# mxnet.ndarray.BatchNorm¶

mxnet.ndarray.BatchNorm(data=None, gamma=None, beta=None, moving_mean=None, moving_var=None, eps=_Null, momentum=_Null, fix_gamma=_Null, use_global_stats=_Null, output_mean_var=_Null, axis=_Null, cudnn_off=_Null, out=None, name=None, **kwargs)

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.

Defined in src/operator/nn/batch_norm.cc:L574

Parameters
• data (NDArray) – Input data to batch normalization

• gamma (NDArray) – gamma array

• beta (NDArray) – beta array

• moving_mean (NDArray) – running mean of input

• moving_var (NDArray) – running variance of input

• eps (double, optional, default=0.001) – 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=0.9) – 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

• out (NDArray, optional) – The output NDArray to hold the result.

Returns

out – The output of this function.

Return type

NDArray or list of NDArrays