This is a PyTorch implementation of the paper Deep Residual Learning for Image Recognition.

ResNets train layers as residual functions to overcome the *degradation problem*. The degradation problem is the accuracy of deep neural networks degrading when the number of layers becomes very high. The accuracy increases as the number of layers increase, then saturates, and then starts to degrade.

The paper argues that deeper models should perform at least as well as shallower models because the extra layers can just learn to perform an identity mapping.

If $H(x)$ is the mapping that needs to be learned by a few layers, they train the residual function

$F(x)=H(x)−x$

instead. And the original function becomes $F(x)+x$.

In this case, learning identity mapping for $H(x)$ is equivalent to learning $F(x)$ to be $0$, which is easier to learn.

In the parameterized form this can be written as,

$F(x,{W_{i}})+x$

and when the feature map sizes of $F(x,W_{i})$ and $x$ are different the paper suggests doing a linear projection, with learned weights $W_{s}$.

$F(x,{W_{i}})+W_{s}x$

Paper experimented with zero padding instead of linear projections and found linear projections to work better. Also when the feature map sizes match they found identity mapping to be better than linear projections.

$F$ should have more than one layer, otherwise the sum $F(x,{W_{i}})+W_{s}x$ also won't have non-linearities and will be like a linear layer.

Here is the training code for training a ResNet on CIFAR-10.

```
57from typing import List, Optional
58
59import torch
60from torch import nn
61
62from labml_helpers.module import Module
```

`65class ShortcutProjection(Module):`

`in_channels`

is the number of channels in $x$`out_channels`

is the number of channels in $F(x,{W_{i}})$`stride`

is the stride length in the convolution operation for $F$. We do the same stride on the shortcut connection, to match the feature-map size.

`72 def __init__(self, in_channels: int, out_channels: int, stride: int):`

`79 super().__init__()`

Convolution layer for linear projection $W_{s}x$

`82 self.conv = nn.Conv2d(in_channels, out_channels, kernel_size=1, stride=stride)`

Paper suggests adding batch normalization after each convolution operation

`84 self.bn = nn.BatchNorm2d(out_channels)`

`86 def forward(self, x: torch.Tensor):`

Convolution and batch normalization

`88 return self.bn(self.conv(x))`

This implements the residual block described in the paper. It has two $3×3$ convolution layers.

The first convolution layer maps from `in_channels`

to `out_channels`

, where the `out_channels`

is higher than `in_channels`

when we reduce the feature map size with a stride length greater than $1$.

The second convolution layer maps from `out_channels`

to `out_channels`

and always has a stride length of 1.

Both convolution layers are followed by batch normalization.

`91class ResidualBlock(Module):`

`in_channels`

is the number of channels in $x$`out_channels`

is the number of output channels`stride`

is the stride length in the convolution operation.

`112 def __init__(self, in_channels: int, out_channels: int, stride: int):`

`118 super().__init__()`

First $3×3$ convolution layer, this maps to `out_channels`

`121 self.conv1 = nn.Conv2d(in_channels, out_channels, kernel_size=3, stride=stride, padding=1)`

Batch normalization after the first convolution

`123 self.bn1 = nn.BatchNorm2d(out_channels)`

First activation function (ReLU)

`125 self.act1 = nn.ReLU()`

Second $3×3$ convolution layer

`128 self.conv2 = nn.Conv2d(out_channels, out_channels, kernel_size=3, stride=1, padding=1)`

Batch normalization after the second convolution

`130 self.bn2 = nn.BatchNorm2d(out_channels)`

Shortcut connection should be a projection if the stride length is not $1$ of if the number of channels change

`134 if stride != 1 or in_channels != out_channels:`

Projection $W_{s}x$

```
136 self.shortcut = ShortcutProjection(in_channels, out_channels, stride)
137 else:
```

Identity $x$

`139 self.shortcut = nn.Identity()`

Second activation function (ReLU) (after adding the shortcut)

`142 self.act2 = nn.ReLU()`

`x`

is the input of shape`[batch_size, in_channels, height, width]`

`144 def forward(self, x: torch.Tensor):`

Get the shortcut connection

`149 shortcut = self.shortcut(x)`

First convolution and activation

`151 x = self.act1(self.bn1(self.conv1(x)))`

Second convolution

`153 x = self.bn2(self.conv2(x))`

Activation function after adding the shortcut

`155 return self.act2(x + shortcut)`

This implements the bottleneck block described in the paper. It has $1×1$, $3×3$, and $1×1$ convolution layers.

The first convolution layer maps from `in_channels`

to `bottleneck_channels`

with a $1×1$ convolution, where the `bottleneck_channels`

is lower than `in_channels`

.

The second $3×3$ convolution layer maps from `bottleneck_channels`

to `bottleneck_channels`

. This can have a stride length greater than $1$ when we want to compress the feature map size.

The third, final $1×1$ convolution layer maps to `out_channels`

. `out_channels`

is higher than `in_channels`

if the stride length is greater than $1$; otherwise, $out_{c}hannels$ is equal to `in_channels`

.

`bottleneck_channels`

is less than `in_channels`

and the $3×3$ convolution is performed on this shrunk space (hence the bottleneck). The two $1×1$ convolution decreases and increases the number of channels.

`158class BottleneckResidualBlock(Module):`

`in_channels`

is the number of channels in $x$`bottleneck_channels`

is the number of channels for the $3×3$ convlution`out_channels`

is the number of output channels`stride`

is the stride length in the $3×3$ convolution operation.

