【深度学习】RNN循环神经网络Python简单实现

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本文链接： https://blog.csdn.net/tudaodiaozhale/article/details/79541187

前言

代码可在Github上下载:代码下载
循环神经网络是一种时间序列预测模型，多应用在自然语言处理上。
原理网上是有很多的，不展开解释，本文基于一个二进制加法，进行python实现。
其实python代码并非本人实现
具体参考两篇博客，第一篇是英语原文，第二篇是译文。
https://iamtrask.github.io/2015/11/15/anyone-can-code-lstm/
http://blog.csdn.net/zzukun/article/details/49968129

原理

前向传播
$\begin{array}{l} {z^h} = {w_{ih}}x + {w_{hh}}{a^{h - 1}}\\ {a^h} = \sigma \left( {{z^h}} \right)\\ {z^k} = {w_{hy}}{a^h}\\ {a^k} = \sigma \left( {{z^k}} \right) \end{array}$

反向传播
$\begin{array}{l} \delta _t^k = \frac{{\partial E}}{{\partial {a^k}}}\frac{{\partial {a^k}}}{{\partial {z^k}}} = ({y_t} - a_t^k) \times \left( {{z^k}} \right)' = ({y_t} - a_t^k) \times \left( {{z^k} \times \left( {1 - {z^k}} \right)} \right)\\ \delta _T^h = \frac{{\partial E}}{{\partial a_T^k}}\frac{{\partial a_T^k}}{{\partial z_T^k}}\frac{{\partial z_T^k}}{{\partial a_{\rm{T}}^h}}\frac{{\partial a_T^h}}{{\partial z_{\rm{T}}^h}} = {\left( {{W_{hy}}} \right)^T}\delta _T^k \times \left( {{a^h}\left( {1 - {a^h}} \right)} \right)\\ {\delta _t^h = \frac{{\partial E}}{{\partial a_t^k}}\frac{{\partial a_t^k}}{{\partial z_t^k}}\frac{{\partial z_t^k}}{{\partial a_t^h}}\frac{{\partial a_t^h}}{{\partial z_t^h}} + \frac{{\partial E}}{{\partial a_{t + 1}^k}}\frac{{\partial a_{t + 1}^k}}{{\partial z_{t + 1}^k}}\frac{{\partial z_{t + 1}^k}}{{\partial a_{t{\rm{ + }}1}^h}}\frac{{\partial a_{t{\rm{ + }}1}^h}}{{\partial z_{t + 1}^h}}\frac{{\partial z_{t + 1}^h}}{{\partial a_t^h}}\frac{{\partial a_t^h}}{{\partial z_t^h}}}\\ {\rm{ }} = \left( {{{\left( {{W_{hh}}} \right)}^T}\delta _{t + 1}^h + {{\left( {{W_{hy}}} \right)}^T}\delta _t^k} \right)\frac{{\partial a_t^h}}{{\partial z_t^h}}\\ {\rm{ }} = \left( {{{\left( {{W_{hh}}} \right)}^T}\delta _{t + 1}^h + {{\left( {{W_{hy}}} \right)}^T}\delta _t^k} \right) \times \left( {{a^h}\left( {1 - {a^h}} \right)} \right)\\ {W_{ih}} = {W_{ih}} - \eta \delta _t^h{\left( {{x_t}} \right)^T}\\ {W_{hh}} = {W_{hh}} - \eta \delta _t^h{\left( {a_{t - 1}^h} \right)^T}\\ {W_{hy}} = {W_{hy}} - \eta \delta _t^k{\left( {a_t^h} \right)^T} \end{array}$

有了前向传播和反向传播的公式，就可以根据这个公式将RNN实现。代码解释在上面的两篇博客中都有所解释，只是他们并没有给出相应的公式，故将公式奉上。

代码实现

import copy, numpy as np

np.random.seed(0)

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

# sigmoid导数
def sigmoid_output_to_derivative(output):
    return output * (1 - output)


# 训练数据生成
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]

# 初始化一些变量
alpha = 0.1 #学习率
input_dim = 2   #输入的大小
hidden_dim = 8  #隐含层的大小
output_dim = 1  #输出层的大小

# 随机初始化权重
synapse_0 = 2 * np.random.random((hidden_dim, input_dim)) - 1   #(8, 2)
synapse_1 = 2 * np.random.random((output_dim, hidden_dim)) - 1  #(1, 8)
synapse_h = 2 * np.random.random((hidden_dim, hidden_dim)) - 1  #(8, 8)

synapse_0_update = np.zeros_like(synapse_0) #(8, 2)
synapse_1_update = np.zeros_like(synapse_1) #(1, 8)
synapse_h_update = np.zeros_like(synapse_h) #(8, 8)

# 开始训练
for j in range(100000):

    # 二进制相加
    a_int = np.random.randint(largest_number / 2)  # 随机生成相加的数
    a = int2binary[a_int]  # 映射成二进制值

    b_int = np.random.randint(largest_number / 2)  # 随机生成相加的数
    b = int2binary[b_int]  # 映射成二进制值

    # 真实的答案
    c_int = a_int + b_int   #结果
    c = int2binary[c_int]   #映射成二进制值

    # 待存放预测值
    d = np.zeros_like(c)

    overallError = 0

    layer_2_deltas = list() #输出层的误差
    layer_2_values = list() #第二层的值（输出的结果）
    layer_1_values = list() #第一层的值（隐含状态）
    layer_1_values.append(copy.deepcopy(np.zeros((hidden_dim, 1)))) #第一个隐含状态需要0作为它的上一个隐含状态

    #前向传播
    for i in range(binary_dim):
        X = np.array([[a[binary_dim - i - 1], b[binary_dim - i - 1]]]).T    #(2,1)
        y = np.array([[c[binary_dim - i - 1]]]).T   #(1,1)
        layer_1 = sigmoid(np.dot(synapse_h, layer_1_values[-1]) + np.dot(synapse_0, X)) #(1,1)
        layer_1_values.append(copy.deepcopy(layer_1))   #(8,1)
        layer_2 = sigmoid(np.dot(synapse_1, layer_1))   #(1,1)
        error = -(y-layer_2)    #使用平方差作为损失函数
        layer_delta2 = error * sigmoid_output_to_derivative(layer_2)    #(1,1)
        layer_2_deltas.append(copy.deepcopy(layer_delta2))
        d[binary_dim - i - 1] = np.round(layer_2[0][0])
    future_layer_1_delta = np.zeros((hidden_dim, 1))
    #反向传播
    for i in range(binary_dim):
        X = np.array([[a[i], b[i]]]).T
        prev_layer_1 = layer_1_values[-i-2]
        layer_1 = layer_1_values[-i-1]
        layer_delta2 = layer_2_deltas[-i-1]
        layer_delta1 = np.multiply(np.add(np.dot(synapse_h.T, future_layer_1_delta),np.dot(synapse_1.T, layer_delta2)), sigmoid_output_to_derivative(layer_1))
        synapse_0_update += np.dot(layer_delta1, X.T)
        synapse_h_update += np.dot(layer_delta1, prev_layer_1.T)
        synapse_1_update += np.dot(layer_delta2, layer_1.T)
        future_layer_1_delta = layer_delta1
    synapse_0 -= alpha * synapse_0_update
    synapse_h -= alpha * synapse_h_update
    synapse_1 -= alpha * synapse_1_update
    synapse_0_update *= 0
    synapse_1_update *= 0
    synapse_h_update *= 0
    # 验证结果
    if (j % 100 == 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("------------")