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


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



(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.


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


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.


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

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).


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.


  • Input: \((N, *)\)

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


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)