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/*
* 2D Scale & Shift layer.
*/
source("scripts/nn/util.dml") as util
forward = function(matrix[double] X, matrix[double] gamma, matrix[double] beta,
int C, int Hin, int Win)
return (matrix[double] out) {
/*
* Computes the forward pass for a 2D scale & shift layer. The input
* data has N examples, each represented as a 3D volume unrolled into
* a single vector.
*
* A 2D scale & shift layer introduces learnable parameters
* (gamma, beta) to scale and shift the input on a per-channel basis.
*
* `y = x*gamma + beta`
*
* Inputs:
* - X: Inputs, of shape (N, C*Hin*Win).
* - gamma: Scale parameters, of shape (C, 1).
* - beta: Shift parameters, of shape (C, 1).
* - C: Number of input channels (dimensionality of input depth).
* - Hin: Input height.
* - Win: Input width.
*
* Outputs:
* - out: Outputs, of shape (N, C*Hin*Win).
*/
# Scale and shift
scaled = bias_multiply(X, gamma) # shape (N, C*Hin*Win)
out = bias_add(scaled, beta) # shape (N, C*Hin*Win)
}
backward = function(matrix[double] dout, matrix[double] out,
matrix[double] X, matrix[double] gamma, matrix[double] beta,
int C, int Hin, int Win)
return (matrix[double] dX, matrix[double] dgamma, matrix[double] dbeta) {
/*
* Computes the backward pass for a 2D scale & shift layer.
*
* Inputs:
* - dout: Gradient wrt `out` from upstream, of shape (N, C*Hin*Win).
* - out: Outputs from the forward pass, of shape (N, C*Hin*Win).
* - X: Input data matrix to the forward pass, of
* shape (N, C*Hin*Win).
* - gamma: Scale parameters, of shape (C, 1).
* - beta: Shift parameters, of shape (C, 1).
* - C: Number of input channels (dimensionality of input depth).
* - Hin: Input height.
* - Win: Input width.
*
* Outputs:
* - dX: Gradient wrt `X`, of shape (N, C*Hin*Win).
* - dgamma: Gradient wrt `W`, of shape (C, 1).
* - dbeta: Gradient wrt `b`, of shape (C, 1).
*
*/
# Compute gradients during training
dgamma = util::channel_sums(dout*X, C, Hin, Win) # shape (C, 1)
dbeta = util::channel_sums(dout, C, Hin, Win) # shape (C, 1)
dX = bias_multiply(dout, gamma) # shape (N, C*Hin*Win)
}
init = function(int C)
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:
* - C: Number of input channels (dimensionality of input depth).
*
* Outputs:
* - gamma: Scale parameters, of shape (C, 1).
* - beta: Shift parameters, of shape (C, 1).
*/
gamma = matrix(1, rows=C, cols=1)
beta = matrix(0, rows=C, cols=1)
}