public void ForwadBackwardTest()
{
var soft = new MLStudy.Deep.Softmax();
soft.PrepareTrain(new TensorOld(3, 4));
//模拟之前的N次操作
for (int i = 0; i < 3; i++)
{
var noiseIn = TensorOld.Rand(3, 4);
var noiseError = TensorOld.Rand(3, 4);
soft.Forward(noiseIn);
soft.Backward(noiseError);
}
//真正的测试开始，等正常输出说明不受前面影响
var input = new TensorOld(new double[] { 7, 9, 1, -1, 2, -7, 2, 4, 7, 8, 4, -1 }, 3, 4);
var y = new TensorOld(new double[] { 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0 }, 3, 4); //第1个样本正确，第2，3个样本错误
var output = soft.Forward(input);
//用交叉熵计算Loss时反向传回的error
var error = TensorOld.DivideElementWise(y, output) * -1;
//计算出来的结果
var actual = soft.Backward(error);
//推导出来的结果，因为要把softmax和损失函数分离，所以实际应用时要分别计算
var expected = output - y;
//存在精度问题，有些值无法完全相等
MyAssert.ApproximatelyEqual(expected, actual);
}
public void ForwardBackwardTest()
{
var fl = new FullLayer(3);
var weights = TensorOld.Ones(4, 3);
var bias = TensorOld.Values(0.5, 1, 3);
var input = new TensorOld(new double[] { 1, 2, 3, 4, 5, 6, 7, 8 }, 2, 4);
var error = new TensorOld(new double[] { -1, 0.8, 1.5, 1, -1, 1 }, 2, 3);
var forward = new TensorOld(new double[] { 10.5, 10.5, 10.5, 26.5, 26.5, 26.5 }, 2, 3);
var backward = new TensorOld(new double[] { 1.3, 1.3, 1.3, 1.3, 1, 1, 1, 1 }, 2, 4);
var biasGradient = new TensorOld(new double[] { 0, -0.2, 2.5 }, 1, 3);
var weightsGradient = new TensorOld(new double[, ]
{
{ 4, -4.2, 6.5 },
{ 4, -4.4, 9 },
{ 4, -4.6, 11.5 },
{ 4, -4.8, 14 },
});
fl.PrepareTrain(input);
fl.SetWeights(weights);
fl.SetBias(bias);
fl.Forward(input);
fl.Backward(error);
Assert.Equal(forward, fl.ForwardOutput);
Assert.Equal(backward, fl.BackwardOutput);
MyAssert.ApproximatelyEqual(biasGradient, fl.BiasGradient);
Assert.Equal(weightsGradient, fl.WeightsGradient);
}
public void MeanSquareErrorTest()
{
var y = new TensorOld(new double[] { 1, 3, 2, 4, 5, 6 });
var yHat = new TensorOld(new double[] { 1.5, 2.6, 2.1, 3.9, 5.3, 6.7 });
var error = Functions.MeanSquareError(y, yHat);
var expected = 0.16833333333333333;
MyAssert.ApproximatelyEqual(expected, error);
}
public void TanhTest()
{
var x = 0;
var d = Derivatives.Tanh(x);
var delta = 0.0001;
var expected = (Functions.Tanh(x + delta) - Functions.Tanh(x)) / delta;
MyAssert.ApproximatelyEqual(expected, d);
}
public void MeanSquareErrorTest()
{
var y = new TensorOld(new double[] { 1, 3, 2, 4, 5, 6 });
var yHat = new TensorOld(new double[] { 1.5, 2.6, 2.1, 3.9, 5.3, 6.7 });
var loss = Functions.MeanSquareError(y, yHat);
var gradient = Derivatives.MeanSquareError(y, yHat);
var delta = 0.00001;
yHat[0] += delta;
var expected = (Functions.MeanSquareError(y, yHat) - loss) / delta;
MyAssert.ApproximatelyEqual(expected, gradient[0]);
}
public void SoftmaxTest()
{
var output = new double[] { 0.05, 0.15, 0.7, 0.1 };
var expected = new double[, ]
{
{ 0.0475, -0.0075, -0.035, -0.005 },
{ -0.0075, 0.1275, -0.105, -0.015 },
{ -0.035, -0.105, 0.21, -0.07 },
{ -0.005, -0.015, -0.07, 0.09 }
};
var actual = Derivatives.SoftmaxFromOutput(output);
MyAssert.ApproximatelyEqual(expected, actual);
}
public void SoftmaxCrossEntropyTest()
{
var y = new double[] { 0, 1, 0, 0 };
var yHat = new double[] { 0.1, 0.7, 0.15, 0.05 };
var der = Derivatives.CrossEntropy(y, yHat);
var delta = 0.00001;
var ce0 = Functions.CrossEntropy(y, yHat);
yHat[0] += delta;
var ce1 = Functions.CrossEntropy(y, yHat);
var expected = (ce1 - ce0) / delta;
MyAssert.ApproximatelyEqual(expected, der[0], 0.0001);
}