`186 def __init__(self, in_channels: int, bottleneck_channels: int, out_channels: int, stride: int):`

`193 super().__init__()`

First $1×1$ convolution layer, this maps to `bottleneck_channels`

`196 self.conv1 = nn.Conv2d(in_channels, bottleneck_channels, kernel_size=1, stride=1)`

Batch normalization after the first convolution

`198 self.bn1 = nn.BatchNorm2d(bottleneck_channels)`

First activation function (ReLU)

`200 self.act1 = nn.ReLU()`

Second $3×3$ convolution layer

`203 self.conv2 = nn.Conv2d(bottleneck_channels, bottleneck_channels, kernel_size=3, stride=stride, padding=1)`

Batch normalization after the second convolution

`205 self.bn2 = nn.BatchNorm2d(bottleneck_channels)`

Second activation function (ReLU)

`207 self.act2 = nn.ReLU()`

Third $1×1$ convolution layer, this maps to `out_channels`

.

`210 self.conv3 = nn.Conv2d(bottleneck_channels, out_channels, kernel_size=1, stride=1)`

Batch normalization after the second convolution

`212 self.bn3 = nn.BatchNorm2d(out_channels)`

`216 if stride != 1 or in_channels != out_channels:`

Projection $W_{s}x$

```
218 self.shortcut = ShortcutProjection(in_channels, out_channels, stride)
219 else:
```

Identity $x$

`221 self.shortcut = nn.Identity()`

Second activation function (ReLU) (after adding the shortcut)

`224 self.act3 = nn.ReLU()`

`x`

is the input of shape`[batch_size, in_channels, height, width]`

`226 def forward(self, x: torch.Tensor):`

Get the shortcut connection

`231 shortcut = self.shortcut(x)`

First convolution and activation

`233 x = self.act1(self.bn1(self.conv1(x)))`

Second convolution and activation

`235 x = self.act2(self.bn2(self.conv2(x)))`

Third convolution

`237 x = self.bn3(self.conv3(x))`

Activation function after adding the shortcut

`239 return self.act3(x + shortcut)`

This is a the base of the resnet model without the final linear layer and softmax for classification.

The resnet is made of stacked residual blocks or bottleneck residual blocks. The feature map size is halved after a few blocks with a block of stride length $2$. The number of channels is increased when the feature map size is reduced. Finally the feature map is average pooled to get a vector representation.

`242class ResNetBase(Module):`

`n_blocks`

is a list of of number of blocks for each feature map size.`n_channels`

is the number of channels for each feature map size.`bottlenecks`

is the number of channels the bottlenecks. If this is`None`

, residual blocks are used.`img_channels`

is the number of channels in the input.`first_kernel_size`

is the kernel size of the initial convolution layer

```
256 def __init__(self, n_blocks: List[int], n_channels: List[int],
257 bottlenecks: Optional[List[int]] = None,
258 img_channels: int = 3, first_kernel_size: int = 7):
```

`267 super().__init__()`

Number of blocks and number of channels for each feature map size

`270 assert len(n_blocks) == len(n_channels)`

If bottleneck residual blocks are used, the number of channels in bottlenecks should be provided for each feature map size

`273 assert bottlenecks is None or len(bottlenecks) == len(n_channels)`

Initial convolution layer maps from `img_channels`

to number of channels in the first residual block (`n_channels[0]`

)

```
277 self.conv = nn.Conv2d(img_channels, n_channels[0],
278 kernel_size=first_kernel_size, stride=2, padding=first_kernel_size // 2)
```

Batch norm after initial convolution

`280 self.bn = nn.BatchNorm2d(n_channels[0])`

List of blocks

`283 blocks = []`

Number of channels from previous layer (or block)

`285 prev_channels = n_channels[0]`

Loop through each feature map size

`287 for i, channels in enumerate(n_channels):`

The first block for the new feature map size, will have a stride length of $2$ except fro the very first block

```
290 stride = 2 if len(blocks) == 0 else 1
291
292 if bottlenecks is None:
```

residual blocks that maps from `prev_channels`

to `channels`

```
294 blocks.append(ResidualBlock(prev_channels, channels, stride=stride))
295 else:
```

bottleneck residual blocks that maps from `prev_channels`

to `channels`

```
298 blocks.append(BottleneckResidualBlock(prev_channels, bottlenecks[i], channels,
299 stride=stride))
```

Change the number of channels

`302 prev_channels = channels`

Add rest of the blocks - no change in feature map size or channels

```
304 for _ in range(n_blocks[i] - 1):
305 if bottlenecks is None:
```

```
307 blocks.append(ResidualBlock(channels, channels, stride=1))
308 else:
```

`310 blocks.append(BottleneckResidualBlock(channels, bottlenecks[i], channels, stride=1))`

Stack the blocks

`313 self.blocks = nn.Sequential(*blocks)`

`x`

has shape`[batch_size, img_channels, height, width]`

`315 def forward(self, x: torch.Tensor):`

Initial convolution and batch normalization

`321 x = self.bn(self.conv(x))`

Residual (or bottleneck) blocks

`323 x = self.blocks(x)`

Change `x`

from shape `[batch_size, channels, h, w]`

to `[batch_size, channels, h * w]`

`325 x = x.view(x.shape[0], x.shape[1], -1)`

Global average pooling

`327 return x.mean(dim=-1)`