R-Drop: Regularized Dropout for Neural Networks

Dropout is a powerful and widely used technique to regularize the training of deep neural networks.

Dropout在训练和推理时存在不一致的问题（集成学习）R 对每个子模型的分布做一个KL散度

import numpy as np

def train_r_drop(ratio, x, w1, b1, w2, b2):
    # 输入复制一份
    x = torch.cat([x, x], dim=0)
    layer1 = np.maximum(0, np.dot(w1, x) + b1)
    mask1 = np.random.binomial(1, 1-ratio, layer1.shape)
    layer1 = layer1 * mask1
    
    layer2 = np.maximum(0, np.dot(w2, layer1) + b2)
    mask2 = np.random.binomial(1, 1-ratio, layer2.shape)
    layer2 = layer2 * mask2
    
    logits = func(layer2)
    logits1, logits2 = logits[:bs, :], logits[bs:, :]
    nll1 = nll(logits1, label)
    nll2 = nll(logits2, label)
    kl_los = kl(logits1, logits2)
    loss = nll1 + nll2 + kl_loss
    
    return loss

def test(ratio, x, w1, b1, w2, b2):
    layer1 = np.maximum(0, np.dot(w1, x) + b1)
    layer1 = layer1 * (1-ratio)
    
    layer2 = np.maximum(0, np.dot(w2, layer1) + b2)
    layer2 = layer2 * (1-ratio)
    return layer2

import torch
conv_layer = torch.nn.Conv2d(in_channels=2, out_channels=2, kernel_size=3, padding="same")
for i in conv_layer.named_parameters():
    print(i)
'''
('weight', Parameter containing:
tensor([[[[-0.1885,  0.1133, -0.0103],
          [-0.0462, -0.1434, -0.0569],
          [ 0.1969,  0.0827, -0.1245]],

         [[ 0.1554,  0.1459,  0.0405],
          [-0.0806,  0.1438, -0.1319],
          [-0.1495, -0.0960,  0.2193]]],


        [[[-0.1748,  0.1517,  0.0040],
          [ 0.0097,  0.1565,  0.1850],
          [-0.0261,  0.1298,  0.0211]],

         [[-0.0964, -0.0133, -0.0378],
          [ 0.0617, -0.2037,  0.0011],
          [-0.0542, -0.1499,  0.0187]]]], requires_grad=True))
('bias', Parameter containing:
tensor([0.0560, 0.2200], requires_grad=True))
'''
conv_layer.weights.size()
'''
对于输出的第1个通道而言：
对于输入的2个通道都有3×3的卷积核分别在这2个输入通道上做卷积再求和，就得到了，第1个输出通道的特征值。
对于输出的第2个通道而言：
又来了2个卷积核，对输入的2个通道做卷积，得到第2个输出通道的特征值。
torch.Size([2, 2, 3, 3])  3,3为Kernel_size大小 2,2  是输出×输入
'''
conv_layer.bias.size()
'''
torch.Size([2])  和输出通道一致
'''
conv_layer = torch.nn.Conv2d(in_channels=2, out_channels=4, kernel_size=3, padding="same")
print(conv_layer.weight.size())

'''
4中每个输出通道，都有2套3×3的矩阵对输入进行滑动卷积，再将2个通道的值加起来再加上bias就构成输出通道的特征值
torch.Size([4, 2, 3, 3])
'''

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)

• stride controls the stride for the cross-correlation, a single number or a tuple.
• padding controls the amount of padding applied to the input. It can be either a string {‘valid’, ‘same’} or an int / a tuple of ints giving the amount of implicit padding applied on both sides.
• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. For example,

  • At groups=1, all inputs are convolved to all outputs.
  • At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels and producing half the output channels, and both subsequently concatenated.
  • At groups= in_channels, each input channel is convolved with its own set of filters (of size out_channelsin_channelsin_channelsout_channels).

  The parameters kernel_size, stride, padding, dilation can either be:

  • a single int – in which case the same value is used for the height and width dimension
  • a tuple of two ints – in which case, the first int is used for the height dimension, and the second int for the width dimension

深度和可分离卷积

groups > 1；且能够被input_channels和out_channels整除

同时将两者分为好多组，单独做卷积。

好处：

1、并没有将通道完全的mix，假设有8个通道，分为2组，前4个通道后4个通道分别做一个卷积组

2、计算量下降

resnet的一个变体网络 RepConv

point-wise convolution

1×1的卷积

卷积基本假设：局部关联性、平移不变性

不考虑周围点，仅考虑自身：只是将每个通道上的值进行加权求和channels mix

depth-wise convolution

groups > 1 不考虑对所有channels进行mix，而是划分部分mix

import torch
# 分为2部分：1、输入通道为1，输出通道为2的卷积；2、也是输入通道为1，输出通道为2的卷积，最后再拼起来 计算量下降
conv_layer = torch.nn.Conv2d(in_channels=2, out_channels=4, kernel_size=3, padding="same", groups=2)
print(conv_layer.weight.size())
print(conv_layer.bias.size())
'''
torch.Size([4, 1, 3, 3])
torch.Size([4])
'''

conv_layer1 = torch.nn.Conv2d(in_channels=1, out_channels=2, kernel_size=3, padding="same")
conv_layer2 = torch.nn.Conv2d(in_channels=1, out_channels=2, kernel_size=3, padding="same")

print(conv_layer1.weight.size())
print(conv_layer2.weight.size())
print(conv_layer1.bias.size())
print(conv_layer2.bias.size())

