Batch normalization applies a transformation that maintains the mean output close to 0 and the output standard deviation close to 1.

Importantly, batch normalization works differently during training and during inference.

**During training** (i.e. when using `fit()`

or when calling the layer/model
with the argument `training = TRUE`

), the layer normalizes its output using
the mean and standard deviation of the current batch of inputs. That is to
say, for each channel being normalized, the layer returns
`gamma * (batch - mean(batch)) / sqrt(var(batch) + epsilon) + beta`

, where:

`epsilon`

is small constant (configurable as part of the constructor arguments)`gamma`

is a learned scaling factor (initialized as 1), which can be disabled by passing`scale = FALSE`

to the constructor.`beta`

is a learned offset factor (initialized as 0), which can be disabled by passing`center = FALSE`

to the constructor.

**During inference** (i.e. when using `evaluate()`

or `predict()`

or when
calling the layer/model with the argument `training = FALSE`

(which is the
default), the layer normalizes its output using a moving average of the
mean and standard deviation of the batches it has seen during training. That
is to say, it returns
`gamma * (batch - self$moving_mean) / sqrt(self$moving_var+epsilon) + beta`

.

`self$moving_mean`

and `self$moving_var`

are non-trainable variables that
are updated each time the layer in called in training mode, as such:

`moving_mean = moving_mean * momentum + mean(batch) * (1 - momentum)`

`moving_var = moving_var * momentum + var(batch) * (1 - momentum)`

As such, the layer will only normalize its inputs during inference
*after having been trained on data that has similar statistics as the
inference data*.

**About setting layer$trainable <- FALSE on a BatchNormalization layer:**

The meaning of setting `layer$trainable <- FALSE`

is to freeze the layer,
i.e. its internal state will not change during training:
its trainable weights will not be updated
during `fit()`

or `train_on_batch()`

, and its state updates will not be run.

Usually, this does not necessarily mean that the layer is run in inference
mode (which is normally controlled by the `training`

argument that can
be passed when calling a layer). "Frozen state" and "inference mode"
are two separate concepts.

However, in the case of the `BatchNormalization`

layer, **setting
trainable <- FALSE on the layer means that the layer will be
subsequently run in inference mode** (meaning that it will use
the moving mean and the moving variance to normalize the current batch,
rather than using the mean and variance of the current batch).

Note that:

## Usage

```
layer_batch_normalization(
object,
axis = -1L,
momentum = 0.99,
epsilon = 0.001,
center = TRUE,
scale = TRUE,
beta_initializer = "zeros",
gamma_initializer = "ones",
moving_mean_initializer = "zeros",
moving_variance_initializer = "ones",
beta_regularizer = NULL,
gamma_regularizer = NULL,
beta_constraint = NULL,
gamma_constraint = NULL,
synchronized = FALSE,
...
)
```

## Arguments

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

- axis
Integer, the axis that should be normalized (typically the features axis). For instance, after a

`Conv2D`

layer with`data_format = "channels_first"`

, use`axis = 2`

.- momentum
Momentum for the moving average.

- epsilon
Small float added to variance to avoid dividing by zero.

- center
If

`TRUE`

, add offset of`beta`

to normalized tensor. If`FALSE`

,`beta`

is ignored.- scale
If

`TRUE`

, multiply by`gamma`

. If`FALSE`

,`gamma`

is not used. When the next layer is linear this can be disabled since the scaling will be done by the next layer.- beta_initializer
Initializer for the beta weight.

- gamma_initializer
Initializer for the gamma weight.

- moving_mean_initializer
Initializer for the moving mean.

- moving_variance_initializer
Initializer for the moving variance.

- beta_regularizer
Optional regularizer for the beta weight.

- gamma_regularizer
Optional regularizer for the gamma weight.

- beta_constraint
Optional constraint for the beta weight.

- gamma_constraint
Optional constraint for the gamma weight.

- synchronized
Only applicable with the TensorFlow backend. If

`TRUE`

, synchronizes the global batch statistics (mean and variance) for the layer across all devices at each training step in a distributed training strategy. If`FALSE`

, each replica uses its own local batch statistics.- ...
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.

## Call Arguments

`inputs`

: Input tensor (of any rank).`training`

: R boolean indicating whether the layer should behave in training mode or in inference mode.`training = TRUE`

: The layer will normalize its inputs using the mean and variance of the current batch of inputs.`training = FALSE`

: The layer will normalize its inputs using the mean and variance of its moving statistics, learned during training.

`mask`

: Binary tensor of shape broadcastable to`inputs`

tensor, with`TRUE`

values indicating the positions for which mean and variance should be computed. Masked elements of the current inputs are not taken into account for mean and variance computation during training. Any prior unmasked element values will be taken into account until their momentum expires.

## See also

Other normalization layers: `layer_group_normalization()`

`layer_layer_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_average()`

`layer_average_pooling_1d()`

`layer_average_pooling_2d()`

`layer_average_pooling_3d()`

`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_dense()`

`layer_depthwise_conv_1d()`

`layer_depthwise_conv_2d()`

`layer_discretization()`

`layer_dot()`

`layer_dropout()`

`layer_einsum_dense()`

`layer_embedding()`

`layer_feature_space()`

`layer_flatten()`

`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_lambda()`

`layer_layer_normalization()`

`layer_lstm()`

`layer_masking()`

`layer_max_pooling_1d()`

`layer_max_pooling_2d()`

`layer_max_pooling_3d()`

`layer_maximum()`

`layer_minimum()`

`layer_multi_head_attention()`

`layer_multiply()`

`layer_normalization()`

`layer_permute()`

`layer_random_brightness()`

`layer_random_contrast()`

`layer_random_crop()`

`layer_random_flip()`

`layer_random_rotation()`

`layer_random_translation()`

`layer_random_zoom()`

`layer_repeat_vector()`

`layer_rescaling()`

`layer_reshape()`

`layer_resizing()`

`layer_rnn()`

`layer_separable_conv_1d()`

`layer_separable_conv_2d()`

`layer_simple_rnn()`

`layer_spatial_dropout_1d()`

`layer_spatial_dropout_2d()`

`layer_spatial_dropout_3d()`

`layer_spectral_normalization()`

`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()`