scripts/nn/layers/rnn.dml

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/*
 * Simple (Vanilla) RNN layer.
 */
source("nn/layers/tanh.dml") as tanh

forward = function(matrix[double] X, matrix[double] W, matrix[double] b, int T, int D,
                   boolean return_sequences, matrix[double] out0)
    return (matrix[double] out, matrix[double] cache_out) {
  /*
   * Computes the forward pass for a simple RNN layer with M neurons.
   * The input data has N sequences of T examples, each with D features.
   *
   * In a simple RNN, the output of the previous timestep is fed back
   * in as an additional input at the current timestep.
   *
   * Inputs:
   *  - X: Inputs, of shape (N, T*D).
   *  - W: Weights, of shape (D+M, M).
   *  - b: Biases, of shape (1, M).
   *  - T: Length of example sequences (number of timesteps).
   *  - D: Dimensionality of the input features (number of features).
   *  - return_sequences: Whether to return `out` at all timesteps,
   *      or just for the final timestep.
   *  - out0: Output matrix from previous timestep, of shape (N, M).
   *      Note: This is *optional* and could just be an empty matrix.
   *
   * Outputs:
   *  - out: If `return_sequences` is True, outputs for all timesteps,
   *      of shape (N, T*M).  Else, outputs for the final timestep, of
   *      shape (N, M).
   *  - cache_out: Cache of outputs, of shape (T, N*M).
   *      Note: This is used for performance during training.
   */
  N = nrow(X)
  M = ncol(W)
  N1 = nrow(out0)
  if(N < N1) {
    # Allow for smaller out0 for last batch
    out0 = out0[1:N,]
  }
  out_prev = out0
  if (return_sequences) {
    out = matrix(0, rows=N, cols=T*M)
  }
  else {
    out = matrix(0, rows=N, cols=M)
  }
  # caches to be used during the backward pass for performance
  cache_out = matrix(0, rows=T, cols=N*M)

  for (t in 1:T) {  # each timestep
    X_t = X[,(t-1)*D+1:t*D]  # shape (N, D)
    input = cbind(X_t, out_prev)  # shape (N, D+M)
    out_t = tanh::forward(input %*% W + b)  # shape (N, M)
    # store
    if (return_sequences) {
      out[,(t-1)*M+1:t*M] = out_t
    }
    else {
      out = out_t
    }
    out_prev = out_t
    cache_out[t,] = matrix(out_t, rows=1, cols=N*M)  # reshape
  }
}

backward = function(matrix[double] dout, matrix[double] X, matrix[double] W, matrix[double] b,
                    int T, int D, boolean given_sequences, matrix[double] out0,
                    matrix[double] cache_out)
    return (matrix[double] dX, matrix[double] dW, matrix[double] db, matrix[double] dout0) {
  /*
   * Computes the backward pass for a simple RNN layer with M neurons.
   *
   * Inputs:
   *  - dout: Gradient wrt `out` from upstream.  If `given_sequences`
   *      is True, contains gradients on outputs for all timesteps,
   *      of shape (N, T*M).  Else, contains gradient on output for
   *      the final timestep, of shape (N, M).
   *  - X: Inputs, of shape (N, T*D).
   *  - W: Weights, of shape (D+M, M).
   *  - b: Biases, of shape (1, M).
   *  - T: Length of example sequences (number of timesteps).
   *  - D: Dimensionality of the input features (number of features).
   *  - given_sequences: Whether `dout` is for all timesteps,
   *      or just for the final timestep.  This is based on whether
   *      `return_sequences` was true in the forward pass.
   *  - out0: Output matrix from previous timestep, of shape (N, M).
   *      Note: This is *optional* and could just be an empty matrix.
   *  - cache_out: Cache of outputs, of shape (T, N*M).
   *      Note: This is used for performance during training.
   *
   * Outputs:
   *  - dX: Gradient wrt `X`, of shape (N, T*D).
   *  - dW: Gradient wrt `W`, of shape (D+M, 4M).
   *  - db: Gradient wrt `b`, of shape (1, 4M).
   *  - dout0: Gradient wrt `out0`, of shape (N, M).
   */
  N = nrow(X)
  M = ncol(W)
  N1 = nrow(out0)
  if(N < N1) {
    # Allow for smaller out0 for last batch
    out0 = out0[1:N,]
    cache_out = cache_out[,1:(N*M)]
  }
  dX = matrix(0, rows=N, cols=T*D)
  dW = matrix(0, rows=D+M, cols=M)
  db = matrix(0, rows=1, cols=M)
  dout0 = matrix(0, rows=N, cols=M)
  if (!given_sequences) {
    # only given dout for output at final timestep, so prepend empty douts for all other timesteps
    dout = cbind(matrix(0, rows=N, cols=(T-1)*M), dout)  # shape (N, T*M)
  }

  t = T
  for (iter in 1:T) {  # each timestep in reverse order
    X_t = X[,(t-1)*D+1:t*D]  # shape (N, D)
    dout_t = dout[,(t-1)*M+1:t*M]  # shape (N, M)
    out_t = matrix(cache_out[t,], rows=N, cols=M)  # shape (N, M)
    if (t == 1) {
      out_prev = out0  # shape (N, M)
    }
    else {
      out_prev = matrix(cache_out[t-1,], rows=N, cols=M)  # shape (N, M)
    }
    input = cbind(X_t, out_prev)  # shape (N, D+M)
    dout_t_raw = (1-out_t^2) * dout_t  # into tanh, shape (N, M)
    dW += t(input) %*% dout_t_raw  # shape (D+M, M)
    db += colSums(dout_t_raw)  # shape (1, M)
    dinput = dout_t_raw %*% t(W)  # shape (N, D+M)
    dX[,(t-1)*D+1:t*D] = dinput[,1:D]
    dout_prev = dinput[,D+1:D+M]  # shape (N, M)
    if (t == 1) {
      dout0 = dout_prev  # shape (N, M)
    }
    else {
      dout[,(t-2)*M+1:(t-1)*M] = dout[,(t-2)*M+1:(t-1)*M] + dout_prev  # shape (N, M)
    }
    t = t - 1
  }
}

init = function(int N, int D, int M)
    return (matrix[double] W, matrix[double] b, matrix[double] out0) {
  /*
   * Initialize the parameters of this layer.
   *
   * Note: This is just a convenience function, and parameters
   * may be initialized manually if needed.
   *
   * We use the Glorot uniform heuristic which limits the magnification
   * of inputs/gradients during forward/backward passes by scaling
   * uniform weights by a factor of sqrt(6/(fan_in + fan_out)).
   *  - http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf
   *
   * Inputs:
   *  - N: Number of examples in batch.
   *  - D: Dimensionality of the input features (number of features).
   *  - M: Number of neurons in this layer.
   *
   * Outputs:
   *  - W: Weights, of shape (D+M, M).
   *  - b: Biases, of shape (1, M).
   *  - out0: Empty previous timestep output matrix, of shape (N, M).
   */
  fan_in = D+M
  fan_out = M
  scale = sqrt(6/(fan_in+fan_out))
  W = rand(rows=D+M, cols=M, min=-scale, max=scale, pdf="uniform")
  b = matrix(0, rows=1, cols=M)
  out0 = matrix(0, rows=N, cols=M)
}