// Backward propagation
public void BackPropagation(ManagedArray input)
{
var last = Weights.GetLength(0) - 1;
D[0] = ManagedMatrix.Diff(Y, Y_true);
var current = 1;
for (var layer = last - 1; layer >= 0; layer--)
{
var prev = current - 1;
var W = new ManagedArray(Weights[layer + 1].x - 1, Weights[layer + 1].y, false);
var DZ = ManagedMatrix.DSigm(Z[layer]);
D[current] = (new ManagedArray(W.x, D[prev].y, false));
ManagedOps.Copy2D(W, Weights[layer + 1], 1, 0);
ManagedMatrix.Multiply(D[current], D[prev], W);
ManagedMatrix.Product(D[current], DZ);
ManagedOps.Free(W, DZ);
current++;
}
for (var layer = 0; layer < Weights.GetLength(0); layer++)
{
var tD = ManagedMatrix.Transpose(D[Weights.GetLength(0) - layer - 1]);
Deltas[layer] = (new ManagedArray(Weights[layer].x, Weights[layer].y, false));
ManagedMatrix.Multiply(Deltas[layer], tD, X[layer]);
ManagedMatrix.Multiply(Deltas[layer], 1.0 / input.y);
ManagedOps.Free(tD);
}
Cost = 0.0;
L2 = 0.0;
for (var i = 0; i < Y_true.Length(); i++)
{
L2 += 0.5 * (D[0][i] * D[0][i]);
Cost += (-Y_true[i] * Math.Log(Y[i]) - (1 - Y_true[i]) * Math.Log(1 - Y[i]));
}
Cost /= input.y;
L2 /= input.y;
// Cleanup
for (var layer = 0; layer < Weights.GetLength(0); layer++)
{
ManagedOps.Free(D[layer], X[layer], Z[layer]);
}
}
// Backward propagation
public void BackPropagation(ManagedArray training)
{
// add bias column to input layer
var InputBias = new ManagedArray(1, training.y);
ManagedOps.Set(InputBias, 1.0);
// x = cbind(array(1, c(nrow(training_set), 1)), training_set)
var x = ManagedMatrix.CBind(InputBias, training);
// compute intermediate delta values per layer
// d3 = y_k - y_matrix
var D3 = ManagedMatrix.Diff(Yk, Y_output);
// d2 = d3 %*% w_kj[, 2:ncol(w_kj)] * nnet_dsigmoid(z_2)
var sWkj = new ManagedArray(Wkj.x - 1, Wkj.y);
ManagedOps.Copy2D(sWkj, Wkj, 1, 0);
var D2 = new ManagedArray(sWkj.x, D3.y);
ManagedMatrix.Multiply(D2, D3, sWkj);
var DZ2 = ManagedMatrix.DSigm(Z2);
ManagedMatrix.Product(D2, DZ2);
// dWji = (t(d2) %*% x)
// dWkj = (t(d3) % *% a_2)
var tD2 = new ManagedArray(D2.y, D2.x);
var tD3 = new ManagedArray(D3.y, D3.x);
ManagedMatrix.Transpose(tD2, D2);
ManagedMatrix.Transpose(tD3, D3);
DeltaWji = new ManagedArray(Wji.x, Wji.y);
DeltaWkj = new ManagedArray(Wkj.x, Wkj.y);
ManagedMatrix.Multiply(DeltaWji, tD2, x);
ManagedMatrix.Multiply(DeltaWkj, tD3, A2);
// cost = sum(-y_matrix * log(y_k) - (1 - y_matrix) * log(1 - y_k))
Cost = 0.0;
L2 = 0.0;
for (var i = 0; i < Y_output.Length(); i++)
{
L2 += 0.5 * (D3[i] * D3[i]);
Cost += (-Y_output[i] * Math.Log(Yk[i]) - (1 - Y_output[i]) * Math.Log(1 - Yk[i]));
}
// cost = cost / m
// dWji = dWji / m
// dWkj = dWkj / m
Cost /= training.y;
L2 /= training.y;
ManagedMatrix.Multiply(DeltaWji, 1.0 / training.y);
ManagedMatrix.Multiply(DeltaWkj, 1.0 / training.y);
// cleanup
ManagedOps.Free(D2, D3, DZ2, InputBias);
ManagedOps.Free(sWkj, tD2, tD3, x);
// cleanup of arrays allocated in Forward
ManagedOps.Free(A2, Yk, Z2);
}