([[[[2., 3.], [5., 1.]]]])  # ceil_mode=True
# tensor([[[[2.]]]])  # ceil_mode=False

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数据集中调用

import torchvision
from torch.utils.data import DataLoader
from torch.utils.tensorboard import SummaryWriter

data_path = '/xxxx/cifar10'
datasets = torchvision.datasets.CIFAR10(data_path, train=False, download=True, 
                                    transform=torchvision.transforms.ToTensor())

data_loader = DataLoader(datasets, batch_size=64)

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.maxpool1 = nn.MaxPool2d(kernel_size=3, ceil_mode=False)
#         self.maxpool = nn.MaxPool2d(kernel_size=3, ceil_mode=False)
        
    def forward(self, input):
        output = self.maxpool1(input)
        return output
        

writer = SummaryWriter('logs_maxpool1')
step = 0
net = Net()
for data in data_loader:
    imgs, targets = data
    writer.add_images('input', imgs, step)
    output = net(imgs) 
    writer.add_images('output', output, step)
    step = step + 1
    
    
writer.close() 

• 启动 tensorboard:

tensorboard --logdir=logs_maxpool1 

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卷积过程动画

图片来自：https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md

Transposed convolution animations

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No padding, no strides

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Arbitrary padding, no strides

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Half padding, no strides

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Full padding, no strides

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No padding, strides

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Padding, strides

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Padding, strides (odd)

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Transposed convolution animations

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No padding, no strides, transposed

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Arbitrary padding, no strides, transposed

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Half padding, no strides, transposed

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Full padding, no strides, transposed

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No padding, strides, transposed

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Padding, strides, transposed

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Padding, strides, transposed (odd)