giagrad.nn.BatchNormND#

class giagrad.nn.BatchNormND(*args, **kwargs)[source]#

Applies Batch Normalization as described in Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

\[y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta\]

The mean and standard-deviation are calculated per-dimension over the mini-batches and \(\gamma\) and \(\beta\) are learnable parameter vectors of size C (where C is the number of features or channels). By default, the elements of \(\gamma\) are set to 1 and the elements of \(\beta\) are set to 0. The standard-deviation is calculated with zero degrees of freedom, equivalent to Tensor.var(ddof=0).

Also by default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default momentum of 0.1.

If track_running_stats is set to False, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.

Note

This momentum argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is \(\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momentum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.

Shape:

  • Input (\(N, C, *\))

  • Output (\(N, C, *\) (same shape as input))

Parameters:

  • eps (default: 1e-5) – A value added to the denominator for numerical stability.

  • momentum (default: 0.1) – The value used for the running_mean and running_var computation. Can be set to None for cumulative moving average (i.e. simple average).

  • affine (default True) – A boolean value that when set to True, this module has learnable affine parameters (\(\gamma\) and \(\beta\)).

  • track_running_stats (default: True) – A boolean value that when set to True, this module tracks the running mean and variance, and when set to False, this module does not track such statistics, in that case this module always uses batch statistics in both training and eval modes.

Examples

>>> # With Learnable Parameters
>>> m = nn.BatchNormND()
>>> # Without Learnable Parameters
>>> m = nn.BatchNormND(affine=False)
>>> t = Tensor.empty(20, 100, 35, 45).uniform()
>>> output = m(t)