Python で ニューラルネット（XOR回路を作ってみる）

Python で ニューラルネット（XOR回路を作ってみる）

→
XOR（排他的論理和）を、ニューラルネットに学習させる例

＜XOR＞
True と True で　False　　（1 & 1 -> 0）
True と False で　True　　 （1 & 0 -> 1）
False と True で　True　　 （0 & 1 -> 1）
False と False で　False　　（0 & 0 -> 0）

※global変数の多用については、眼をつぶって下さい、、、
※バックプロパゲーション（Backpropagation、誤差逆伝播法）をつかったベーシックな例です

NNetXOR.ps

import random
import math

iINPUT = 2
iHIDDEN = 4
iOUTPUT = 1

iPR = 1000
iMAX_T = 300000
dETA = 2.5
dEPS = 0.00001
dALPHA = 0.92
dBETA = 0.35
dW0 = 0.9

xi = [0 for i in range(iINPUT +1)] 
v =  [0 for i in range(iHIDDEN+1)] 
o =  [0 for i in range(iOUTPUT)]
zeta =  [0 for i in range(iOUTPUT)] 

#------------
def arand():
    r = random.random()
    r = r * 2 *dW0 - dW0
    return r
#------------

w1 = [[arand() for i in range(iINPUT+1)]  for i in range(iHIDDEN)]
w2 = [[arand() for i in range(iHIDDEN+1)] for i in range(iOUTPUT)]

d_w1 = [[0 for i in range(iINPUT+1)]  for i in range(iHIDDEN)]
d_w2 = [[0 for i in range(iHIDDEN+1)] for i in range(iOUTPUT)]

pre_dw1 = [[0 for i in range(iINPUT+1)]  for i in range(iHIDDEN)]
pre_dw2 = [[0 for i in range(iHIDDEN+1)] for i in range(iOUTPUT)]

#入力する値              
data =  [[0,0],[0,1],[1,0],[1,1],[1,0],[1,1],[0,1],[0,0]]
for i in range(8):
    data[i].append(1)

#教師信号（所謂、模範解答）
t_data =[[0],  [1],  [1],  [0],  [1],  [0],  [1],  [0]]
#お試し用の問題
d_data =[[1,0],[1,1],[0,1],[0,0]]

for i in range(4):
    d_data[i].append(1)

##-----------------------------

def dw_init():
    global d_w1
    global d_w2
    global pre_dw1
    global pre_dw2
    pre_dw1 = d_w1
    pre_dw2 = d_w2
    d_w1 = [[0 for i in range(iINPUT+1)]  for i in range(iHIDDEN)]
    d_w2 = [[0 for i in range(iHIDDEN+1)] for i in range(iOUTPUT)]

def sigmoid(u):
    return  1.0 / (1.0 +  math.exp(-dBETA * u));

def xi_set(p):
    global xi
    global zeta
    xi = data[p]
    zeta = t_data[p]

def forward():
    global xi
    global w1
    global v
    global w2
    global o
    for j in range(iHIDDEN):
        sm = 0
        for k in range(iINPUT+1):
            sm += xi[k] * w1[j][k]
        v[j] = sigmoid(sm)
    v[iHIDDEN] = 1.0
    for j2 in range(iOUTPUT):
        sm = 0
        for j in range(iHIDDEN+1):
            sm += v[j] * w2[j2][j]
        o[j2] = sigmoid(sm)

def backward():
    global o
    global zeta
    global v
    global xi
    global d_w1
    global d_w2
    global w2

    delta2 = [0 for i in range(iOUTPUT)]
    delta1 = [0 for i in range(iHIDDEN+1)]
    for i in range(iOUTPUT):
        delta2[i] = dBETA * o[i] * (1-o[i]) * (zeta[i]-o[i])
    for j in range(iHIDDEN):
        sm = 0
        for j2 in range(iOUTPUT):
            sm = sm + w2[j2][j] * delta2[j2]
            delta1[j] = dBETA * v[j] * (1-v[j]) * sm
    for j2 in range(iOUTPUT):
        for j in range(iHIDDEN+1):
            d_w2[j2][j] = d_w2[j2][j] + delta2[j2] * v[j]
    for j in range(iHIDDEN):
        for k in range(iINPUT+1):
            d_w1[j][k] = d_w1[j][k] + delta1[j] * xi[k]

def w_modify():
    for j2 in range(iOUTPUT):
        for j in range(iHIDDEN+1):
            d_w2[j2][j] = dALPHA * dETA * d_w2[j2][j] + dALPHA * pre_dw2[j2][j]
            w2[j2][j] = w2[j2][j] + d_w2[j2][j]
    for j in range(iHIDDEN):
        for k in range(iINPUT+1):
            d_w1[j][k] = dALPHA * dETA * d_w1[j][k] + dALPHA * pre_dw1[j][k]
            w1[j][k] = w1[j][k] + d_w1[j][k]

def calc_error():
    e = 0.0
    for i in range(iOUTPUT):
        e = e +(zeta[i]-o[i])*(zeta[i]-o[i])
    return e

def back_propagation_main():
    global zeta
    e = 0.0
    esum = 0.0
    for t in range(iMAX_T):
        dw_init()
        esum = 0.0
        for p in range(iPATTERNz):
            xi_set(p)
            forward()
            backward()
            esum = esum + calc_error()
        w_modify()
        e = esum #/ (iOUTPUT * iPATTERNz)
        if t % iPR ==0:
            print(t, " / ", iMAX_T, " / ", "{0:.7f}".format(e))
        if(e<dEPS):
            break

def tryTest():
    global xi
    global o
    print("-------------------")
    for p in range(iPATTERNo):
        xi = d_data[p]
        forward()
        print(xi[0],"-",xi[1],"  -> {0:.4f}".format(o[0]))
##-----------------------------
iPATTERNz =8
iPATTERNo =4

print ("---- Start ----")
back_propagation_main()
tryTest()
print("---- End ----")

結果はこちら

---- Start ----
0  /  300000  /  2.1139707
1000  /  300000  /  0.0014984
2000  /  300000  /  0.0006751
略
99000  /  300000  /  0.0000102
100000  /  300000  /  0.0000101
-------------------
1 - 0   -> 0.9989
1 - 1   -> 0.0011
0 - 1   -> 0.9989
0 - 0   -> 0.0012
---- End ----