keras 使用RNN实现2进制加法
一.使用python实现RNN 2进制加法
这在很多文章中都出现了
#coding=utf-8
'''
Created on 2018年8月28日
'''
import copy, numpy as np
np.random.seed(0)
# compute sigmoid nonlinearity #定义sigmoid函数
def sigmoid(x):
output = 1/(1+np.exp(-x))
return output
# convert output of sigmoid function to its derivative #计算sigmoid函数的倒数
def sigmoid_output_to_derivative(output):
return output*(1-output)
# training dataset generation
int2binary = {} #用于将输入的整数转为计算机可运行的二进制数用
binary_dim = 8 #定义了二进制数的长度=8
largest_number = pow(2,binary_dim) #二进制数最大能取的数就=256喽
binary = np.unpackbits(
np.array([range(largest_number)],dtype=np.uint8).T,axis=1)
for i in range(largest_number): #将二进制数与十进制数做个一一对应关系
int2binary[i] = binary[i]
# input variables
alpha = 0.1 #反向传播时参数w更新的速度
input_dim = 2 #输入数据的维度，程序是实现两个数相加的
hidden_dim = 16 #隐藏层神经元个数=16
output_dim = 1 #输出结果值是1维的
# initialize neural network weights #初始化神经网络的权重参数
synapse_0 = 2*np.random.random((input_dim,hidden_dim)) - 1 #输入至神经元的w0，维度为2X16，取值约束在[-1,1]间
synapse_1 = 2*np.random.random((hidden_dim,output_dim)) - 1 #神经元至输出层的权重w1,维度为16X1，取值约束在[-1,1]间
synapse_h = 2*np.random.random((hidden_dim,hidden_dim)) - 1 #神经元前一时刻状态至当前状态权重wh,维度为16X16，取值约束在[-1,1]间
print(synapse_0.shape)
print(synapse_h.shape)
print(synapse_1.shape)
synapse_0_update = np.zeros_like(synapse_0) #构造与w0相同维度的矩阵，并初始化为全0；
synapse_1_update = np.zeros_like(synapse_1)
synapse_h_update = np.zeros_like(synapse_h)
# training logic
for j in range(10000): #模型迭代次数，可自行更改
# generate a simple addition problem (a + b = c)
a_int = np.random.randint(largest_number/2) # int version #约束初始化的输入加数a的值不超过128
a = int2binary[a_int] # binary encoding #将加数a的转为对应二进制数
b_int = np.random.randint(largest_number/2) # int version
b = int2binary[b_int] # binary encoding
# true answer
c_int = a_int + b_int #真实和
c = int2binary[c_int]
# where we'll store our best guess (binary encoded)
d = np.zeros_like(c) #用于存储预测的和
overallError = 0 #打印显示误差
layer_2_deltas = list() #反向求导用
layer_1_values = list()
layer_1_values.append(np.zeros(hidden_dim)) #先对隐藏层前一时刻状态初始化为0
# moving along the positions in the binary encoding
for position in range(binary_dim): #前向传播；二进制求和，低位在右，高位在左
# generate input and output
X = np.array([[a[binary_dim - position - 1],b[binary_dim - position - 1]]]) #输入的a与b（二进制形式）
y = np.array([[c[binary_dim - position - 1]]]).T #真实label值
# hidden layer (input ~+ prev_hidden)
layer_1 = sigmoid(np.dot(X,synapse_0) + np.dot(layer_1_values[-1],synapse_h)) # X*w0+RNN前一时刻状态值*wh
# output layer (new binary representation)
layer_2 = sigmoid(np.dot(layer_1,synapse_1)) #layer_1*w1
# did we miss?... if so, by how much?
layer_2_error = y - layer_2 #求误差
layer_2_deltas.append((layer_2_error)*sigmoid_output_to_derivative(layer_2)) #代价函数
overallError += np.abs(layer_2_error[0]) #误差，打印显示用
# decode estimate so we can print it out
d[binary_dim - position - 1] = np.round(layer_2[0][0]) #预测的和
# store hidden layer so we can use it in the next timestep
layer_1_values.append(copy.deepcopy(layer_1)) #深拷贝，将RNN模块状态值存储，用于反向传播
future_layer_1_delta = np.zeros(hidden_dim)
for position in range(binary_dim): #反向传播，计算从左到右，即二进制高位到低位
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) #对w1进行更新
synapse_h_update += np.atleast_2d(prev_layer_1).T.dot(layer_1_delta) #对wh进行更新
synapse_0_update += X.T.dot(layer_1_delta) #对w0进行更新
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): #每1000次打印结果
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 ("------------")二.使用keras实现上述RNN
上述一中的输入对应下面第3种输入数据
#coding=utf-8
'''
Created on 2018年8月27日
第一种输入数据:
77 + 11 = 88
3个整数的二进制分别为(低位->高危表示):
[0 1 0 0 1 1 0 1] [0 0 0 0 1 0 1 1] [0 1 0 1 1 0 0 0]
1-4列分别表示 00，10,01,11
X:
[[ 1. 0. 0. 0.]
