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Applies Batch Normalization over a 5D input (a mini-batch of 3D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift.


  eps = 1e-05,
  momentum = 0.1,
  affine = TRUE,
  track_running_stats = TRUE



\(C\) from an expected input of size \((N, C, D, H, W)\)


a value added to the denominator for numerical stability. Default: 1e-5


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


a boolean value that when set to TRUE, this module has learnable affine parameters. 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 and uses batch statistics instead in both training and eval modes if the running mean and variance are None. Default: TRUE


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

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 input size). By default, the elements of \(\gamma\) are set to 1 and the elements of \(\beta\) are set to 0. The standard-deviation is calculated via the biased estimator, equivalent to torch_var(input, unbiased = FALSE).

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.


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: \(\hat{x}_{\mbox{new}} = (1 - \mbox{momentum}) \times \hat{x} + \mbox{momentum} \times x_t\), where \(\hat{x}\) is the estimated statistic and \(x_t\) is the new observed value.

Because the Batch Normalization is done over the C dimension, computing statistics on (N, D, H, W) slices, it's common terminology to call this Volumetric Batch Normalization or Spatio-temporal Batch Normalization.


  • Input: \((N, C, D, H, W)\)

  • Output: \((N, C, D, H, W)\) (same shape as input)


if (torch_is_installed()) {
# With Learnable Parameters
m <- nn_batch_norm3d(100)
# Without Learnable Parameters
m <- nn_batch_norm3d(100, affine = FALSE)
input <- torch_randn(20, 100, 35, 45, 55)
output <- m(input)