scripts/nn/test/conv2d_simple.dml

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/*
 * 2D Convolutional layer.
 *
 * This implementation is intended to be a simple, reference version.
 */

forward = function(matrix[double] X, matrix[double] W, matrix[double] b,
                   int C, int Hin, int Win, int Hf, int Wf,
                   int strideh, int stridew, int padh, int padw)
    return (matrix[double] out, int Hout, int Wout) {
  /*
   * Computes the forward pass for a 2D spatial convolutional layer with
   * F filters.  The input data has N examples, each represented as a 3D
   * volume unrolled into a single vector.
   *
   * This implementation is intended to be a simple, reference version.
   *
   * Inputs:
   *  - X: Inputs, of shape (N, C*Hin*Win).
   *  - W: Weights, of shape (F, C*Hf*Wf).
   *  - b: Biases, of shape (F, 1).
   *  - C: Number of input channels (dimensionality of input depth).
   *  - Hin: Input height.
   *  - Win: Input width.
   *  - Hf: Filter height.
   *  - Wf: Filter width.
   *  - strideh: Stride over height.
   *  - stridew: Stride over width.
   *  - padh: Padding for top and bottom sides.
   *  - padw: Padding for left and right sides.
   *
   * Outputs:
   *  - out: Outputs, of shape (N, F*Hout*Wout).
   *  - Hout: Output height.
   *  - Wout: Output width.
   */
  N = nrow(X)
  F = nrow(W)
  Hout = as.integer(floor((Hin + 2*padh - Hf)/strideh + 1))
  Wout = as.integer(floor((Win + 2*padw - Wf)/stridew + 1))

  # Create output volume
  out = matrix(0, rows=N, cols=F*Hout*Wout)

  # Convolution - Simple reference implementation
  parfor (n in 1:N) {  # all examples
    Xn = matrix(X[n,], rows=C, cols=Hin*Win)
    # Pad image
    Xn_padded = matrix(0, rows=C, cols=(Hin+2*padh)*(Win+2*padw))  # zeros
    parfor (c in 1:C) {
      Xn_slice = matrix(Xn[c,], rows=Hin, cols=Win)  # depth slice C reshaped
      Xn_padded_slice = matrix(Xn_padded[c,], rows=Hin+2*padh, cols=Win+2*padw)
      Xn_padded_slice[padh+1:padh+Hin, padw+1:padw+Win] = Xn_slice
      Xn_padded[c,] = matrix(Xn_padded_slice, rows=1, cols=(Hin+2*padh)*(Win+2*padw))  # reshape
    }
    # Convolve image with filters
    parfor (f in 1:F, check=0) {  # all filters
      parfor (hout in 1:Hout, check=0) {  # all output rows
        h0 = (hout-1)*strideh + 1
        parfor (wout in 1:Wout, check=0) {  # all output columns
          w0 = (wout-1)*stridew + 1
          # Create a patch of the input example corresponding spatially to the filter sizes
          Xn_padded_patch = matrix(0, rows=C, cols=Hf*Wf)  # zeros
          parfor (c in 1:C, check=0) {
            Xn_padded_slice = matrix(Xn_padded[c,], rows=Hin+2*padh, cols=Win+2*padw)  # reshape
            Xn_padded_patch[c,] = matrix(Xn_padded_slice[h0:h0-1+Hf, w0:w0-1+Wf], rows=1,
                                         cols=Hf*Wf)  # reshape
          }
          out[n, (f-1)*Hout*Wout + (hout-1)*Wout + wout] =
              W[f,] %*% matrix(Xn_padded_patch, rows=C*Hf*Wf, cols=1) + b[f,]
        }
      }
    }
  }
}

backward = function(matrix[double] dout, int Hout, int Wout,
                    matrix[double] X, matrix[double] W, matrix[double] b,
                    int C, int Hin, int Win, int Hf, int Wf,
                    int strideh, int stridew, int padh, int padw)
    return (matrix[double] dX, matrix[double] dW, matrix[double] db) {
  /*
   * Computes the backward pass for a 2D spatial convolutional layer
   * with F filters.
   *
   * This implementation is intended to be a simple, reference version.
   *
   * Inputs:
   *  - dout: Gradient wrt `out` from upstream, of
   *      shape (N, F*Hout*Wout).
   *  - Hout: Output height.
   *  - Wout: Output width.
   *  - X: Inputs, of shape (N, C*Hin*Win).
   *  - W: Weights, of shape (F, C*Hf*Wf).
   *  - b: Biases, of shape (F, 1).
   *  - C: Number of input channels (dimensionality of input depth).
   *  - Hin: Input height.
   *  - Win: Input width.
   *  - Hf: Filter height.
   *  - Wf: Filter width.
   *  - strideh: Stride over height.
   *  - stridew: Stride over width.
   *  - padh: Padding for top and bottom sides.
   *  - padw: Padding for left and right sides.
   *
   * Outputs:
   *  - dX: Gradient wrt `X`, of shape (N, C*Hin*Win).
   *  - dW: Gradient wrt `W`, of shape (F, C*Hf*Wf).
   *  - db: Gradient wrt `b`, of shape (F, 1).
   */
  N = nrow(X)
  F = nrow(W)

