class torch.nn.LayerNorm(normalized_shape, eps=1e-05, elementwise_affine=True, device=None, dtype=None)[source]

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

y=xE[x]Var[x]+ϵγ+βy = \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. γ\gamma and β\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.

  • normalized_shape (int or list or torch.Size) –

    input shape from an expected input of size

    [×normalized_shape[0]×normalized_shape[1]××normalized_shape[1]][* \times \text{normalized\_shape}[0] \times \text{normalized\_shape}[1] \times \ldots \times \text{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.

  • Input: (N,)(N, *)

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


>>> input = torch.randn(20, 5, 10, 10)
>>> # With Learnable Parameters
>>> m = nn.LayerNorm(input.size()[1:])
>>> # Without Learnable Parameters
>>> m = nn.LayerNorm(input.size()[1:], elementwise_affine=False)
>>> # Normalize over last two dimensions
>>> m = nn.LayerNorm([10, 10])
>>> # Normalize over last dimension of size 10
>>> m = nn.LayerNorm(10)
>>> # Activating the module
>>> output = m(input)


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