Applies Layer Normalization over a mini-batch of inputs as described in the paper Layer Normalization

## Usage

nn_layer_norm(normalized_shape, eps = 1e-05, elementwise_affine = TRUE)

## Arguments

normalized_shape

(int or list): input shape from an expected input of size $$[* \times \mbox{normalized\_shape}[0] \times \mbox{normalized\_shape}[1] \times \ldots \times \mbox{normalized\_shape}[-1]]$$ If a single integer is used, it is treated as a singleton list, and this module will normalize over the last dimension which is expected to be of that specific size.

eps

a value added to the denominator for numerical stability. Default: 1e-5

elementwise_affine

a boolean value that when set to TRUE, this module has learnable per-element affine parameters initialized to ones (for weights) and zeros (for biases). Default: TRUE.

## Details

$$y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta$$

The mean and standard-deviation are calculated separately over the last certain number dimensions which have to be of the shape specified by normalized_shape.

$$\gamma$$ and $$\beta$$ are learnable affine transform parameters of normalized_shape if elementwise_affine is TRUE.

The standard-deviation is calculated via the biased estimator, equivalent to torch_var(input, unbiased=FALSE).

## Note

Unlike Batch Normalization and Instance Normalization, which applies scalar scale and bias for each entire channel/plane with the affine option, Layer Normalization applies per-element scale and bias with elementwise_affine.

This layer uses statistics computed from input data in both training and evaluation modes.

## Shape

• Input: $$(N, *)$$

• Output: $$(N, *)$$ (same shape as input)

## Examples

if (torch_is_installed()) {

input <- torch_randn(20, 5, 10, 10)
# With Learnable Parameters
m <- nn_layer_norm(input$size()[-1]) # Without Learnable Parameters m <- nn_layer_norm(input$size()[-1], elementwise_affine = FALSE)
# Normalize over last two dimensions
m <- nn_layer_norm(c(10, 10))
# Normalize over last dimension of size 10
m <- nn_layer_norm(10)
# Activating the module
output <- m(input)
}