Layer normalization layer (Ba et al., 2016).

Normalize the activations of the previous layer for each given example in a batch independently, rather than across a batch like Batch Normalization. i.e. applies a transformation that maintains the mean activation within each example close to 0 and the activation standard deviation close to 1.

If scale or center are enabled, the layer will scale the normalized outputs by broadcasting them with a trainable variable gamma, and center the outputs by broadcasting with a trainable variable beta. gamma will default to a ones tensor and beta will default to a zeros tensor, so that centering and scaling are no-ops before training has begun.

So, with scaling and centering enabled the normalization equations are as follows:

Let the intermediate activations for a mini-batch to be the inputs.

For each sample x in a batch of inputs, we compute the mean and variance of the sample, normalize each value in the sample (including a small factor epsilon for numerical stability), and finally, transform the normalized output by gamma and beta, which are learned parameters:

outputs <- inputs |> apply(1, function(x) {
  x_normalized <- (x - mean(x)) /
                  sqrt(var(x) + epsilon)
  x_normalized * gamma + beta
})

gamma and beta will span the axes of inputs specified in axis, and this part of the inputs' shape must be fully defined.

For example:

layer <- layer_layer_normalization(axis = c(2, 3, 4))

layer(op_ones(c(5, 20, 30, 40))) |> invisible() # build()
shape(layer$beta)

## shape(20, 30, 40)

shape(layer$gamma)

## shape(20, 30, 40)

Note that other implementations of layer normalization may choose to define gamma and beta over a separate set of axes from the axes being normalized across. For example, Group Normalization (Wu et al. 2018) with group size of 1 corresponds to a layer_layer_normalization() that normalizes across height, width, and channel and has gamma and beta span only the channel dimension. So, this layer_layer_normalization() implementation will not match a layer_group_normalization() layer with group size set to 1.

Usage

layer_layer_normalization(
  object,
  axis = -1L,
  epsilon = 0.001,
  center = TRUE,
  scale = TRUE,
  beta_initializer = "zeros",
  gamma_initializer = "ones",
  beta_regularizer = NULL,
  gamma_regularizer = NULL,
  beta_constraint = NULL,
  gamma_constraint = NULL,
  ...
)

Arguments

object

Object to compose the layer with. A tensor, array, or sequential model.

axis

Integer or list. The axis or axes to normalize across. Typically, this is the features axis/axes. The left-out axes are typically the batch axis/axes. -1 is the last dimension in the input. Defaults to -1.

epsilon

Small float added to variance to avoid dividing by zero. Defaults to 1e-3.

center

If TRUE, add offset of beta to normalized tensor. If FALSE, beta is ignored. Defaults to TRUE.

scale

If TRUE, multiply by gamma. If FALSE, gamma is not used. When the next layer is linear (also e.g. layer_activation_relu()), this can be disabled since the scaling will be done by the next layer. Defaults to TRUE.

beta_initializer

Initializer for the beta weight. Defaults to zeros.

gamma_initializer

Initializer for the gamma weight. Defaults to ones.

beta_regularizer

Optional regularizer for the beta weight. NULL by default.

gamma_regularizer

Optional regularizer for the gamma weight. NULL by default.

beta_constraint

Optional constraint for the beta weight. NULL by default.

gamma_constraint

Optional constraint for the gamma weight. NULL by default.

...

Base layer keyword arguments (e.g. name and dtype).

Value

The return value depends on the value provided for the first argument. If object is:

• a keras_model_sequential(), then the layer is added to the sequential model (which is modified in place). To enable piping, the sequential model is also returned, invisibly.

• a keras_input(), then the output tensor from calling layer(input) is returned.

• NULL or missing, then a Layer instance is returned.

Reference

• Lei Ba et al., 2016.

See also

• https://keras.io/api/layers/normalization_layers/layer_normalization#layernormalization-class

Other normalization layers:
layer_batch_normalization()
layer_group_normalization()
layer_rms_normalization()
layer_spectral_normalization()
layer_unit_normalization()

Other layers:
Layer()
layer_activation()
layer_activation_elu()
layer_activation_leaky_relu()
layer_activation_parametric_relu()
layer_activation_relu()
layer_activation_softmax()
layer_activity_regularization()
layer_add()
layer_additive_attention()
layer_alpha_dropout()
layer_attention()
layer_aug_mix()
layer_auto_contrast()
layer_average()
layer_average_pooling_1d()
layer_average_pooling_2d()
layer_average_pooling_3d()
layer_batch_normalization()
layer_bidirectional()
layer_category_encoding()
layer_center_crop()
layer_concatenate()
layer_conv_1d()
layer_conv_1d_transpose()
layer_conv_2d()
layer_conv_2d_transpose()
layer_conv_3d()
layer_conv_3d_transpose()
layer_conv_lstm_1d()
layer_conv_lstm_2d()
layer_conv_lstm_3d()
layer_cropping_1d()
layer_cropping_2d()
layer_cropping_3d()
layer_cut_mix()
layer_dense()
layer_depthwise_conv_1d()
layer_depthwise_conv_2d()
layer_discretization()
layer_dot()
layer_dropout()
layer_einsum_dense()
layer_embedding()
layer_equalization()
layer_feature_space()
layer_flatten()
layer_flax_module_wrapper()
layer_gaussian_dropout()
layer_gaussian_noise()
layer_global_average_pooling_1d()
layer_global_average_pooling_2d()
layer_global_average_pooling_3d()
layer_global_max_pooling_1d()
layer_global_max_pooling_2d()
layer_global_max_pooling_3d()
layer_group_normalization()
layer_group_query_attention()
layer_gru()
layer_hashed_crossing()
layer_hashing()
layer_identity()
layer_integer_lookup()
layer_jax_model_wrapper()
layer_lambda()
layer_lstm()
layer_masking()
layer_max_num_bounding_boxes()
layer_max_pooling_1d()
layer_max_pooling_2d()
layer_max_pooling_3d()
layer_maximum()
layer_mel_spectrogram()
layer_minimum()
layer_mix_up()
layer_multi_head_attention()
layer_multiply()
layer_normalization()
layer_permute()
layer_rand_augment()
layer_random_brightness()
layer_random_color_degeneration()
layer_random_color_jitter()
layer_random_contrast()
layer_random_crop()
layer_random_elastic_transform()
layer_random_erasing()
layer_random_flip()
layer_random_gaussian_blur()
layer_random_grayscale()
layer_random_hue()
layer_random_invert()
layer_random_perspective()
layer_random_posterization()
layer_random_rotation()
layer_random_saturation()
layer_random_sharpness()
layer_random_shear()
layer_random_translation()
layer_random_zoom()
layer_repeat_vector()
layer_rescaling()
layer_reshape()
layer_resizing()
layer_rms_normalization()
layer_rnn()
layer_separable_conv_1d()
layer_separable_conv_2d()
layer_simple_rnn()
layer_solarization()
layer_spatial_dropout_1d()
layer_spatial_dropout_2d()
layer_spatial_dropout_3d()
layer_spectral_normalization()
layer_stft_spectrogram()
layer_string_lookup()
layer_subtract()
layer_text_vectorization()
layer_tfsm()
layer_time_distributed()
layer_torch_module_wrapper()
layer_unit_normalization()
layer_upsampling_1d()
layer_upsampling_2d()
layer_upsampling_3d()
layer_zero_padding_1d()
layer_zero_padding_2d()
layer_zero_padding_3d()
rnn_cell_gru()
rnn_cell_lstm()
rnn_cell_simple()
rnn_cells_stack()