python - 多层感知器，反向传播，无法学习XOR

Question

我正在尝试实现一个多层感知器（就是一种神经网络）并使用反向传播算法来训练它，但我还是教不会它解决异或问题（XOR）。而且我经常会遇到数学范围错误（就是计算的时候数值超出了能表示的范围）。我查了很多书和在谷歌上找了学习规则和错误反向传播的方法，但我还是不知道我的错误在哪里。

def logsig(net):
    return 1/(1+math.exp(-net))

def perceptron(coef = 0.5, iterations = 10000):
    inputs = [[0,0],[0,1],[1,0],[1,1]]
    desiredOuts = [0,1,1,0]
    bias = -1
    [input.append(bias) for input in inputs] 
    weights_h1 = [random.random() for e in range(len(inputs[0]))]
    weights_h2 = [random.random() for e in range(len(inputs[0]))]
    weights_out = [random.random() for e in range(3)]
    for itteration in range(iterations):
        out = [] 
        for input, desiredOut in zip(inputs, desiredOuts):
              #1st hiden neuron
            net_h1 = sum(x * w for x, w in zip(input, weights_h1)) 
            aktivation_h1 = logsig(net_h1)
              #2st hiden neuron
            net_h2 = sum(x * w for x, w in zip(input, weights_h2))
            aktivation_h2 = logsig(net_h2)
              #output neuron
            input_out = [aktivation_h1, aktivation_h2, bias]
            net_out = sum(x * w for x, w in zip(input_out, weights_out))
            aktivation_out = logsig(net_out)            
              #error propagation        
            error_out = (desiredOut - aktivation_out) * aktivation_out * (1-    aktivation_out)
            error_h1 = aktivation_h1 * (1-aktivation_h1) * weights_out[0] * error_out
            error_h2 = aktivation_h2 * (1-aktivation_h2) * weights_out[1] * error_out
              #learning            
            weights_out = [w + x * coef * error_out for w, x in zip(weights_out, input_out)]
            weights_h1 = [w + x * coef * error_out for w, x in zip(weights_h1, input)]
            weights_h2 = [w + x * coef * error_out for w, x in zip(weights_h2, input)]            
            out.append(aktivation_out) 
    formatedOutput = ["%.2f" % e for e in out]
    return formatedOutput

Answer 1

这个数学范围错误很可能是因为在计算 math.exp(-net) 时，net 是一个很大的负数。

Answer 2

我注意到的唯一一点是，你在用 error_out 来更新 weights_h1 和 weights_h2，而不是用 error_h1 和 error_h2。换句话说：

weights_h1 = [w + x * coef * error_h1 for w, x in zip(weights_h1, input)]
weights_h2 = [w + x * coef * error_h2 for w, x in zip(weights_h2, input)]