# mx.nd.BatchNorm¶

## Description¶

Batch normalization.

Normalizes a data batch by mean and variance, and applies a scale gamma as well as offset beta.

Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis:

$\begin{split}data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...])\end{split}$

Then compute the normalized output, which has the same shape as input, as following:

$out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i]$

Both mean and var returns a scalar by treating the input as a vector.

Assume the input has size k on axis 1, then both gamma and beta have shape (k,). If output_mean_var is set to be true, then outputs both data_mean and the inverse of data_var, which are needed for the backward pass. Note that gradient of these two outputs are blocked.

Besides the inputs and the outputs, this operator accepts two auxiliary states, moving_mean and moving_var, which are k-length vectors. They are global statistics for the whole dataset, which are updated by:

moving_mean = moving_mean * momentum + data_mean * (1 - momentum)
moving_var = moving_var * momentum + data_var * (1 - momentum)

If use_global_stats is set to be true, then moving_mean and
moving_var are used instead of data_mean and data_var to compute
the output. It is often used during inference.

The parameter axis specifies which axis of the input shape denotes
the 'channel' (separately normalized groups).  The default is 1.  Specifying -1 sets the channel
axis to be the last item in the input shape.

Both gamma and beta are learnable parameters. But if fix_gamma is true,
then set gamma to 1 and its gradient to 0.


Note

When fix_gamma is set to True, no sparse support is provided. If fix_gamma is set to False, the sparse tensors will fallback.

## Arguments¶

Argument

Description

data

NDArray-or-Symbol.

Input data to batch normalization

gamma

NDArray-or-Symbol gamma array

beta

NDArray-or-Symbol beta array

moving.mean

NDArray-or-Symbol running mean of input

moving.var

NDArray-or-Symbol running variance of input

eps

double, optional, default=0.0010000000474974513.

Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined in cudnn.h when using cudnn (usually 1e-5)

momentum

float, optional, default=0.899999976.

Momentum for moving average

fix.gamma

boolean, optional, default=1.

Fix gamma while training

use.global.stats

boolean, optional, default=0.

Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.

output.mean.var

boolean, optional, default=0.

Output the mean and inverse std

axis

int, optional, default=’1’.

Specify which shape axis the channel is specified

cudnn.off

boolean, optional, default=0.

Do not select CUDNN operator, if available

min.calib.range

float or None, optional, default=None.

The minimum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output.

max.calib.range

float or None, optional, default=None.

The maximum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output.

## Value¶

out The result mx.ndarray