python - 为什么我的 RNN 不学习？

Question

我正在尝试使用 numpy 实现一个简单的 RNN(基于 this article )，并且我正在训练它进行二进制加法，其中它一次一位地添加两个 8 位无符号整数(从end)，目的是让它在必要时学会在添加过程中“携带那个”。不过，好像并没有学习到。对于训练，我选择两个随机数，前向传播 8 个步骤，其中 a 和 b 中的一位作为输入，并存储每个时间步的输出和隐藏层值，然后反向传播 8 个步骤，计算隐藏层误差 (output_error.dot(weights_hidden_​​to_output.T)) * sigmoid_to_derivative(hidden) + future_hidden_​​error.dot(weights_hidden_​​to_hidden.T)) 以及通过父层乘以子层误差的矩阵来更新每个权重矩阵层。这是正确的方法吗？

这是我的代码，如果它能让它更清楚的话。我注意到，由于某种原因，每次训练时权重都会突然开始疯狂增加，并导致 sigmoid 函数溢出，从而导致训练失败。知道什么可能导致这种情况吗？

import numpy as np
np.random.seed(0)

def sigmoid(x):
    return np.atleast_2d(1/(1+np.exp(-x)))
    #return np.atleast_2d(np.max(x, 0.01))
def sig_deriv(x):
    return x*(1-x)
def add_bias(x):
    return np.hstack([np.ones((len(x), 1)), x])
def dec_to_bin(dec):
    return np.array(map(int, list(format(dec, '#010b'))[2:]))
def bin_to_dec(b):
    out = 0
    for bit in b:
        out = (out << 1) | bit
    return out


batch_size = 8
learning_rate = .1

input_size = 2
hidden_size = 16
output_size = 1

weights_xh = 2 * np.random.random((input_size+1, hidden_size)) - 1
weights_hh = 2 * np.random.random((hidden_size+1, hidden_size)) - 1
weights_hy = 2 * np.random.random((hidden_size+1, output_size)) - 1

xh_update = np.zeros_like(weights_xh)
hh_update = np.zeros_like(weights_hh)
hy_update = np.zeros_like(weights_hy)

for i in xrange(10000):
    a = np.random.randint(0, 2**batch_size/2)
    b = np.random.randint(0, 2**batch_size/2)
    sum_ = a+b
    X = add_bias(np.hstack([np.atleast_2d(dec_to_bin(a)).T, np.atleast_2d(dec_to_bin(b)).T]))
    y = np.atleast_2d(dec_to_bin(sum_)).T

    error = 0

    output_errors = []
    outputs = []
    hiddens = [add_bias(np.zeros((1, hidden_size)))]
    #forward propagation through time
    for j in xrange(batch_size):
        hidden = sigmoid(X[-j-1].dot(weights_xh) + hiddens[-1].dot(weights_hh))
        hidden = add_bias(hidden)
        hiddens.append(hidden)
        output = sigmoid(hidden.dot(weights_hy))
        outputs.append(output[0][0])
        output_error = (y[-j-1] - output)
        error += np.abs(output_error[0])
        output_errors.append((output_error * sig_deriv(output)))

    future_hidden_error = np.zeros((1,hidden_size))
    #backward ppropagation through time
    for j in xrange(batch_size):
        output_error = output_errors[-j-1]
        hidden = hiddens[-j-1]
        prev_hidden = hiddens[-j-2]

        hidden_error = (output_error.dot(weights_hy.T) * sig_deriv(hidden)) + future_hidden_error.dot(weights_hh.T)
        hidden_error = np.delete(hidden_error, 0, 1) #delete bias error

        xh_update += np.atleast_2d(X[j]).T.dot(hidden_error)
        hh_update += prev_hidden.T.dot(hidden_error)
        hy_update += hidden.T.dot(output_error)

        future_hidden_error = hidden_error

    weights_xh += (xh_update * learning_rate)/batch_size
    weights_hh += (hh_update * learning_rate)/batch_size
    weights_hy += (hy_update * learning_rate)/batch_size

    xh_update *= 0
    hh_update *= 0
    hy_update *= 0

    if i%1000==0:
        guess = map(int, map(round, outputs[::-1]))
        print "Iteration {}".format(i)
        print "Error: {}".format(error)
        print "Problem: {} + {} = {}".format(a, b, sum_)
        print "a:        {}".format(list(dec_to_bin(a)))
        print "+ b:      {}".format(list(dec_to_bin(b)))
        print "Solution: {}".format(map(int, y))
        print "Guess:    {} ({})".format(guess, bin_to_dec(guess))
        print

Answer 1

我明白了。如果有人想知道为什么它不起作用，那是因为我只将隐藏错误的一部分(来自输出错误的部分)乘以隐藏层激活的导数。现在，它可以在几千次迭代内轻松学习加法问题。