我怀疑反向传播没有正确实施。概述在例如http://users.pja.edu.pl/~msyd/wyk-nai/multiLayerNN-en.pdf 尤其是第 17 至 20 页。
Output_Neuron-class 的tuneWeigths- 和delta_weights- 方法已正确实现。但是，在此步骤中，必须确定数组 weightDeltaHidden（参见代码中的注释），稍后调整 Hidden_Neuron 类的权重时将需要该数组。
Hidden_Neuron-class 的 tuneWeigths- 和 delta_weights- 方法似乎没有正确实现。在这里，除其他外，必须使用先前确定的数组weightDeltaHidden。
在下面的代码中，我进行了必要的更改，但实际上并未更改代码的设计。但也许重构是有意义的。
Output_Neuron-class 的变化：
...
private double[] weightedDeltaHidden;
...
Output_Neuron(int hiddenNeurons) {
...
this.weightedDeltaHidden = new double[hiddenNeurons];
}
...
void tuneWeights(double LR, double[] hidden_output, int target) {
double delta = (target - output) * f.dSigmoid(output);
for (int i = 0; i < weights.length; i++) {
weights[i] += delta_weights(i, LR, delta, hidden_output);
}
}
double delta_weights(int i, double LR, double delta, double[] hidden_output) {
weightedDeltaHidden[i] = delta * weights[i]; // weightedDeltaHidden is the product of delta of this output neuron and the weight of the i-th hidden neuron.
// That value is needed when the weights of the hidden neurons are tuned...
return LR * delta * hidden_output[i];
}
...
double[] getWeightedDeltaHidden() {
return weightedDeltaHidden;
}
Hidden_Neuron-class 的变化：
...
void tuneWeights(double LR, int[] inputs, double weightedDeltaHiddenTotal) {
for (int i = 0; i < weights.length; i++) {
weights[i] += delta_weights(LR, inputs[i], weightedDeltaHiddenTotal);
}
}
private double delta_weights(double LR, double input, double weightedDeltaHiddenTotal) {
double deltaOutput = f.dSigmoid(output) * weightedDeltaHiddenTotal;
return LR * deltaOutput * input;
}
...
train-方法中的 Network-class 的变化，其中隐藏权重的调整发生：
void train(int[] inputs, int target) {
...
//tune Hidden weights
for (int i = 0; i < numOfHiddenNeurons; i++) {
double weightedDeltaHiddenTotal = 0;
for (int j = 0; j < numOfOutputNeurons; j++) {
weightedDeltaHiddenTotal += output_neurons[j].getWeightedDeltaHidden()[i]; // weightedDeltaHiddenTotal is the sum of the weightedDeltaHidden over all output neurons. Each weightedDeltaHidden
} // is the product of delta of the j-th output neuron and the weight of the i-th hidden neuron.
hidden_neurons[i].tuneWeights(LR, inputs, weightedDeltaHiddenTotal);
}
}
随着这些变化，1_000_000 train-calls（2 个隐藏神经元）的典型输出是
Error: 1.9212e-01 in cycle 0
Error: 8.9284e-03 in cycle 100000
Error: 1.5049e-03 in cycle 200000
Error: 4.7214e-03 in cycle 300000
Error: 4.4727e-03 in cycle 400000
Error: 2.1179e-03 in cycle 500000
Error: 2.9165e-04 in cycle 600000
Error: 2.0655e-03 in cycle 700000
Error: 1.5381e-03 in cycle 800000
Error: 1.0440e-03 in cycle 900000
0 0: 0.0170
1 0: 0.9616
0 1: 0.9612
1 1: 0.0597
对于 100_000_000 train-calls（2 个隐藏神经元）
Error: 2.4755e-01 in cycle 0
Error: 2.7771e-04 in cycle 5000000
Error: 6.8378e-06 in cycle 10000000
Error: 5.4317e-05 in cycle 15000000
Error: 6.8956e-05 in cycle 20000000
Error: 2.1072e-06 in cycle 25000000
Error: 2.6281e-05 in cycle 30000000
Error: 2.1630e-05 in cycle 35000000
Error: 1.1546e-06 in cycle 40000000
Error: 1.7690e-05 in cycle 45000000
Error: 8.6837e-07 in cycle 50000000
Error: 1.3603e-05 in cycle 55000000
Error: 1.2905e-05 in cycle 60000000
Error: 2.1657e-05 in cycle 65000000
Error: 1.1594e-05 in cycle 70000000
Error: 1.9191e-05 in cycle 75000000
Error: 1.7273e-05 in cycle 80000000
Error: 9.1364e-06 in cycle 85000000
Error: 1.5221e-05 in cycle 90000000
Error: 1.4501e-05 in cycle 95000000
0 0: 0.0008
1 0: 0.9961
0 1: 0.9961
1 1: 0.0053
隐藏神经元的增加会提高性能。下面显示了 1_000_000 train-calls（4 个隐藏神经元）的典型输出：
Error: 1.2617e-02 in cycle 0
Error: 7.9950e-04 in cycle 100000
Error: 4.2567e-04 in cycle 200000
Error: 1.7279e-04 in cycle 300000
Error: 1.2246e-04 in cycle 400000
Error: 1.0456e-04 in cycle 500000
Error: 6.9140e-05 in cycle 600000
Error: 6.8698e-05 in cycle 700000
Error: 5.1640e-05 in cycle 800000
Error: 4.4534e-05 in cycle 900000
0 0: 0.0092
1 0: 0.9905
0 1: 0.9912
1 1: 0.0089