'''
torch.Size([2, 1, 3, 3])
torch.Size([2, 1, 3, 3])
torch.Size([2])
torch.Size([2])
'''

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如何将3×3卷积、1×1、x融合为1个3×3卷积?

import torch
import torch.nn as nn
import torch.nn.functional as F


in_channels = 2
out_channels = 2
kernel_size = 3
w = 9
h = 9
# res_block = 3 * 3 conv + 1 * 1 conv + input
# 定义输入图片大小
x = torch.ones(1, in_channels, w, h)
# 方法1：原生写法
# 输入与输出通道一致  3 * 3 conv 要做padding
conv_2d = nn.Conv2d(in_channels, out_channels, kernel_size, padding="same")
# 定义1 * 1 conv只考虑像素点的通道而不考虑周围点的关联性 不需要padding
conv_2d_pointwise = nn.Conv2d(in_channels, out_channels, kernel_size=1, padding="same")
result1 = conv_2d(x) + conv_2d_pointwise(x) + x

# print(result1)

# 方法2：算子融合 RepConv
# 1) 改造
# 将point-wise卷积和x本身都写为3*3的卷积
# 最终把3个卷积融合为1个卷积
# 扩充point-wise卷积核的weight 1*1 => 3*3
#                          1 * 1 => 3 * 3 weight:2(O) 2(I) 1(k) 1(k) => 2(O) 2(I) 3(K1) 3(K2)
#                          上下、左右各pad 0 pad为从内到外pad 先pad K2上下、左右再pad K1上下、左右 O与I上下、左右不pad
pointwise_to_conv_weight = F.pad(conv_2d_pointwise.weight, pad=[1, 1, 1, 1, 0, 0, 0, 0])
conv_2d_for_pointwise = nn.Conv2d(in_channels, out_channels, kernel_size, padding="same")
conv_2d_for_pointwise.weight = nn.Parameter(pointwise_to_conv_weight)
conv_2d_for_pointwise.bias = conv_2d_pointwise.bias

# 将x本身变为1个3*3卷积 x经过卷积后仍为x
# 不考虑相邻点融合=>`point-wise convolution`
# 不考虑通道间融合=>`depth-wise convolution`
# weight:2*2*3*3
# 第1个3*3中间为1, 其余部分为0, 第2个3*3全0;
# 第4个3*3中间为1, 其余部分为0, 第3个3*3全0;
# 不考虑相邻通道
zeros = torch.unsqueeze(torch.zeros(kernel_size, kernel_size), 0)
# 不考虑相邻点
stars = torch.unsqueeze(F.pad(torch.ones(1, 1), pad=[1, 1, 1, 1]), 0)

# 第1个channel
stars_zeros = torch.unsqueeze(torch.cat([stars, zeros], 0), 0)
# 第2个channel
zeros_stars = torch.unsqueeze(torch.cat([zeros, stars], 0), 0)

identity_to_conv_weight = torch.cat([stars_zeros, zeros_stars], 0)
identity_to_conv_bias = torch.zeros([out_channels])

conv_2d_for_identity = nn.Conv2d(in_channels, out_channels, kernel_size, padding="same")
conv_2d_for_identity.weight = nn.Parameter(identity_to_conv_weight)
conv_2d_for_identity.bias = nn.Parameter(identity_to_conv_bias)

result2 = conv_2d(x) + conv_2d_for_pointwise(x) + conv_2d_for_identity(x)
# print(result2)

print(torch.all(torch.isclose(result1, result2)))
# 目前将1*1和x本身都改为3*3
# 2) 融合
conv_2d_for_fussion = nn.Conv2d(in_channels, out_channels, kernel_size, padding="same")
conv_2d_for_fussion.weight = nn.Parameter(conv_2d.weight.data + conv_2d_for_pointwise.weight.data + conv_2d_for_identity.weight.data)
conv_2d_for_fussion.bias = nn.Parameter(conv_2d.bias.data + conv_2d_for_pointwise.bias.data + conv_2d_for_identity.bias.data)

result3 = conv_2d_for_fussion(x)

print(torch.all(torch.isclose(result2, result3)))

'''
tensor(True)
tensor(True)
'''

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