一、背景介绍

问题： 当网络层数越来越深时，模型性能不如层数相对较少的模型。这将不利于构建更深的模型。现阶段有采用BatchNorm层来缓解梯度消失或者爆炸，但效果并不明显。训练集上就出现了退化情况，故不是过拟合导致。

在这里插入图片描述
方法：

按道理，给网络叠加更多层，浅层网络的解空间是包含在深层网络的解空间中的，深层网络的解空间至少存在不差于浅层网络的解，因为只需将增加的层变成恒等映射，其他层的权重原封不动copy浅层网络，就可以获得与浅层网络同样的性能。更好的解明明存在，为什么找不到？找到的反而是更差的解？

显然，这是个优化问题，反映出结构相似的模型，其优化难度是不一样的，且难度的增长并不是线性的，越深的模型越难以优化。
出现该问题可能有两种解决方法一种是调整求解方法，比如更好的初始化、更好的梯度下降算法等；另一种是调整模型结构，让模型更易于优化——改变模型结构实际上是改变了error surface的形态。

这里作者采用了第二种解决方法。如下图所示，作者认为采用这种结构能够便于网络进行优化。
在这里插入图片描述

Instead of hoping each few stacked layers directly fit a desired underlying mapping, we explicitly let these layers fit a residual mapping. Formally, denoting the desired underlying mapping as H(x), we let the stacked nonlinear layers fit another mapping of F(x):=H(x)−x. The original mapping is recast into F(x)+x. We hypothesize that it is easier to optimize the residual mapping than to optimize the original, unreferenced mapping. To the extreme, if an identity mapping were optimal, it would be easier to push the residual to zero than to fit an identity mapping by a stack of nonlinear layers.
我们不是希望每几个堆叠层直接拟合所需的底层映射，而是明确让这些层拟合残差映射。形式上，将所需的底层映射表示为 H(x)，我们让堆叠的非线性层拟合 F(x):=H(x)−x 的另一个映射。原始映射被重铸为 F(x)+x。我们假设优化残差映射比优化原始的、未引用的映射更容易。在极端情况下，如果恒等映射是最优的，则将残差推到零比通过一堆非线性层拟合恒等映射更容易。

二、ResNet网络结构

1.ResNet34结构示意图

在这里插入图片描述

2.不同层数的ResNet采用的Block结构。

在原论文中，残差路径可以大致分成2种，一种没有bottleneck结构，如下图左所示，称之为“basic block”，另一种有bottleneck结构，即下图右中的1×1 卷积层，用于先降维再升维，主要出于降低计算复杂度的现实考虑，称之为“bottleneck block”。
在这里插入图片描述
shortcut路径大致也可以分成2种，取决于残差路径是否改变了feature map数量和尺寸，一种是将输入x原封不动地输出，另一种则需要经过1×1卷积来升维 or/and 降采样，主要作用是将输出与F(x)路径的输出保持shape一致，对网络性能的提升并不明显，两种结构如下图所示。
在这里插入图片描述

3.不同层数的ResNet网络结构示意图

在这里插入图片描述

4.实验结果

在这里插入图片描述

三、Pytroch代码

1.代码简单介绍

ResNet根据网络层数不同有着两种卷积模块，如下图。
在这里插入图片描述
这两个模块代码如下，其中downsample指的是shortcut时可能会遇到输入维度或者大小不一样时需要改变输入维度或者大小(通常使用1X1卷积）。


def conv3x3(in_planes, out_planes, stride=1, groups=1, dilation=1):
    """3x3 convolution with padding"""
    return nn.Conv2d(in_planes, out_planes, kernel_size=3, stride=stride,
                     padding=dilation, groups=groups, bias=False, dilation=dilation)


def conv1x1(in_planes, out_planes, stride=1):
    """1x1 convolution"""
    return nn.Conv2d(in_planes, out_planes, kernel_size=1, stride=stride, bias=False)