[ 0. 1. 0. 0.]
[ 1. 0. 0. 0.]
[ 1. 0. 0. 0.]
[ 0. 0. 0. 1.]
[ 0. 1. 0. 0.]
[ 0. 0. 1. 0.]
[ 0. 0. 0. 1.]]
Y:
[[0]
[1]
[0]
[1]
[1]
[0]
[0]
[0]]
第二种输入数据:
60 + 72 = 132
3个整数的二进制分别为(低位->高危表示):
[0, 0, 1, 1, 1, 1, 0, 0] [0, 0, 0, 1, 0, 0, 1, 0] [0, 0, 1, 0, 0, 0, 0, 1]
1,2列表示60这个[0, 0, 1, 1, 1, 1, 0, 0]进行了one-hot编码
3,4列表示72这个[0, 0, 0, 1, 0, 0, 1, 0]进行了one-hot编码
X:
[[ 1. 0. 1. 0.]
[ 1. 0. 1. 0.]
[ 0. 1. 1. 0.]
[ 0. 1. 0. 1.]
[ 0. 1. 1. 0.]
[ 0. 1. 1. 0.]
[ 1. 0. 0. 1.]
[ 1. 0. 1. 0.]]
Y:
[[0]
[0]
[1]
[0]
[0]
[0]
[0]
[1]]
第三种输入数据:
3 + 23 = 26
3个整数的二进制分别为(低位->高危表示):
[1, 1, 0, 0, 0, 0, 0, 0] [1, 1, 1, 0, 1, 0, 0, 0] [0, 1, 0, 1, 1, 0, 0, 0]
1,2列分别表示3,23这两个数字的二进制
X:
[[1 1]
[1 1]
[0 1]
[0 0]
[0 1]
[0 0]
[0 0]
[0 0]]
Y:
[[0]
[1]
[0]
[1]
[1]
[0]
[0]
[0]]
第4种可以参考:https://blog.csdn.net/whai362/article/details/52523439
"789+123"这样的序列
'''
from keras.models import Sequential
from keras.layers import Activation, TimeDistributed, Dense,SimpleRNN
import numpy as np
from keras.utils import to_categorical
from keras.optimizers import SGD
from sklearn.model_selection import train_test_split
# training dataset generation
int2binary = {} #用于将输入的整数转为计算机可运行的二进制数用
binary_dim = 8 #定义了二进制数的长度=8
largest_number = pow(2,binary_dim) #二进制数最大能取的数就=256喽
binary = np.unpackbits(
np.array([range(largest_number)],dtype=np.uint8).T,axis=1)
for i in range(largest_number): #将二进制数与十进制数做个一一对应关系
int2binary[i] = binary[i]
x_train = []
y_train = []
for j in range(1): #模型迭代次数，可自行更改
# generate a simple addition problem (a + b = c)
a_int = np.random.randint(largest_number/2) # int version #约束初始化的输入加数a的值不超过128
a = list(int2binary[a_int]) # binary encoding #将加数a的转为对应二进制数
a.reverse()
b_int = np.random.randint(largest_number/2) # int version
b = list(int2binary[b_int]) # binary encoding
b.reverse()
c_int = a_int + b_int #真实和
c = list(int2binary[c_int])
c.reverse()
#第2种输入数据，记得修改最后的keras model的输入维度
#tempx = np.hstack((to_categorical(np.array([a]).T,num_classes=2),to_categorical(np.array([b]).T,num_classes=2)))
#第3种输入数据，记得修改最后的keras model的输入维度
#tempx = np.hstack((np.array([a]).T,np.array([b]).T))
#第一种输入数据
tempx = np.hstack((np.array([a]).T,np.array([b]).T))
tempx_2 = []
for i in range(8):
if tempx[i][0] == 0 and tempx[i][1]==0:
tempx_2.append(0)
if tempx[i][0] == 1 and tempx[i][1]==0:
tempx_2.append(1)
if tempx[i][0] == 0 and tempx[i][1]==1:
tempx_2.append(2)
if tempx[i][0] == 1 and tempx[i][1]==1:
tempx_2.append(3)
tempx = to_categorical(np.array([tempx_2]).T,num_classes=4)
tempy = np.array([c]).reshape((8,1))
x_train.append(tempx)
y_train.append(tempy)
x_train = np.array(x_train)
y_train = np.array(y_train)
x_train, x_val, y_train, y_val = train_test_split(x_train, y_train, test_size=0.3, random_state=0)
print(x_train.shape)
print(y_train.shape)
model = Sequential()
model.add(SimpleRNN(128, input_shape=(8, 4),return_sequences=True,activation="sigmoid"))
model.add(TimeDistributed(Dense(1)))
model.add(Activation('sigmoid'))
#经过测试最好不要用sgd,训练速度慢，建议使用adam
#sgd = SGD(lr=0.001, decay=0.0002, momentum=0.9, nesterov=True)
model.compile(loss='binary_crossentropy',
optimizer='adam',
metrics=['accuracy'])
model.summary()
model.fit(x_train, y_train, 32, 1000,validation_data=(x_val, y_val))