Batch-Channel Normalization

This is a PyTorch implementation of Batch-Channel Normalization from the paper Micro-Batch Training with Batch-Channel Normalization and Weight Standardization. We also have an annotated implementation of Weight Standardization.

Batch-Channel Normalization performs batch normalization followed by a channel normalization (similar to a Group Normalization. When the batch size is small a running mean and variance is used for batch normalization.

Here is the training code for training a VGG network that uses weight standardization to classify CIFAR-10 data.

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26import torch
27from torch import nn
28
29from labml_helpers.module import Module
30from labml_nn.normalization.batch_norm import BatchNorm

Batch-Channel Normalization

This first performs a batch normalization - either normal batch norm or a batch norm with estimated mean and variance (exponential mean/variance over multiple batches). Then a channel normalization performed.

33class BatchChannelNorm(Module):
  • channels is the number of features in the input
  • groups is the number of groups the features are divided into
  • eps is , used in for numerical stability
  • momentum is the momentum in taking the exponential moving average
  • estimate is whether to use running mean and variance for batch norm
43    def __init__(self, channels: int, groups: int,
44                 eps: float = 1e-5, momentum: float = 0.1, estimate: bool = True):
52        super().__init__()

Use estimated batch norm or normal batch norm.

55        if estimate:
56            self.batch_norm = EstimatedBatchNorm(channels,
57                                                 eps=eps, momentum=momentum)
58        else:
59            self.batch_norm = BatchNorm(channels,
60                                        eps=eps, momentum=momentum)

Channel normalization

63        self.channel_norm = ChannelNorm(channels, groups, eps)
65    def forward(self, x):
66        x = self.batch_norm(x)
67        return self.channel_norm(x)

Estimated Batch Normalization

When input is a batch of image representations, where is the batch size, is the number of channels, is the height and is the width. and .

where,

are the running mean and variances. is the momentum for calculating the exponential mean.

70class EstimatedBatchNorm(Module):
  • channels is the number of features in the input
  • eps is , used in for numerical stability
  • momentum is the momentum in taking the exponential moving average
  • estimate is whether to use running mean and variance for batch norm
91    def __init__(self, channels: int,
92                 eps: float = 1e-5, momentum: float = 0.1, affine: bool = True):
99        super().__init__()
100
101        self.eps = eps
102        self.momentum = momentum
103        self.affine = affine
104        self.channels = channels

Channel wise transformation parameters

107        if self.affine:
108            self.scale = nn.Parameter(torch.ones(channels))
109            self.shift = nn.Parameter(torch.zeros(channels))

Tensors for and

112        self.register_buffer('exp_mean', torch.zeros(channels))
113        self.register_buffer('exp_var', torch.ones(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]

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

Keep old shape

123        x_shape = x.shape

Get the batch size

125        batch_size = x_shape[0]

Sanity check to make sure the number of features is correct

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

Reshape into [batch_size, channels, n]

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

Update and in training mode only

134        if self.training:

No backpropagation through and

136            with torch.no_grad():

Calculate the mean across first and last dimensions;

139                mean = x.mean(dim=[0, 2])

Calculate the squared mean across first and last dimensions;

142                mean_x2 = (x ** 2).mean(dim=[0, 2])

Variance for each feature

145                var = mean_x2 - mean ** 2

Update exponential moving averages

153                self.exp_mean = (1 - self.momentum) * self.exp_mean + self.momentum * mean
154                self.exp_var = (1 - self.momentum) * self.exp_var + self.momentum * var

Normalize

158        x_norm = (x - self.exp_mean.view(1, -1, 1)) / torch.sqrt(self.exp_var + self.eps).view(1, -1, 1)

Scale and shift

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

Reshape to original and return

167        return x_norm.view(x_shape)

Channel Normalization

This is similar to Group Normalization but affine transform is done group wise.

170class ChannelNorm(Module):
  • groups is the number of groups the features are divided into
  • channels is the number of features in the input
  • eps is , used in for numerical stability
  • affine is whether to scale and shift the normalized value
177    def __init__(self, channels, groups,
178                 eps: float = 1e-5, affine: bool = True):
185        super().__init__()
186        self.channels = channels
187        self.groups = groups
188        self.eps = eps
189        self.affine = affine

Parameters for affine transformation.

Note that these transforms are per group, unlike in group norm where they are transformed channel-wise.

194        if self.affine:
195            self.scale = nn.Parameter(torch.ones(groups))
196            self.shift = nn.Parameter(torch.zeros(groups))

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]

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

Keep the original shape

207        x_shape = x.shape

Get the batch size

209        batch_size = x_shape[0]

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

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

Reshape into [batch_size, groups, n]

214        x = x.view(batch_size, self.groups, -1)

Calculate the mean across last dimension; i.e. the means for each sample and channel group

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

Calculate the squared mean across last dimension; i.e. the means for each sample and channel group

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

Variance for each sample and feature group

224        var = mean_x2 - mean ** 2

Normalize

229        x_norm = (x - mean) / torch.sqrt(var + self.eps)

Scale and shift group-wise

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

Reshape to original and return

237        return x_norm.view(x_shape)