class BasicBlock(nn.Module):
    expansion = 1

    def __init__(self, inplanes, planes, stride=1, downsample=None, groups=1,
                 base_width=64, dilation=1, norm_layer=None):
        super(BasicBlock, self).__init__()
        if norm_layer is None:
            norm_layer = nn.BatchNorm2d
        if groups != 1 or base_width != 64:
            raise ValueError('BasicBlock only supports groups=1 and base_width=64')
        if dilation > 1:
            dilation = 1
            # raise NotImplementedError("Dilation > 1 not supported in BasicBlock")
        # Both self.conv1 and self.downsample layers downsample the input when stride != 1
        self.conv1 = conv3x3(inplanes, planes, stride)
        self.bn1 = norm_layer(planes)
        self.relu = nn.ReLU(inplace=True)
        self.conv2 = conv3x3(planes, planes)
        self.bn2 = norm_layer(planes)
        self.downsample = downsample
        self.stride = stride

    def forward(self, x):
        identity = x

        out = self.conv1(x)
        out = self.bn1(out)
        out = self.relu(out)

        out = self.conv2(out)
        out = self.bn2(out)

        if self.downsample is not None:
            identity = self.downsample(x)

        out += identity
        out = self.relu(out)

        return out


class Bottleneck(nn.Module):
    # Bottleneck in torchvision places the stride for downsampling at 3x3 convolution(self.conv2)
    # while original implementation places the stride at the first 1x1 convolution(self.conv1)
    # according to "Deep residual learning for image recognition"https://arxiv.org/abs/1512.03385.
    # This variant is also known as ResNet V1.5 and improves accuracy according to
    # https://ngc.nvidia.com/catalog/model-scripts/nvidia:resnet_50_v1_5_for_pytorch.

    expansion = 4

    def __init__(self, inplanes, planes, stride=1, downsample=None, groups=1,
                 base_width=64, dilation=1, norm_layer=None):
        super(Bottleneck, self).__init__()
        if norm_layer is None:
            norm_layer = nn.BatchNorm2d
        width = int(planes * (base_width / 64.)) * groups
        # Both self.conv2 and self.downsample layers downsample the input when stride != 1
        self.conv1 = conv1x1(inplanes, width)
        self.bn1 = norm_layer(width)
        self.conv2 = conv3x3(width, width, stride, groups, dilation)
        self.bn2 = norm_layer(width)
        self.conv3 = conv1x1(width, planes * self.expansion)
        self.bn3 = norm_layer(planes * self.expansion)
        self.relu = nn.ReLU(inplace=True)
        self.downsample = downsample
        self.stride = stride

    def forward(self, x):
        identity = x

        out = self.conv1(x)
        out = self.bn1(out)
        out = self.relu(out)

        out = self.conv2(out)
        out = self.bn2(out)
        out = self.relu(out)

        out = self.conv3(out)
        out = self.bn3(out)

        if self.downsample is not None:
            identity = self.downsample(x)

        out += identity
        out = self.relu(out)

        return out

2. 常见ResNet网络代码汇总

代码来源：BIT_CD/models/resnet.py
在这里插入图片描述

import torch
import torch.nn as nn
from torchvision.models.utils import load_state_dict_from_url


__all__ = ['ResNet', 'resnet18', 'resnet34', 'resnet50', 'resnet101',
           'resnet152', 'resnext50_32x4d', 'resnext101_32x8d',
           'wide_resnet50_2', 'wide_resnet101_2']


model_urls = {
    'resnet18': 'https://download.pytorch.org/models/resnet18-5c106cde.pth',
    'resnet34': 'https://download.pytorch.org/models/resnet34-333f7ec4.pth',
    'resnet50': 'https://download.pytorch.org/models/resnet50-19c8e357.pth',
    'resnet101': 'https://download.pytorch.org/models/resnet101-5d3b4d8f.pth',
    'resnet152': 'https://download.pytorch.org/models/resnet152-b121ed2d.pth',
    'resnext50_32x4d': 'https://download.pytorch.org/models/resnext50_32x4d-7cdf4587.pth',
    'resnext101_32x8d': 'https://download.pytorch.org/models/resnext101_32x8d-8ba56ff5.pth',
    'wide_resnet50_2': 'https://download.pytorch.org/models/wide_resnet50_2-95faca4d.pth',
    'wide_resnet101_2': 'https://download.pytorch.org/models/wide_resnet101_2-32ee1156.pth',
}


