modeci_mdf.functions.onnx.batchnormalization(*args, **kwargs)

Carries out batch normalization as described in the paper Depending on the mode it is being run, There are five required inputs ‘X’, ‘scale’, ‘B’, ‘input_mean’ and ‘input_var’. Note that ‘input_mean’ and ‘input_var’ are expected to be the estimated statistics in inference mode (training_mode=False, default), and the running statistics in training mode (training_mode=True). There are multiple cases for the number of outputs, which we list below:

Output case #1: Y, running_mean, running_var (training_mode=True) Output case #2: Y (training_mode=False)

When training_mode=False, extra outputs are invalid. The outputs are updated as follows when training_mode=True: ``` running_mean = input_mean * momentum + current_mean * (1 - momentum) running_var = input_var * momentum + current_var * (1 - momentum)

Y = (X - current_mean) / sqrt(current_var + epsilon) * scale + B


current_mean = ReduceMean(X, axis=all_except_channel_index) current_var = ReduceVar(X, axis=all_except_channel_index)

Notice that ReduceVar refers to the population variance, and it equals to sum(sqrd(x_i - x_avg)) / N where N is the population size (this formula does not use sample size N - 1).


The computation of ReduceMean and ReduceVar uses float to avoid overflow for float16 inputs.

When training_mode=False: ` Y = (X - input_mean) / sqrt(input_var + epsilon) * scale + B `

For previous (depreciated) non-spatial cases, implementors are suggested to flatten the input shape to (N x C * D1 * D2 * … * Dn) before a BatchNormalization Op. This operator has optional inputs/outputs. See [the doc]( for more details about the representation of optional arguments. An empty string may be used in the place of an actual argument’s name to indicate a missing argument. Trailing optional arguments (those not followed by an argument that is present) may also be simply omitted.