# LayerNorm¶

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

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

The mean and standard-deviation are calculated over the last D dimensions, where D is the dimension of normalized_shape. For example, if normalized_shape is (3, 5) (a 2-dimensional shape), the mean and standard-deviation are computed over the last 2 dimensions of the input (i.e. input.mean((-2, -1))). $\gamma$ 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.

Variables
• ~LayerNorm.weight – the learnable weights of the module of shape $\text{normalized\_shape}$ when elementwise_affine is set to True. The values are initialized to 1.

• ~LayerNorm.bias – the learnable bias of the module of shape $\text{normalized\_shape}$ when elementwise_affine is set to True. The values are initialized to 0.

Shape:
• Input: $(N, *)$

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

Examples:

>>> # NLP Example
>>> batch, sentence_length, embedding_dim = 20, 5, 10
>>> embedding = torch.randn(batch, sentence_length, embedding_dim)
>>> layer_norm = nn.LayerNorm(embedding_dim)
>>> # Activate module
>>> layer_norm(embedding)
>>>
>>> # Image Example
>>> N, C, H, W = 20, 5, 10, 10
>>> input = torch.randn(N, C, H, W)
>>> # Normalize over the last three dimensions (i.e. the channel and spatial dimensions)
>>> # as shown in the image below
>>> layer_norm = nn.LayerNorm([C, H, W])
>>> output = layer_norm(input)