一文彻底搞懂RNN、BPTT（递归神经网络）

RNN：递归神经网络（RNN）是时间递归神经网络（recurrent neural network）和结构递归神经网络（recursive neural network）的总称。时间递归神经网络的神经元间连接构成矩阵，而结构递归神经网络结构更加复杂。

【基本描述】

1、递归神经网络RNN主要用来处理序列有关数据，比如时间序列、文本序列等。序列是被排成一列的对象，RNN处理序列对象之所以存在优势，是因为RNN神经元中充分考虑了序列输入中前段时间一定的权重。

2、RNN网络结构：和传统神经网络一样，RNN网络结构分为输入层、隐藏层和输出层

RNN网络特别之处在于如下：SYNAPSE_h会连接当前t时刻的隐藏层神经元，同时也连接着t-1时刻的神经元结构，所以RNN神经网络中的参数主要有SYNAPSE_O对应的U矩阵，SYNAPSE_h对应的W矩阵和SYNAPSE_1对应的V矩阵，如下图U是3*3矩阵，W是4*4矩阵，V是4*2矩阵。

3、公式推导_前向传播

前向传播相对简单，其主要涉及的公式见下：

4、公式推导_反向传播

 

 

【实例】

例：用RNN来实现一个八位的二进制数加法运算。

import copy, numpy as np

np.random.seed(0)

# compute sigmoid nonlinearity
def sigmoid(x):
    output = 1 / (1 + np.exp(-x))
    return output

# convert output of sigmoid function to its derivative
def sigmoid_output_to_derivative(output):
    return output * (1 - output)

# training dataset generation
int2binary = {}
binary_dim = 8

largest_number = pow(2, binary_dim)
binary = np.unpackbits(
    np.array([range(largest_number)], dtype=np.uint8).T, axis=1)
for i in range(largest_number):
    int2binary[i] = binary[i]

# input variables
alpha = 0.1
input_dim = 2
hidden_dim = 16
output_dim = 1

# initialize neural network weights
synapse_0 = 2 * np.random.random((input_dim, hidden_dim)) - 1
synapse_1 = 2 * np.random.random((hidden_dim, output_dim)) - 1
synapse_h = 2 * np.random.random((hidden_dim, hidden_dim)) - 1

synapse_0_update = np.zeros_like(synapse_0)
synapse_1_update = np.zeros_like(synapse_1)
synapse_h_update = np.zeros_like(synapse_h)

# training logic
for j in range(10000):

    # generate a simple addition problem (a + b = c)
    a_int = np.random.randint(largest_number / 2)  # int version
    a = int2binary[a_int]  # binary encoding

    b_int = np.random.randint(largest_number / 2)  # int version
    b = int2binary[b_int]  # binary encoding

    # true answer
    c_int = a_int + b_int
    c = int2binary[c_int]

    # where we'll store our best guess (binary encoded)
    d = np.zeros_like(c)

    overallError = 0

    layer_2_deltas = list()
    layer_1_values = list()
    layer_1_values.append(np.zeros(hidden_dim))

    # moving along the positions in the binary encoding
    for position in range(binary_dim):
        # generate input and output
        X = np.array([[a[binary_dim - position - 1], b[binary_dim - position - 1]]])
        y = np.array([[c[binary_dim - position - 1]]]).T

        # hidden layer (input ~+ prev_hidden)
        layer_1 = sigmoid(np.dot(X, synapse_0) + np.dot(layer_1_values[-1], synapse_h))

        # output layer (new binary representation)
        layer_2 = sigmoid(np.dot(layer_1, synapse_1))

        # did we miss?... if so, by how much?
        layer_2_error = y - layer_2
        layer_2_deltas.append((layer_2_error) * sigmoid_output_to_derivative(layer_2))
        overallError += np.abs(layer_2_error[0])

        # decode estimate so we can print it out
        d[binary_dim - position - 1] = np.round(layer_2[0][0])

        # store hidden layer so we can use it in the next timestep
        layer_1_values.append(copy.deepcopy(layer_1))

    future_layer_1_delta = np.zeros(hidden_dim)

    for position in range(binary_dim):
        X = np.array([[a[position], b[position]]])
        layer_1 = layer_1_values[-position - 1]
        prev_layer_1 = layer_1_values[-position - 2]

        # error at output layer
        layer_2_delta = layer_2_deltas[-position - 1]
        # error at hidden layer
        layer_1_delta = (future_layer_1_delta.dot(synapse_h.T) + layer_2_delta.dot(
            synapse_1.T)) * sigmoid_output_to_derivative(layer_1)

        # let's update all our weights so we can try again
        synapse_1_update += np.atleast_2d(layer_1).T.dot(layer_2_delta)
        synapse_h_update += np.atleast_2d(prev_layer_1).T.dot(layer_1_delta)
        synapse_0_update += X.T.dot(layer_1_delta)

        future_layer_1_delta = layer_1_delta

    synapse_0 += synapse_0_update * alpha
    synapse_1 += synapse_1_update * alpha
    synapse_h += synapse_h_update * alpha

    synapse_0_update *= 0
    synapse_1_update *= 0
    synapse_h_update *= 0

    # print out progress
    if (j % 1000 == 0):
        print("Error:" + str(overallError))
        print("Pred:" + str(d))
        print("True:" + str(c))
        out = 0
        for index, x in enumerate(reversed(d)):
            out += x * pow(2, index)
        print(str(a_int) + " + " + str(b_int) + " = " + str(out))

        print("------------")

以上源码经过几次得到就能得到很好的效果，详细的执行逻辑可以跟踪代码进行查看！

【总结】

时间递归神经网络可以描述动态时间行为，但是简单递归神经网络无法处理随着递归，梯度爆炸或者梯度消失的问题，并且难以捕捉长期时间关联；有效的处理方法是忘掉错误的信息，记住正确的信息。LSTM能够比较好的解决这个问题。