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# tf.compat.v1.keras.layers.BatchNormalization

Normalize and scale inputs or activations. (Ioffe and Szegedy, 2014).

tf.compat.v1.keras.layers.BatchNormalization(
axis=-1, 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=None, gamma_regularizer=None, beta_constraint=None,
gamma_constraint=None, renorm=False, renorm_clipping=None, renorm_momentum=0.99,
**kwargs
)


Normalize the activations of the previous layer at each batch, i.e. applies a transformation that maintains the mean activation close to 0 and the activation standard deviation close to 1.

Batch normalization differs from other layers in several key aspects:

1) Adding BatchNormalization with training=True to a model causes the result of one example to depend on the contents of all other examples in a minibatch. Be careful when padding batches or masking examples, as these can change the minibatch statistics and affect other examples.

2) Updates to the weights (moving statistics) are based on the forward pass of a model rather than the result of gradient computations.

3) When performing inference using a model containing batch normalization, it is generally (though not always) desirable to use accumulated statistics rather than mini-batch statistics. This is acomplished by passing training=False when calling the model, or using model.predict.

#### Arguments:

• 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.
• renorm: Whether to use Batch Renormalization (arxiv.org/abs/1702.03275). This adds extra variables during training. The inference is the same for either value of this parameter.
• renorm_clipping: A dictionary that may map keys 'rmax', 'rmin', 'dmax' to scalar Tensors used to clip the renorm correction. The correction (r, d) is used as corrected_value = normalized_value * r + d, with r clipped to [rmin, rmax], and d to [-dmax, dmax]. Missing rmax, rmin, dmax are set to inf, 0, inf, respectively.
• renorm_momentum: Momentum used to update the moving means and standard deviations with renorm. Unlike momentum, this affects training and should be neither too small (which would add noise) nor too large (which would give stale estimates). Note that momentum is still applied to get the means and variances for inference.
• fused: if None or True, use a faster, fused implementation if possible. If False, use the system recommended implementation.
• trainable: Boolean, if True the variables will be marked as trainable.
• virtual_batch_size: An int. By default, virtual_batch_size is None, which means batch normalization is performed across the whole batch. When virtual_batch_size is not None, instead perform "Ghost Batch Normalization", which creates virtual sub-batches which are each normalized separately (with shared gamma, beta, and moving statistics). Must divide the actual batch size during execution.
• adjustment: A function taking the Tensor containing the (dynamic) shape of the input tensor and returning a pair (scale, bias) to apply to the normalized values (before gamma and beta), only during training. For example, if axis==-1, adjustment = lambda shape: ( tf.random.uniform(shape[-1:], 0.93, 1.07), tf.random.uniform(shape[-1:], -0.1, 0.1)) will scale the normalized value by up to 7% up or down, then shift the result by up to 0.1 (with independent scaling and bias for each feature but shared across all examples), and finally apply gamma and/or beta. If None, no adjustment is applied. Cannot be specified if virtual_batch_size is specified.

#### 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.

Normalization equations: Consider the intermediate activations (x) of a mini-batch of size (m):

We can compute the mean and variance of the batch

({\muB} = \frac{1}{m} \sum{i=1}^{m} {x_i})

({\sigmaB^2} = \frac{1}{m} \sum{i=1}^{m} ({x_i} - {\mu_B})^2)

and then compute a normalized (x), including a small factor ({\epsilon}) for numerical stability.

(\hat{x_i} = \frac{x_i - \mu_B}{\sqrt{\sigma_B^2 + \epsilon} })

And finally (\hat{x}) is linearly transformed by ({\gamma}) and ({\beta}), which are learned parameters:

({y_i} = {\gamma * \hat{x_i} + \beta})