private static Tensor CalculateY(Tensor w, Tensor x, Tensor b, Kernel kernel, int numberOfFilters, MatrixLayout matrixLayout)
{
Tensor y = new Tensor(null,
new Shape(
Shape.BWHC,
x.Shape.GetAxis(Axis.B),
kernel.CalculateOutputWidth(x.Shape.GetAxis(Axis.X)),
kernel.CalculateOutputHeight(x.Shape.GetAxis(Axis.Y)),
x.Shape.GetAxis(Axis.C)));
for (int ib = 0, iib = y.Shape.GetAxis(Axis.B); ib < iib; ib++)
{
for (int ix = 0, xpos = -kernel.PaddingX, iix = y.Shape.GetAxis(Axis.X); ix < iix; ix++, xpos += kernel.StrideX)
{
for (int iy = 0, ypos = -kernel.PaddingY, iiy = y.Shape.GetAxis(Axis.Y); iy < iiy; iy++, ypos += kernel.StrideY)
{
Tensor k = x.CropKernel(ib, xpos, ypos, kernel, false, out int kernelArea);
float[] features = FullyConnectedLayerTest.CalculateNeurons(w, k, b, numberOfFilters, matrixLayout);
for (int ic = 0, iic = y.Shape.GetAxis(Axis.C); ic < iic; ic++)
{
y[ib, ix, iy, ic] = features[ic];
}
}
}
}
return(y);
}
private static Tensor CalculateDW(Tensor w, Tensor x, Tensor y, Kernel kernel, int numberOfFilters, MatrixLayout matrixLayout)
{
Tensor dw = new Tensor(null, w.Axes);
for (int ib = 0, iib = y.Shape.GetAxis(Axis.B); ib < iib; ib++)
{
for (int ix = 0, xpos = -kernel.PaddingX, iix = y.Shape.GetAxis(Axis.X); ix < iix; ix++, xpos += kernel.StrideX)
{
for (int iy = 0, ypos = -kernel.PaddingY, iiy = y.Shape.GetAxis(Axis.Y); iy < iiy; iy++, ypos += kernel.StrideY)
{
Tensor k = x.CropKernel(ib, xpos, ypos, kernel, false, out int kernelArea);
Tensor kdy = y.CropKernel(ib, ix, iy, new Kernel(1, 1, 1, 1), true, out kernelArea);
float[] dww = FullyConnectedLayerTest.CalculateDW(k, kdy, matrixLayout);
Mathematics.Add(dw.Length, dww, 0, dw.Gradient, 0);
}
}
}
return(dw);
}
private static Tensor CalculateDX(Tensor w, Tensor x, Tensor y, Kernel kernel, int numberOfFilters, MatrixLayout matrixLayout)
{
Tensor dx = new Tensor(null, x.Axes);
int xb = Math.Max(-kernel.PaddingX, 0);
int xe = x.Shape.GetAxis(Axis.X) - 1 - xb;
int yb = Math.Max(-kernel.PaddingY, 0);
int ye = x.Shape.GetAxis(Axis.Y) - 1 - yb;
for (int ib = 0, iib = x.Shape.GetAxis(Axis.B); ib < iib; ib++)
{
for (int ix = 0, xpos = -kernel.PaddingX, iix = y.Shape.GetAxis(Axis.X); ix < iix; ix++, xpos += kernel.StrideX)
{
for (int iy = 0, ypos = -kernel.PaddingY, iiy = y.Shape.GetAxis(Axis.Y); iy < iiy; iy++, ypos += kernel.StrideY)
{
Tensor kdy = y.CropKernel(ib, ix, iy, new Kernel(1, 1, 1, 1), true, out int kernelArea);
Tensor kdx = new Tensor(null, new Shape(Shape.BWHC, 1, kernel.Width, kernel.Height, numberOfFilters));
kdx.Set(FullyConnectedLayerTest.CalculateDx(w, kdy, numberOfFilters, matrixLayout));
for (int kx = xpos; kx < xpos + kernel.Width; kx++)
{
for (int ky = ypos; ky < ypos + kernel.Height; ky++)
{
if (kx.Between(xb, xe) && ky.Between(yb, ye))
{
for (int kc = 0; kc < numberOfFilters; kc++)
{
dx.Gradient[x.Shape.Position(ib, kx, ky, kc)] += kdx[0, kx - xpos, ky - ypos, kc];
}
}
}
}
}
}
}
return(dx);
}
public void ForwardBackwardTest()
{
Shape shape = new Shape(new[] { -1, 2, 3, 2 });
const int NumberOfNeurons = 2;
foreach (MatrixLayout matrixLayout in Enum.GetValues(typeof(MatrixLayout)).OfType <MatrixLayout>())
{
FullyConnectedLayer layer = new FullyConnectedLayer(shape, NumberOfNeurons, matrixLayout, null);
////layer.SetLearningMode(true);
layer.W.Set(new float[]
{
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32
});
layer.B.Set(new float[] { 1, 2 });
Tensor xTemp = new Tensor(null, new[] { 1, 12 });
xTemp.Set(new float[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 });
// should be W * x + b
Tensor expectedTemp = new Tensor(null, new[] { 1, NumberOfNeurons });
expectedTemp.Set(FullyConnectedLayerTest.CalculateNeurons(layer.W, xTemp, layer.B, NumberOfNeurons, matrixLayout));
Tensor dyTemp = new Tensor(null, new[] { 1, NumberOfNeurons });
dyTemp.Set(new float[] { 1, 2 });
// should be W' * dy
Tensor expectedDxTemp = new Tensor(null, xTemp.Shape);
expectedDxTemp.Set(FullyConnectedLayerTest.CalculateDx(layer.W, dyTemp, NumberOfNeurons, matrixLayout));
Tensor expectedDBTemp = new Tensor(null, layer.B.Shape);
expectedDBTemp.Set(FullyConnectedLayerTest.CalculateDB(dyTemp));
// should be sum(x' * dy)
Tensor expectedDWTemp = new Tensor(null, layer.W.Shape);
expectedDWTemp.Set(FullyConnectedLayerTest.CalculateDW(xTemp, dyTemp, matrixLayout));
for (int i = 1; i <= 3; i++)
{
Session session = new Session();
layer.W.ClearGradient();
layer.B.ClearGradient();
Tensor x = session.Tile(xTemp, (int)Axis.B, i);
Tensor y = layer.Forward(session, new[] { x })[0];
Tensor expected = session.Tile(expectedTemp, (int)Axis.B, i);
Helpers.AreTensorsEqual(expected, y);
// unroll the graph
y.SetGradient(session.Tile(dyTemp, (int)Axis.B, i).Weights);
session.Unroll();
Tensor expectedDx = session.Tile(expectedDxTemp, (int)Axis.B, i);
Helpers.AreArraysEqual(expectedDx.Length, expectedDx.Weights, x.Gradient);
// should be dy
Tensor expectedDB = session.Multiply(expectedDBTemp, i);
Helpers.AreArraysEqual(expectedDB.Length, expectedDB.Weights, layer.B.Gradient);
// should be x * dy
Tensor expectedDW = session.Multiply(expectedDWTemp, i);
Helpers.AreArraysEqual(expectedDW.Length, expectedDW.Weights, layer.W.Gradient);
}
}
}