AdvancedOCR.SubsamplingWeights.EstimateWeightSecondDerivative C# (CSharp) Method

        protected void EstimateWeightSecondDerivative(RectangularStep upstream, RectangularStep downstream, int downstreamX, int downstreamY)
        {
            double weight2ndDerivative = 0;

            int downstreamIndex = downstreamY * downstream.Width + downstreamX;
            int upstreamIndex = (downstreamY * Height * upstream.Width) + downstreamX * Width;

            double downstreamSecondDerivative = downstream.ErrorDerivative[downstreamIndex];
            double upstreamSecondDerivative = Weight * Weight * downstreamSecondDerivative;

            // This loop here is equivalent to the sigma in equation 19 in Gradient-Based Learning Applied to Document Recognition.
            for (int y = 0; y < Height; y++)
            {
                for (int x = 0; x < Width; x++)
                {
                    double upstreamState = upstream.Output[upstreamIndex];

                    // Here we calculate (d^2)Ej/(dWij)^2 by multiplying the 2nd derivative of E with respect to the sum of inputs, Ai
                    // 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 += downstreamSecondDerivative * upstreamState * upstreamState;

                    // 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] = upstreamSecondDerivative;

                    upstreamIndex += 1;
                }
                upstreamIndex += upstream.Width - Width;
            }

            WeightStepSize += weight2ndDerivative;
        }