[deeplearning-015]一文理解rnn

1.参考文档 https://iamtrask.github.io/2015/11/15/anyone-can-code-lstm/

  前提，熟悉bp算法推导，熟悉bptt算法推导

2.py源码

#!/usr/bin/env python3

#参考文献 https://iamtrask.github.io/2015/11/15/anyone-can-code-lstm/

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 = {}#空字典
binary_dim = 8

#=256
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 #把值调整到(-1,1)
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)

# 随机生成ab两个整数，c=a+b。将abc转成二进制，a和b的二进制是rnn的输入，c的二进制是目标值，训练rnn。

# training logic
for j in range(50000):
    # 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]

    # print(a_int, a, b_int, b,c_int,c)
    # exit(1)

    # where we'll store our best guess (binary encoded)
    d = np.zeros_like(c)
    overallError = 0
    #记录第二层的deta值
    layer_2_deltas = list()
    #记录第一层的输出值
    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
        # 从abc三个数的二进制的最低位开始，每次取一位，生成训练样本
        # print("\nposition=", position)
        # print("a=",a)
        # print("b=",b)
        # print("c=", c)
        #比如，取第一位的时候，X=[[1,0]],y=[[1]]，是训练样本和目标值
        X = np.array([[a[binary_dim - position - 1], b[binary_dim - position - 1]]])
        y = np.array([[c[binary_dim - position - 1]]]).T
        # print('X=',X)
        # print('y=',y)
        # hidden layer (input ~+ prev_hidden)
        # 计算第一层的输出值：sigmoid里面有两个部分，分别是input*synapse_0和前次第一层输出值*synapse_h隐层
        layer_1 = sigmoid(np.dot(X, synapse_0) + np.dot(layer_1_values[-1], synapse_h))
        # output layer (new binary representation)
        #第二层输出就很直接了
        layer_2 = sigmoid(np.dot(layer_1, synapse_1))
        # did we miss?... if so, by how much?
        # 计算输出误差
        layer_2_error = y - layer_2
        #根据误差，计算第二层权重系数的deta，这个公式是对第二层微分求导得到的，熟悉BP算法的都清楚，不在叙述
        layer_2_deltas.append((layer_2_error) * sigmoid_output_to_derivative(layer_2))
        #计算绝对误差之和，以衡量8个位的总误差大小
        overallError += np.abs(layer_2_error[0])
        # decode estimate so we can print it out
        # 记录下 rnn对当前位的预测值
        d[binary_dim - position - 1] = np.round(layer_2[0][0])
        # store hidden layer so we can use it in the next timestep
        # 把本轮第一层的输出记录到layer_1_values，以备bptt使用。
        layer_1_values.append(copy.deepcopy(layer_1))

    #计算第一个隐层的delta
    future_layer_1_delta = np.zeros(hidden_dim)
    for position in range(binary_dim):
        #注意喽，X这一轮循环是从ab的二进制的高位开始往低位走的
        X = np.array([[a[position], b[position]]])
        #高位二进制是后计算的，因此其值在layer_1的尾部
        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("------------")