scripts/nn/layers/affine.dml

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/*
 * Affine (fully-connected) layer.
 */

forward = function(matrix[double] X, matrix[double] W, matrix[double] b)
    return (matrix[double] out) {
  /*
   * Computes the forward pass for an affine (fully-connected) layer
   * with M neurons.  The input data has N examples, each with D
   * features.
   *
   * Inputs:
   *  - X: Inputs, of shape (N, D).
   *  - W: Weights, of shape (D, M).
   *  - b: Biases, of shape (1, M).
   *
   * Outputs:
   *  - out: Outputs, of shape (N, M).
   */
  out = X %*% W + b
}

backward = function(matrix[double] dout, matrix[double] X,
                    matrix[double] W, matrix[double] b)
    return (matrix[double] dX, matrix[double] dW, matrix[double] db) {
  /*
   * Computes the backward pass for a fully-connected (affine) layer
   * with M neurons.
   *
   * Inputs:
   *  - dout: Gradient wrt `out` from upstream, of shape (N, M).
   *  - X: Inputs, of shape (N, D).
   *  - W: Weights, of shape (D, M).
   *  - b: Biases, of shape (1, M).
   *
   * Outputs:
   *  - dX: Gradient wrt `X`, of shape (N, D).
   *  - dW: Gradient wrt `W`, of shape (D, M).
   *  - db: Gradient wrt `b`, of shape (1, M).
   */
  dX = dout %*% t(W)
  dW = t(X) %*% dout
  db = colSums(dout)
}

init = function(int D, int M)
    return (matrix[double] W, matrix[double] b) {
  /*
   * Initialize the parameters of this layer.
   *
   * Note: This is just a convenience function, and parameters
   * may be initialized manually if needed.
   *
   * We use the heuristic by He et al., which limits the magnification
   * of inputs/gradients during forward/backward passes by scaling
   * unit-Gaussian weights by a factor of sqrt(2/n), under the
   * assumption of relu neurons.
   *  - http://arxiv.org/abs/1502.01852
   *
   * Inputs:
   *  - D: Dimensionality of the input features (number of features).
   *  - M: Number of neurons in this layer.
   *
   * Outputs:
   *  - W: Weights, of shape (D, M).
   *  - b: Biases, of shape (1, M).
   */
  W = rand(rows=D, cols=M, pdf="normal") * sqrt(2.0/D)
  b = matrix(0, rows=1, cols=M)
}