# mx.nd.InstanceNorm¶

## Description¶

Applies instance normalization to the n-dimensional input array.

This operator takes an n-dimensional input array where (n>2) and normalizes the input using the following formula:

$out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta$

This layer is similar to batch normalization layer (BatchNorm) with two differences: first, the normalization is carried out per example (instance), not over a batch. Second, the same normalization is applied both at test and train time. This operation is also known as contrast normalization.

If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, …], gamma and beta parameters must be vectors of shape [channel].

This implementation is based on this paper 1

1

Instance Normalization: The Missing Ingredient for Fast Stylization, D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2).

Example:

// Input of shape (2,1,2)
x = [[[ 1.1,  2.2]],
[[ 3.3,  4.4]]]

// gamma parameter of length 1
gamma = [1.5]

// beta parameter of length 1
beta = [0.5]

// Instance normalization is calculated with the above formula
InstanceNorm(x,gamma,beta) = [[[-0.997527  ,  1.99752665]],
[[-0.99752653,  1.99752724]]]


## Arguments¶

Argument

Description

data

NDArray-or-Symbol.

An n-dimensional input array (n > 2) of the form [batch, channel, spatial_dim1, spatial_dim2, …].

gamma

NDArray-or-Symbol.

A vector of length ‘channel’, which multiplies the normalized input.

beta

NDArray-or-Symbol.

A vector of length ‘channel’, which is added to the product of the normalized input and the weight.

eps

float, optional, default=0.00100000005.

An epsilon parameter to prevent division by 0.

## Value¶

out The result mx.ndarray