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Declarative Machine Learning
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/*
 * 1D Scale & Shift layer.
 */

forward = function(matrix[double] X, matrix[double] gamma, matrix[double] beta)
    return (matrix[double] out) {
  /*
   * Computes the forward pass for a 1D scale & shift layer. The input
   * data has N examples, each with D features.
   *
   * A 1D scale & shift layer introduces learnable parameters
   * (gamma, beta) to scale and shift the input on a per-feature basis.
   *
   *   `y = x*gamma + beta`
   *
   * Inputs:
   *  - X: Inputs, of shape (N, D).
   *  - gamma: Scale parameters, of shape (1, D).
   *  - beta: Shift parameters, of shape (1, D).
   *
   * Outputs:
   *  - out: Outputs, of shape (N, D).
   */
  # Scale and shift
  out = X*gamma + beta  # shape (N, D)
}

backward = function(matrix[double] dout, matrix[double] out,
                    matrix[double] X, matrix[double] gamma, matrix[double] beta)
      return (matrix[double] dX, matrix[double] dgamma, matrix[double] dbeta) {
  /*
   * Computes the backward pass for a 1D scale & shift layer.
   *
   * Inputs:
   *  - dout: Gradient wrt `out` from upstream, of shape (N, D).
   *  - out: Outputs from the forward pass, of shape (N, D).
   *  - X: Inputs, of shape (N, D).
   *  - gamma: Scale parameters, of shape (1, D).
   *  - beta: Shift parameters, of shape (1, D).
   *
   * Outputs:
   *  - dX: Gradient wrt `X`, of shape (N, D).
   *  - dgamma: Gradient wrt `W`, of shape (1, D).
   *  - dbeta: Gradient wrt `b`, of shape (1, D).
   *
   */
  # Compute gradients during training
  dgamma = colSums(dout*X)  # shape (1, D)
  dbeta = colSums(dout)  # shape (1, D)
  dX = dout * gamma  # shape (N, D)
}

init = function(int D)
    return (matrix[double] gamma, matrix[double] beta) {
  /*
   * Initialize the parameters of this layer.
   *
   * By default, we initialize to an identity function, with a scale
   * filler of `1`, and a shift filler of `0`.
   *
   * Note: This is just a convenience function, and parameters
   * may be initialized manually if needed.
   *
   * Inputs:
   *  - D: Dimensionality of the input features (number of features).
   *
   * Outputs:
   *  - gamma: Scale parameters, of shape (1, D).
   *  - beta: Shift parameters, of shape (1, D).
   */
   gamma = matrix(1, rows=1, cols=D)
   beta = matrix(0, rows=1, cols=D)
}