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Adds a Layer Normalization layer.

Based on the paper:

"Layer Normalization"

Jimmy Lei Ba, Jamie Ryan Kiros, Geoffrey E. Hinton

Can be used as a normalizer function for conv2d and fully_connected.

Given a tensor inputs of rank R, moments are calculated and normalization is performed over axes begin_norm_axis ... R - 1. Scaling and centering, if requested, is performed over axes begin_params_axis .. R - 1.

By default, begin_norm_axis = 1 and begin_params_axis = -1, meaning that normalization is performed over all but the first axis (the HWC if inputs is NHWC), while the beta and gamma trainable parameters are calculated for the rightmost axis (the C if inputs is NHWC). Scaling and recentering is performed via broadcast of the beta and gamma parameters with the normalized tensor.

The shapes of beta and gamma are inputs.shape[begin_params_axis:], and this part of the inputs' shape must be fully defined.

inputs A tensor having rank R. The normalization is performed over axes begin_norm_axis ... R - 1 and centering and scaling parameters are calculated over begin_params_axis ... R - 1.
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 can be done by the next layer.
activation_fn Activation function, default set to None to skip it and maintain a linear activation.
reuse Whether or not the layer and its variables should be reused. To be able to reuse the layer scope must be given.
variables_collections Optional collections for the variables.
outputs_collections Collections to add the outputs.
trainable If True also add variables to the graph collection GraphKeys.TRAINABLE_VARIABLES (see tf.Variable).
begin_norm_axis The first normalization dimension: normalization will be performed along dimensions begin_norm_axis : rank(inputs)
begin_params_axis The first parameter (beta, gamma) dimension: scale and centering parameters will have dimensions begin_params_axis : rank(inputs) and will be broadcast with the normalized inputs accordingly.
scope Optional scope for variable_scope.

A Tensor representing the output of the operation, having the same shape and dtype as inputs.

ValueError If the rank of inputs is not known at graph build time, or if inputs.shape[begin_params_axis:] is not fully defined at graph build time.