neural_network.py 文件源码

def neural_network_cost_gradient(parameters, input, output):
    """
    3-layer network cost and gradient function
    :param parameters: pair of (W1, W2)
    :param input: input vector
    :param output: index to correct label
    :return: cross entropy cost and gradient
    """
    W1, W2 = parameters
    input = input.reshape(-1, 1)

    hidden_layer = expit(W1.dot(input))
    inside_softmax = W2.dot(hidden_layer)

    # TODO: allow softmax to normalize column vector
    prediction = softmax(inside_softmax.reshape(-1)).reshape(-1, 1)
    cost = -np.sum(np.log(prediction[output]))

    one_hot = np.zeros_like(prediction)
    one_hot[output] = 1
    delta = prediction - one_hot
    gradient_W2 = delta.dot(hidden_layer.T)
    gradient_W1 = sigmoid_gradient(hidden_layer) * W2.T.dot(delta).dot(input.T)

    gradient = [gradient_W1, gradient_W2]
    return cost, gradient