# LayerNorm¶

class torch.nn.LayerNorm(normalized_shape: Union[int, List[int], torch.Size], eps: float = 1e-05, elementwise_affine: bool = True)[source]

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

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

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.

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

input shape from an expected input of size

$[* \times \text{normalized\_shape}[0] \times \text{normalized\_shape}[1] \times \ldots \times \text{normalized\_shape}[-1]]$

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.

Shape:
• Input: $(N, *)$

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

Examples:

>>> 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)