def conv3x3(in_planes, out_planes, stride=1, groups=1, dilation=1):
    """3x3 convolution with padding"""
    return nn.Conv2d(in_planes, out_planes, kernel_size=3, stride=stride,
                     padding=dilation, groups=groups, bias=False, dilation=dilation)


def conv1x1(in_planes, out_planes, stride=1):
    """1x1 convolution"""
    return nn.Conv2d(in_planes, out_planes, kernel_size=1, stride=stride, bias=False)


class BasicBlock(nn.Module):
    expansion = 1

    def __init__(self, inplanes, planes, stride=1, downsample=None, groups=1,
                 base_width=64, dilation=1, norm_layer=None):
        super(BasicBlock, self).__init__()
        if norm_layer is None:
            norm_layer = nn.BatchNorm2d
        if groups != 1 or base_width != 64:
            raise ValueError('BasicBlock only supports groups=1 and base_width=64')
        if dilation > 1:
            dilation = 1
            # raise NotImplementedError("Dilation > 1 not supported in BasicBlock")
        # Both self.conv1 and self.downsample layers downsample the input when stride != 1
        self.conv1 = conv3x3(inplanes, planes, stride)
        self.bn1 = norm_layer(planes)
        self.relu = nn.ReLU(inplace=True)
        self.conv2 = conv3x3(planes, planes)
        self.bn2 = norm_layer(planes)
        self.downsample = downsample
        self.stride = stride

    def forward(self, x):
        identity = x

        out = self.conv1(x)
        out = self.bn1(out)
        out = self.relu(out)

        out = self.conv2(out)
        out = self.bn2(out)

        if self.downsample is not None:
            identity = self.downsample(x)

        out += identity
        out = self.relu(out)

        return out


class Bottleneck(nn.Module):
    # Bottleneck in torchvision places the stride for downsampling at 3x3 convolution(self.conv2)
    # while original implementation places the stride at the first 1x1 convolution(self.conv1)
    # according to "Deep residual learning for image recognition"https://arxiv.org/abs/1512.03385.
    # This variant is also known as ResNet V1.5 and improves accuracy according to
    # https://ngc.nvidia.com/catalog/model-scripts/nvidia:resnet_50_v1_5_for_pytorch.

    expansion = 4

    def __init__(self, inplanes, planes, stride=1, downsample=None, groups=1,
                 base_width=64, dilation=1, norm_layer=None):
        super(Bottleneck, self).__init__()
        if norm_layer is None:
            norm_layer = nn.BatchNorm2d
        width = int(planes * (base_width / 64.)) * groups
        # Both self.conv2 and self.downsample layers downsample the input when stride != 1
        self.conv1 = conv1x1(inplanes, width)
        self.bn1 = norm_layer(width)
        self.conv2 = conv3x3(width, width, stride, groups, dilation)
        self.bn2 = norm_layer(width)
        self.conv3 = conv1x1(width, planes * self.expansion)
        self.bn3 = norm_layer(planes * self.expansion)
        self.relu = nn.ReLU(inplace=True)
        self.downsample = downsample
        self.stride = stride

    def forward(self, x):
        identity = x

        out = self.conv1(x)
        out = self.bn1(out)
        out = self.relu(out)

        out = self.conv2(out)
        out = self.bn2(out)
        out = self.relu(out)

        out = self.conv3(out)
        out = self.bn3(out)

        if self.downsample is not None:
            identity = self.downsample(x)

        out += identity
        out = self.relu(out)

        return out


class ResNet(nn.Module):

    def __init__(self, block, layers, num_classes=1000, zero_init_residual=False,
                 groups=1, width_per_group=64, replace_stride_with_dilation=None,
                 norm_layer=None, strides=None):
        super(ResNet, self).__init__()
        if norm_layer is None:
            norm_layer = nn.BatchNorm2d
        self._norm_layer = norm_layer

