public void Given__BiasesHigh_WeightsHigh__Returns111__ForAnyInput(params double[] inputs)
{
const double h = Neuron.High;
var net = new NeuralNet3LayerSigmoid(new[, ] {
{ h }, { h }, { h }
}, new[, ] {
{ h, h, h }
}, new[] { h }, new[] { h, h, h });
//
Console.WriteLine(net.OutputFor(inputs));
net.OutputFor(inputs).ToArray().ShouldBe(new ZeroToOne[] { 1, 1, 1 });
}
public void Given_Biases0_Weights0__ReturnsHalfHalfHalf__ForAnyInput(params double[] inputs)
{
var net = new NeuralNet3LayerSigmoid(3, 1, 3)
.SetBiases(new[] { 0d }, new [] { 0d, 0d, 0d })
.SetInputToHiddenWeights(new double[3, 1] {
{ 0 }, { 0 }, { 0 }
})
.SetHiddenToOutputWeights(new double[1, 3] {
{ 0, 0, 0 }
});
//
Console.WriteLine(net.OutputFor(inputs).ToArray());
//
net.OutputFor(inputs).ShouldEqualByValue(new ZeroToOne[] { 0.5, 0.5, 0.5 });
}
public void Given__BiasesLow_WeightsLow__Returns000__ForAnyInput(params double[] inputs)
{
const double low = Neuron.Low;
var net = new NeuralNet3LayerSigmoid(3, 1, 3)
.SetBiases(new[] { low }, new[] { low, low, low })
.SetInputToHiddenWeights(new double[3, 1] {
{ low }, { low }, { low }
})
.SetHiddenToOutputWeights(new double[1, 3] {
{ low, low, low }
});
//
Console.WriteLine(net.OutputFor(inputs));
net.OutputFor(inputs).ToArray().ShouldBe(new ZeroToOne[] { 0, 0, 0 });
}
public static DeltasFor2LayersOfNet DeltasFor(NeuralNet3LayerSigmoid net, IEnumerable <double> inputs, IEnumerable <ZeroToOne> targets)
{
var outputs = net.OutputFor(inputs).ToArray();
var outputDeltas = outputs
.Zip(targets, (o, target) => (target - o) * o * (1 - o)) /* see e.g. wikipedia https://en.wikipedia.org/wiki/Backpropagation#Derivation */
.ToArray();
var outputWeightDeltas = new MatrixD(net.HiddenToOutput.RowCount, net.HiddenToOutput.ColumnCount);
var hiddenDeltaParts = new MatrixD(net.HiddenToOutput.RowCount, net.HiddenToOutput.ColumnCount);
for (int i = 0; i < outputWeightDeltas.RowCount; i++)
{
for (int j = 0; j < outputWeightDeltas.ColumnCount; j++)
{
outputWeightDeltas[i, j] = net.HiddenLayer[i].FiringRate * outputDeltas[j];
hiddenDeltaParts[i, j] = outputDeltas[j] * (net.HiddenToOutput[i, j] + outputWeightDeltas[i, j]) * outputs[j] * (1 - outputs[j]);
}
}
var hiddenDeltas = hiddenDeltaParts.ByRows().Select(row => row.Sum()).ToArray();
var hiddenWeightDeltas = new MatrixD(net.InputToHidden.RowCount, net.InputToHidden.ColumnCount);
for (int i = 0; i < hiddenWeightDeltas.RowCount; i++)
{
for (int j = 0; j < hiddenWeightDeltas.ColumnCount; j++)
{
hiddenWeightDeltas[i, j] = net.InputLayer[i].FiringRate * hiddenDeltas[j];
}
}
return(new DeltasFor2LayersOfNet
{
OutputBiases = net.OutputLayer.Zip(outputDeltas, (neuron, delta) => neuron.Bias * delta).ToArray(),
OutputWeights = outputWeightDeltas,
HiddenBiases = net.HiddenLayer.Zip(hiddenDeltas, (neuron, delta) => neuron.Bias * delta).ToArray(),
HiddenWeights = hiddenWeightDeltas
});
}
