神经网络训练批次中每个输入的相似输出

Question

我正在尝试创建一个神经网络，该神经网络采用权重边作为输入的邻接矩阵，并且输出大于1。我以此处给出的神经网络为基础：http://neuralnetworksanddeeplearning.com/chap1.html 。

每当我检查第一个批次之后的批次时，输出都是相似的，但是每个批次都会给出不同的输出。另外，当我检查测试时，每个输入都给出不同的输出，但是它们要大得多。

我正在使用ReLU作为最后一层的激活，并且尝试了不同的权重标准差。我还在每层中尝试了越来越少的神经元，并尝试了不同数量的层（1-3），但是我遇到了同样的问题。计算可能有些问题，但是我什么也找不到。我该如何解决这个问题？

代码：

class Network(object):

    def __init__(self, sizes):
        self.num_layers = len(sizes)
        self.sizes = sizes
        self.biases = [np.random.rand(y, 1) for y in sizes[1:]]
        self.weights = [np.random.rand(y, x) for x, y in zip(sizes[:-1], sizes[1:])]

    def feedforward(self, a):
        i = 0
        for b, w in zip(self.biases, self.weights):
            if i == len(self.biases)-1:
                a = relu(np.dot(w, a)+b)
            else:
                a = sigmoid(np.dot(w, a)+b
        i+=1
        return a

    def SGD(self, training_data, epochs, mini_batch_size, eta, test_data=None):
        if test_data: n_test = len(test_data)
        n = len(training_data)
        for j in range(epochs):
            random.shuffle(training_data)
            mini_batches = [
                training_data[k:k+mini_batch_size]
                for k in range(0, n, mini_batch_size)]
            for mini_batch in mini_batches:
                self.update_mini_batch(mini_batch, eta)
            if test_data:
                print("Epoch {0}: {1} / {2}".format(j, self.evaluate(test_data), n_test))
            else:
                print("Epoch {0} complete".format(j))

    def update_mini_batch(self, mini_batch, eta):
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        for x, y in mini_batch:
            delta_nabla_b, delta_nabla_w = self.backprop(x, y)
            nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
            nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
        self.weights = [w-(eta/len(mini_batch))*nw for w, nw in zip(self.weights, nabla_w)]
        self.biases = [b-(eta/len(mini_batch))*nb for b, nb in zip(self.biases, nabla_b)]

    def backprop(self, x, y):
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        activation = x
        activations = [x]
        zs = []
        i = 0
        for b, w in zip(self.biases, self.weights):
            z = np.dot(w, activation)+b
            zs.append(z)
            if i == len(self.biases)-1:
                activation = relu(z)
            else:
                activation = sigmoid(z)
            activations.append(activation)
            i+=1
        print(activations[-1])
        delta = self.cost_derivative(activations[-1], y)
        nabla_b[-1] = delta
        nabla_w[-1] = np.dot(delta, activations[-2].transpose())
        for l in range(2, self.num_layers):
            z = zs[-l]
            sp = sigmoid_prime(z)
            delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
            nabla_b[-l] = delta
            nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())+0.1*self.weights[-l]/(len(self.weights[-1])*len(self.weights[-l][0]))
        return(nabla_b, nabla_w)

    def evaluate(self, test_data):
        test_results = [(self.feedforward(x), y)
                for (x, y) in test_data]
        #for i in test_results:
            #print(i[0], i[1])
        return sum(int(x[0][0]) == y for (x, y) in test_results)

    def cost_derivative(self, output_activations, y):
        return(output_activations-y)