        self.strides = strides
        if self.strides is None:
            self.strides = [2, 2, 2, 2, 2]

        self.inplanes = 64
        self.dilation = 1
        if replace_stride_with_dilation is None:
            # each element in the tuple indicates if we should replace
            # the 2x2 stride with a dilated convolution instead
            replace_stride_with_dilation = [False, False, False]
        if len(replace_stride_with_dilation) != 3:
            raise ValueError("replace_stride_with_dilation should be None "
                             "or a 3-element tuple, got {}".format(replace_stride_with_dilation))
        self.groups = groups
        self.base_width = width_per_group
        self.conv1 = nn.Conv2d(3, self.inplanes, kernel_size=7, stride=self.strides[0], padding=3,
                               bias=False)
        self.bn1 = norm_layer(self.inplanes)
        self.relu = nn.ReLU(inplace=True)
        self.maxpool = nn.MaxPool2d(kernel_size=3, stride=self.strides[1], padding=1)
        self.layer1 = self._make_layer(block, 64, layers[0])
        self.layer2 = self._make_layer(block, 128, layers[1], stride=self.strides[2],
                                       dilate=replace_stride_with_dilation[0])
        self.layer3 = self._make_layer(block, 256, layers[2], stride=self.strides[3],
                                       dilate=replace_stride_with_dilation[1])
        self.layer4 = self._make_layer(block, 512, layers[3], stride=self.strides[4],
                                       dilate=replace_stride_with_dilation[2])
        self.avgpool = nn.AdaptiveAvgPool2d((1, 1))
        self.fc = nn.Linear(512 * block.expansion, num_classes)

        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                nn.init.kaiming_normal_(m.weight, mode='fan_out', nonlinearity='relu')
            elif isinstance(m, (nn.BatchNorm2d, nn.GroupNorm)):
                nn.init.constant_(m.weight, 1)
                nn.init.constant_(m.bias, 0)

        # Zero-initialize the last BN in each residual branch,
        # so that the residual branch starts with zeros, and each residual block behaves like an identity.
        # This improves the model by 0.2~0.3% according to https://arxiv.org/abs/1706.02677
        if zero_init_residual:
            for m in self.modules():
                if isinstance(m, Bottleneck):
                    nn.init.constant_(m.bn3.weight, 0)
                elif isinstance(m, BasicBlock):
                    nn.init.constant_(m.bn2.weight, 0)

    def _make_layer(self, block, planes, blocks, stride=1, dilate=False):
        norm_layer = self._norm_layer
        downsample = None
        previous_dilation = self.dilation
        if dilate:
            self.dilation *= stride
            stride = 1
        if stride != 1 or self.inplanes != planes * block.expansion:
            downsample = nn.Sequential(
                conv1x1(self.inplanes, planes * block.expansion, stride),
                norm_layer(planes * block.expansion),
            )

        layers = []
        layers.append(block(self.inplanes, planes, stride, downsample, self.groups,
                            self.base_width, previous_dilation, norm_layer))
        self.inplanes = planes * block.expansion
        for _ in range(1, blocks):
            layers.append(block(self.inplanes, planes, groups=self.groups,
                                base_width=self.base_width, dilation=self.dilation,
                                norm_layer=norm_layer))

        return nn.Sequential(*layers)

    def _forward_impl(self, x):
        # See note [TorchScript super()]
        x = self.conv1(x)
        x = self.bn1(x)
        x = self.relu(x)
        x = self.maxpool(x)

        x = self.layer1(x)
        x = self.layer2(x)
        x = self.layer3(x)
        x = self.layer4(x)

        x = self.avgpool(x)
        x = torch.flatten(x, 1)
        x = self.fc(x)

        return x

    def forward(self, x):
        return self._forward_impl(x)


def _resnet(arch, block, layers, pretrained, progress, **kwargs):
    model = ResNet(block, layers, **kwargs)
    if pretrained:
        state_dict = load_state_dict_from_url(model_urls[arch],
                                              progress=progress)
        model.load_state_dict(state_dict)
    return model


def resnet18(pretrained=False, progress=True, **kwargs):
    r"""ResNet-18 model from
    `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_

