# Instance Normalization

This is a PyTorch implementation of Instance Normalization: The Missing Ingredient for Fast Stylization.

Instance normalization was introduced to improve style transfer. It is based on the observation that stylization should not depend on the contrast of the content image. The “contrast normalization” is

where $x$ is a batch of images with dimensions image index $t$, feature channel $i$, and spatial position $j, k$.

Since it’s hard for a convolutional network to learn “contrast normalization”, this paper introduces instance normalization which does that.

Here’s a CIFAR 10 classification model that uses instance normalization.

29import torch
30from torch import nn
31
32from labml_helpers.module import Module

## Instance Normalization Layer

Instance normalization layer $\text{IN}$ normalizes the input $X$ as follows:

When input $X \in \mathbb{R}^{B \times C \times H \times W}$ is a batch of image representations, where $B$ is the batch size, $C$ is the number of channels, $H$ is the height and $W$ is the width. $\gamma \in \mathbb{R}^{C}$ and $\beta \in \mathbb{R}^{C}$. The affine transformation with $gamma$ and $beta$ are optional.

35class InstanceNorm(Module):
• channels is the number of features in the input
• eps is $\epsilon$, used in $\sqrt{Var[X] + \epsilon}$ for numerical stability
• affine is whether to scale and shift the normalized value
51    def __init__(self, channels: int, *,
52                 eps: float = 1e-5, affine: bool = True):
58        super().__init__()
59
60        self.channels = channels
61
62        self.eps = eps
63        self.affine = affine

Create parameters for $\gamma$ and $\beta$ for scale and shift

65        if self.affine:
66            self.scale = nn.Parameter(torch.ones(channels))
67            self.shift = nn.Parameter(torch.zeros(channels))

x is a tensor of shape [batch_size, channels, *]. * denotes any number of (possibly 0) dimensions. For example, in an image (2D) convolution this will be [batch_size, channels, height, width]

69    def forward(self, x: torch.Tensor):

Keep the original shape

77        x_shape = x.shape

Get the batch size

79        batch_size = x_shape[0]

Sanity check to make sure the number of features is the same

81        assert self.channels == x.shape[1]

Reshape into [batch_size, channels, n]

84        x = x.view(batch_size, self.channels, -1)

Calculate the mean across last dimension i.e. the means for each feature $\mathbb{E}[x_{t,i}]$

88        mean = x.mean(dim=[-1], keepdim=True)

Calculate the squared mean across first and last dimension; i.e. the means for each feature $\mathbb{E}[(x_{t,i}^2]$

91        mean_x2 = (x ** 2).mean(dim=[-1], keepdim=True)

Variance for each feature $Var[x_{t,i}] = \mathbb{E}[x_{t,i}^2] - \mathbb{E}[x_{t,i}]^2$

93        var = mean_x2 - mean ** 2

Normalize

96        x_norm = (x - mean) / torch.sqrt(var + self.eps)
97        x_norm = x_norm.view(batch_size, self.channels, -1)

Scale and shift

100        if self.affine:
101            x_norm = self.scale.view(1, -1, 1) * x_norm + self.shift.view(1, -1, 1)

Reshape to original and return

104        return x_norm.view(x_shape)

Simple test

107def _test():
111    from labml.logger import inspect
112
113    x = torch.zeros([2, 6, 2, 4])
114    inspect(x.shape)
115    bn = InstanceNorm(6)
116
117    x = bn(x)
118    inspect(x.shape)
122if __name__ == '__main__':
123    _test()