2D Batch Normalisation Layer

batchnorm2d_layer_type

batchnorm2d_layer_type(
  num_channels=...,
  momentum=0.99,
  epsilon=1.0e-5,
  gamma_init_mean=1.0,
  gamma_init_std=0.02,
  beta_init_mean=0.0,
  beta_init_std=0.02,
  kernel_initialiser=...,
  bias_initialiser=...,
  moving_mean_initialiser=...,
  moving_variance_initialiser=...,
  input_shape=...
)

The batchnorm2d_layer_type derived type provides a 2D batch normalisation layer. This layer applies batch normalisation over 4D inputs (width, height, channels, batch), normalizing over the spatial dimensions and batch.

\[y = \gamma \frac{x - \mu}{\sqrt{\sigma^2 + \epsilon}} + \beta\]

where \(\mu\) and \(\sigma^2\) are the batch mean and variance computed per channel, and \(\gamma\) and \(\beta\) are learned parameters.

Arguments

  • num_channels (integer): Number of channels in the input.

  • momentum (real(real32)): Momentum for running mean and variance. Default: 0.99.

  • epsilon (real(real32)): Small value added to variance for numerical stability. Default: 1.0e-5.

  • gamma_init_mean (real(real32)): Mean for gamma (scale) initialisation. Default: 1.0.

  • gamma_init_std (real(real32)): Standard deviation for gamma initialisation. Default: 0.02.

  • beta_init_mean (real(real32)): Mean for beta (shift) initialisation. Default: 0.0.

  • beta_init_std (real(real32)): Standard deviation for beta initialisation. Default: 0.02.

  • kernel_initialiser (character(*)): Initialiser for gamma parameters (see Initialisers).

  • bias_initialiser (character(*)): Initialiser for beta parameters (see Initialisers).

  • moving_mean_initialiser (character(*)): Initialiser for running mean (see Initialisers).

  • moving_variance_initialiser (character(*)): Initialiser for running variance (see Initialisers).

  • input_shape (integer, dimension(:)): Shape of the input data (channels, height, width).

Shape:

  • Input: (width, height, num_channels, batch_size).

  • Output: (width, height, num_channels, batch_size).