protected void PropogateUnitSecondDerivatives(RectangularStep upstream, RectangularStep downstream, int weightX, int weightY, int mapNumber)
{
double weight2ndDerivative = 0;
int weightIndex = mapNumber * Width * Height + weightY * Width + weightX;
double weight = Weight[weightIndex];
int downstreamIndex = 0;
int upstreamIndex = (weightY * upstream.Width) + weightX;
// This loop here is equivalent to the sigma in equation 19 in Gradient-Based Learning Applied to Document Recognition.
for (int y = 0; y < downstream.Height; y++)
{
for (int x = 0; x < downstream.Width; x++)
{
double upstreamInput = upstream.Output[upstreamIndex];
double downstreamError2ndDerivative = downstream.ErrorDerivative[downstreamIndex]; // (d^2)E/(dAj)^2, where Aj is the sum of inputs to this downstream unit.
// Here we calculate (d^2)Ej/(dWij)^2 by multiplying the 2nd derivative of E with respect to the sum of inputs, Aj
// by the state of Oi, the upstream unit, squared. Refer to Equation 25 in document.
// The summing happening here is described by equation 23.
weight2ndDerivative += downstreamError2ndDerivative * upstreamInput * upstreamInput;
// This is implementing the last sigma of Equation 27.
// This propogates error second derivatives back to previous layer, but will need to be multiplied by the second derivative
// of the activation function at the previous layer.
upstream.ErrorDerivative[upstreamIndex] += weight * weight * downstreamError2ndDerivative;
downstreamIndex += 1;
upstreamIndex += 1;
}
upstreamIndex += Width - 1; // Equal to: upstream.Width - downstream.Width;
}
WeightStepSize[weightIndex] += weight2ndDerivative;
}
