随着网络的加深，在训练过程中常常会出现梯度消失或是梯度爆炸的问题。对于一些较小的数据集来说，网络过深也常常会导致过拟合，如图1所示。
图1：CIFAR-10 上的训练误差（左）和测试误差（右）
但是，许多网络优异的效果依赖于网络的深度。因此，我们需要一种方法，在加深网络的同时，优化网络的训练效果。
假如我们把神经网络分层，每一层都看作一个函数。那么从第$1$层到第$n$层，对应的函数分别为$f_1(x), f_2(x), f_3(x), ..., f_i(x), ..., f_n(x)$，$x$是输入。前面提到过，网络加深会造成梯度消失或者梯度爆炸的问题。那么，如果能够在每一层的网络输出中涵盖上一层的网络输出，在一定程度上就降低了网络的深度。
ResNet的思路其实很简单，对于第$i$层，如果输入是$x_{i-1}$，那么输出就是$f_i(x_{i-1}) + x_{i-1}$。我们可以考虑一种极端情况，假设第$i-1$层的输出是最优输出，也就是可以使得任务达到最好的输出。如果我们的优化器足够强大，我们可以通过将$f_{i+1}$及后续的所有层的参数都优化为0，使得最终的输出为是$x_i$。这或许也就是采用加法连接而非concat的原因。在官方实现中，残差块一种有两种实现形式，如图2所示。
图2：残差块
实际上，残差网络就是多个$11$卷积块，$33$卷积块和激活函数的组合，如图3和表1所示。
图3：ResNet34网络架构
表1：ResNet网络架构
我们以PyTorch中ResNet34为例进行讲解。
@register_model()
@handle_legacy_interface(weights=("pretrained", ResNet34_Weights.IMAGENET1K_V1))
def resnet34(*, weights: Optional[ResNet34_Weights] = None, progress: bool = True, **kwargs: Any) -> ResNet:
"""ResNet-34 from `Deep Residual Learning for Image Recognition <https://arxiv.org/pdf/1512.03385.pdf>`__.
Args:
weights (:class:`~torchvision.models.ResNet34_Weights`, optional): The
pretrained weights to use. See
:class:`~torchvision.models.ResNet34_Weights` below for
more details, and possible values. By default, no pre-trained
weights are used.
progress (bool, optional): If True, displays a progress bar of the
download to stderr. Default is True.
**kwargs: parameters passed to the ``torchvision.models.resnet.ResNet``
base class. Please refer to the `source code
<https://github.com/pytorch/vision/blob/main/torchvision/models/resnet.py>`_
for more details about this class.
.. autoclass:: torchvision.models.ResNet34_Weights
:members:
"""
weights = ResNet34_Weights.verify(weights)
return _resnet(BasicBlock, [3, 4, 6, 3], weights, progress, **kwargs)从renet34函数中可以看出，ResNet的创建是通过_resnet函数以及多个BasicBlock实现的，[3, 4, 6, 3]对应的是每层BasicBlock的个数。
class BasicBlock(nn.Module):
expansion: int = 1
def __init__(
self,
inplanes: int,
planes: int,
stride: int = 1,
downsample: Optional[nn.Module] = None,
groups: int = 1,
base_width: int = 64,
dilation: int = 1,
norm_layer: Optional[Callable[..., nn.Module]] = None,
) -> None:
super().__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:
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: Tensor) -> Tensor:
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 outBasicBlock是按照图2搭建的，中间加入了一些norm layer。
def _resnet(
block: Type[Union[BasicBlock, Bottleneck]],
layers: List[int],
weights: Optional[WeightsEnum],
progress: bool,
**kwargs: Any,
) -> ResNet:
if weights is not None:
_ovewrite_named_param(kwargs, "num_classes", len(weights.meta["categories"]))
model = ResNet(block, layers, **kwargs)
if weights is not None:
model.load_state_dict(weights.get_state_dict(progress=progress))
return model_resnet函数通过ResNet类创建ResNet模型。
class ResNet(nn.Module):
def __init__(
self,
block: Type[Union[BasicBlock, Bottleneck]],
layers: List[int],
num_classes: int = 1000,
zero_init_residual: bool = False,
groups: int = 1,
width_per_group: int = 64,
replace_stride_with_dilation: Optional[List[bool]] = None,
norm_layer: Optional[Callable[..., nn.Module]] = None,
) -> None:
super().__init__()
_log_api_usage_once(self)
if norm_layer is None:
norm_layer = nn.BatchNorm2d
self._norm_layer = norm_layer
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 "
f"or a 3-element tuple, got {replace_stride_with_dilation}"
)
self.groups = groups
self.base_width = width_per_group
self.conv1 = nn.Conv2d(3, self.inplanes, kernel_size=7, stride=2, padding=3, bias=False)
self.bn1 = norm_layer(self.inplanes)
self.relu = nn.ReLU(inplace=True)
self.maxpool = nn.MaxPool2d(kernel_size=3, stride=2, padding=1)
self.layer1 = self._make_layer(block, 64, layers[0])
self.layer2 = self._make_layer(block, 128, layers[1], stride=2, dilate=replace_stride_with_dilation[0])
self.layer3 = self._make_layer(block, 256, layers[2], stride=2, dilate=replace_stride_with_dilation[1])
self.layer4 = self._make_layer(block, 512, layers[3], stride=2, 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) and m.bn3.weight is not None:
nn.init.constant_(m.bn3.weight, 0) # type: ignore[arg-type]
elif isinstance(m, BasicBlock) and m.bn2.weight is not None:
nn.init.constant_(m.bn2.weight, 0) # type: ignore[arg-type]
def _make_layer(
self,
block: Type[Union[BasicBlock, Bottleneck]],
planes: int,
blocks: int,
stride: int = 1,
dilate: bool = False,
) -> nn.Sequential:
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: Tensor) -> Tensor:
# 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: Tensor) -> Tensor:
return self._forward_impl(x)ResNet类的实现。
残差网络最大的创新点就是残差块的设计，这种设计思想已经被广泛应用在各种模型中，例如transformer中也有残差的思想。