  # Create gradient volumes
  dX = matrix(0, rows=N, cols=C*Hin*Win)
  dW = matrix(0, rows=F, cols=C*Hf*Wf)
  db = matrix(0, rows=F, cols=1)

  # Partial derivatives for convolution - Simple reference implementation
  for (n in 1:N) {  # all examples
    Xn = matrix(X[n,], rows=C, cols=Hin*Win)
    # Pad image
    Xn_padded = matrix(0, rows=C, cols=(Hin+2*padh)*(Win+2*padw))  # zeros
    parfor (c in 1:C) {
      Xn_slice = matrix(Xn[c,], rows=Hin, cols=Win)  # depth slice C reshaped
      Xn_padded_slice = matrix(Xn_padded[c,], rows=Hin+2*padh, cols=Win+2*padw)
      Xn_padded_slice[padh+1:padh+Hin, padw+1:padw+Win] = Xn_slice
      Xn_padded[c,] = matrix(Xn_padded_slice, rows=1, cols=(Hin+2*padh)*(Win+2*padw))  # reshape
    }
    dXn_padded = matrix(0, rows=C, cols=(Hin+2*padh)*(Win+2*padw))
    for (f in 1:F) {  # all filters
      for (hout in 1:Hout) {  # all output rows
        h0 = (hout-1) * strideh + 1
        for (wout in 1:Wout) {  # all output columns
          w0 = (wout-1) * stridew + 1
          # Create a patch of the input example corresponding spatially to the filter sizes
          Xn_padded_patch = matrix(0, rows=C, cols=Hf*Wf)  # zeros
          dXn_padded_patch = matrix(W[f,] * dout[n, (f-1)*Hout*Wout + (hout-1)*Wout + wout],
                                    rows=C, cols=Hf*Wf)  # reshape
          for (c in 1:C) {
            Xn_padded_slice = matrix(Xn_padded[c,], rows=Hin+2*padh, cols=Win+2*padw)  # reshape
            Xn_padded_patch[c,] = matrix(Xn_padded_slice[h0:h0-1+Hf, w0:w0-1+Wf],
                                         rows=1, cols=Hf*Wf)  # reshape
            dXn_padded_slice = matrix(0, rows=Hin+2*padh, cols=Win+2*padw)
            dXn_padded_slice[h0:h0-1+Hf, w0:w0-1+Wf] = matrix(dXn_padded_patch[c,],
                                                              rows=Hf, cols=Wf)  # reshape
            dXn_padded[c,] = dXn_padded[c,] + matrix(dXn_padded_slice,
                                                     rows=1, cols=(Hin+2*padh)*(Win+2*padw))
          }
          dW[f,] = dW[f,]
                   + matrix(Xn_padded_patch, rows=1, cols=C*Hf*Wf)
                   * dout[n, (f-1)*Hout*Wout + (hout-1)*Wout + wout]
          db[f,] = db[f,] + dout[n, (f-1)*Hout*Wout + (hout-1)*Wout + wout]
        }
      }
    }
    # Unpad derivs on input
    dXn = matrix(0, rows=C, cols=Hin*Win)
    parfor (c in 1:C, check=0) {
      dXn_padded_slice = matrix(dXn_padded[c,], rows=(Hin+2*padh), cols=(Win+2*padw))
      dXn_slice = dXn_padded_slice[padh+1:padh+Hin, padw+1:padw+Win]
      dXn[c,] = matrix(dXn_slice, rows=1, cols=Hin*Win)
    }
    dX[n,] = matrix(dXn, rows=1, cols=C*Hin*Win)
  }
}

init = function(int F, int C, int Hf, int Wf)
    return (matrix[double] W, matrix[double] b) {
  /*
   * Initialize the parameters of this layer.
   *
   * 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:
   *  - F: Number of filters.
   *  - C: Number of input channels (dimensionality of depth).
   *  - Hf: Filter height.
   *  - Wf: Filter width.
   *
   * Outputs:
   *  - W: Weights, of shape (F, C*Hf*Wf).
   *  - b: Biases, of shape (F, 1).
   */
  W = rand(rows=F, cols=C*Hf*Wf, pdf="normal") * sqrt(2.0/(C*Hf*Wf))
  b = matrix(0, rows=F, cols=1)
}