    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
        progress (bool): If True, displays a progress bar of the download to stderr
    """
    return _resnet('resnet18', BasicBlock, [2, 2, 2, 2], pretrained, progress,
                   **kwargs)


def resnet34(pretrained=False, progress=True, **kwargs):
    r"""ResNet-34 model from
    `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_

    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
        progress (bool): If True, displays a progress bar of the download to stderr
    """
    return _resnet('resnet34', BasicBlock, [3, 4, 6, 3], pretrained, progress,
                   **kwargs)


def resnet50(pretrained=False, progress=True, **kwargs):
    r"""ResNet-50 model from
    `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_

    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
        progress (bool): If True, displays a progress bar of the download to stderr
    """
    return _resnet('resnet50', Bottleneck, [3, 4, 6, 3], pretrained, progress,
                   **kwargs)


def resnet101(pretrained=False, progress=True, **kwargs):
    r"""ResNet-101 model from
    `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_

    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
        progress (bool): If True, displays a progress bar of the download to stderr
    """
    return _resnet('resnet101', Bottleneck, [3, 4, 23, 3], pretrained, progress,
                   **kwargs)


def resnet152(pretrained=False, progress=True, **kwargs):
    r"""ResNet-152 model from
    `"Deep Residual Learning for Image Recognition" <https://arxiv.org/pdf/1512.03385.pdf>`_

    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
        progress (bool): If True, displays a progress bar of the download to stderr
    """
    return _resnet('resnet152', Bottleneck, [3, 8, 36, 3], pretrained, progress,
                   **kwargs)


def resnext50_32x4d(pretrained=False, progress=True, **kwargs):
    r"""ResNeXt-50 32x4d model from
    `"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_

    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
        progress (bool): If True, displays a progress bar of the download to stderr
    """
    kwargs['groups'] = 32
    kwargs['width_per_group'] = 4
    return _resnet('resnext50_32x4d', Bottleneck, [3, 4, 6, 3],
                   pretrained, progress, **kwargs)


def resnext101_32x8d(pretrained=False, progress=True, **kwargs):
    r"""ResNeXt-101 32x8d model from
    `"Aggregated Residual Transformation for Deep Neural Networks" <https://arxiv.org/pdf/1611.05431.pdf>`_

    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
        progress (bool): If True, displays a progress bar of the download to stderr
    """
    kwargs['groups'] = 32
    kwargs['width_per_group'] = 8
    return _resnet('resnext101_32x8d', Bottleneck, [3, 4, 23, 3],
                   pretrained, progress, **kwargs)


def wide_resnet50_2(pretrained=False, progress=True, **kwargs):
    r"""Wide ResNet-50-2 model from
    `"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_

    The model is the same as ResNet except for the bottleneck number of channels
    which is twice larger in every block. The number of channels in outer 1x1
    convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048
    channels, and in Wide ResNet-50-2 has 2048-1024-2048.

    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
        progress (bool): If True, displays a progress bar of the download to stderr
    """
    kwargs['width_per_group'] = 64 * 2
    return _resnet('wide_resnet50_2', Bottleneck, [3, 4, 6, 3],
                   pretrained, progress, **kwargs)


def wide_resnet101_2(pretrained=False, progress=True, **kwargs):
    r"""Wide ResNet-101-2 model from
    `"Wide Residual Networks" <https://arxiv.org/pdf/1605.07146.pdf>`_

    The model is the same as ResNet except for the bottleneck number of channels
    which is twice larger in every block. The number of channels in outer 1x1
    convolutions is the same, e.g. last block in ResNet-50 has 2048-512-2048
    channels, and in Wide ResNet-50-2 has 2048-1024-2048.

    Args:
        pretrained (bool): If True, returns a model pre-trained on ImageNet
        progress (bool): If True, displays a progress bar of the download to stderr
    """
    kwargs['width_per_group'] = 64 * 2
    return _resnet('wide_resnet101_2', Bottleneck, [3, 4, 23, 3],
                   pretrained, progress, **kwargs)