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# tf.keras.layers.BatchNormalization

Layer that normalizes its inputs.

Inherits From: Layer, Module

### Used in the notebooks

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.

axis Integer, the axis that should be normalized (typically the features axis). For instance, after a Conv2D layer with data_format="channels_first", set axis=1 in BatchNormalization.
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 (also e.g. nn.relu), 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.

#### Call arguments:

• inputs: Input tensor (of any rank).
• training: Python 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.

#### Input shape:

Arbitrary. Use the keyword argument input_shape (tuple of integers, does not include the samples axis) when using this layer as the first layer in a model.

#### Output shape:

Same shape as input.

#### Reference:

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).

This behavior has been introduced in TensorFlow 2.0, in order to enable layer.trainable = False to produce the most commonly expected behavior in the convnet fine-tuning use case.

#### Note that:

• Setting trainable on an model containing other layers will recursively set the trainable value of all inner layers.
• If the value of the trainable attribute is changed after calling compile() on a model, the new value doesn't take effect for this model until compile() is called again.