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我正在尝试在 python 中使用 numpy 实现反向传播算法。我一直在使用这个站点来实现反向传播的矩阵形式。在 XOR 上测试此代码时，即使经过数千次迭代，我的网络也不会收敛。我认为存在某种逻辑错误。如果有人愿意看一下，我将不胜感激。完全可运行的代码可以在github上找到

import numpy as np

def backpropagate(network, tests, iterations=50):

    #convert tests into numpy matrices
    tests = [(np.matrix(inputs, dtype=np.float64).reshape(len(inputs), 1),
            np.matrix(expected, dtype=np.float64).reshape(len(expected), 1))
            for inputs, expected in tests]

    for _ in range(iterations):

        #accumulate the weight and bias deltas
        weight_delta = [np.zeros(matrix.shape) for matrix in network.weights]
        bias_delta = [np.zeros(matrix.shape) for matrix in network.bias]

        #iterate over the tests
        for potentials, expected in tests:

            #input the potentials into the network
            #calling the network with trace == True returns a list of matrices,
            #representing the potentials of each layer 
            trace = network(potentials, trace=True)
            errors = [expected - trace[-1]]

            #iterate over the layers backwards
            for weight_matrix, layer in reversed(list(zip(network.weights, trace))):
                #compute the error vector for a layer
                errors.append(np.multiply(weight_matrix.transpose()*errors[-1],
                                          network.sigmoid.derivative(layer)))

            #remove the input layer
            errors.pop()
            errors.reverse()

            #compute the deltas for bias and weight
            for index, error in enumerate(errors):
                bias_delta[index] += error
                weight_delta[index] += error * trace[index].transpose()

        #apply the deltas
        for index, delta in enumerate(weight_delta):
            network.weights[index] += delta
        for index, delta in enumerate(bias_delta):
            network.bias[index] += delta

此外，这里是计算输出的代码和我的 sigmoid 函数。错误在这里的可能性较小；我能够训练一个网络来使用模拟退火来模拟 XOR。

# the call function of the neural network
def __call__(self, potentials, trace=True):

    #ensure the input is properly formated
    potentials = np.matrix(potentials, dtype=np.float64).reshape(len(potentials), 1)

    #accumulate the trace
    trace = [potentials]

    #iterate over the weights
    for index, weight_matrix in enumerate(self.weights):
        potentials = weight_matrix * potentials + self.bias[index]
        potentials = self.sigmoid(potentials)
        trace.append(potentials)

    return trace

#The sigmoid function that is stored in the network
def sigmoid(x):
    return np.tanh(x)
sigmoid.derivative = lambda x : (1-np.square(x))
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1 回答 1

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问题是缺少步长参数。梯度应该额外缩放，而不是一次在权重空间中完成整个步骤。所以不是：network.weights[index] += delta它network.bias[index] += delta应该是：

def backpropagate(network, tests, stepSize = 0.01, iterations=50):

    #...

    network.weights[index] += stepSize * delta

    #...

    network.bias[index] += stepSize * delta
于 2013-11-15T10:00:50.783 回答