硬编码单隐层Ann求解异或问题

Python

# -*- coding: utf-8 -*-
import random
import numpy as np
# (x1, x2, y)
train_set = ((0, 0, 0), (1, 1, 0), (0, 1, 1), (1, 0, 1))
eta = 0.2
# 阈值
threshold = 0.1
# [
#  [w_13, w_23, w_b13],
#  [w_14, w_24, w_b14],
#  [w_1b2, w_2b2, w_b1b2],
#  [w35, w45, wb25]
# ]
w = [[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]]
def sigmoid(x):
    return 1. / (1. + np.e ** (-x))
def total_err_var():
    global train_set, threshold
    total = 0
    for sample in train_set:
        total += (result_of(sample[0], sample[1]) - sample[2]) ** 2
    return total / len(train_set)
def make_data():
    global w
    for arr in w:
        r = 2 * np.random.random((3, 1)) - 1
        for i in range(0, 3):
            arr[i] = r[i][0]
def result_of(x1, x2):
    global w
    o3  = sigmoid(w[0][0] * x1 + w[0][1] * x2 + w[0][2])
    o4  = sigmoid(w[1][0] * x1 + w[1][1] * x2 + w[1][2])
    ob2 = sigmoid(w[2][0] * x1 + w[2][1] * x2 + w[2][2])
    o5  = sigmoid(w[3][0] * o3 + w[3][1] * o4 + w[3][2] * ob2)
    return o5
def outputs(x1, x2):
    global w
    # O3 = Sigmoid[w_13 * x1 + w_23 * x2 + w_b13 * 1]
    o3  = sigmoid(w[0][0] * x1 + w[0][1] * x2 + w[0][2])
    # O4 = Sigmoid[w_14 * x1 + w_24 * x2 + w_b14 * 1]
    o4  = sigmoid(w[1][0] * x1 + w[1][1] * x2 + w[1][2])
    # Ob2 = Sigmoid[w_1b2 * x1 + w_2b2 * x2 + w_b1b2 * 1]
    ob2 = sigmoid(w[2][0] * x1 + w[2][1] * x2 + w[2][2])
    # O5 = Sigmoid[w_35 * O3 + w_45 * O4 + w_b25 * Ob2]
    o5  = sigmoid(w[3][0] * o3 + w[3][1] * o4 + w[3][2] * ob2)
    arr = [x1, x2, o3, o4, ob2, o5]
    return x1, x2, o3, o4, ob2, o5, arr
def err_of(y, o3, o4, ob2, o5):
    global w
    e5  = o5 * (1 - o5) * (y - o5)
    e3  = o3 * (1 - o3) * e5 * w[3][0]
    e4  = o4 * (1 - o4) * e5 * w[3][1]
    eb2 = ob2 * (1 - ob2) * e5 * w[3][2]
    return e5, e3, e4, eb2, [e5, e3, e4, eb2]
def train():    
    global train_set, w
    go_through = False
    cnter = 0
    while (cnter < 20000):
        if total_err_var() < threshold:
            go_through = True
            print ("Counter: %d" % cnter)
            break
        # 随机选择一个样本
        sample = random.choice(train_set)
        # 计算每个神经元的值
        x1, x2 = sample[0], sample[1]
        O1, O2, O3, O4, Ob2, O5, arr_o = outputs(x1, x2)
        # 计算误差
        e5, e3, e4, eb2, arr_e = err_of(sample[2], O3, O4, Ob2, O5)
        # 调整权重
        param = [x1, x2, 1]
        errs = [e3, e4, eb2]
        outs = [O3, O4, Ob2]
        for i in range(0, 3):
            for j in range(0, 3):
                w[i][j] += eta * errs[i] * param[j]
            w[3][i] += eta * e5 * outs[i]
        # 计数
        cnter += 1
    test_output()
    print (go_through)
    return go_through 
def test_output():
    print ("Result of (0, 0) = %f" % result_of(0, 0))
    print ("Result of (1, 1) = %f" % result_of(1, 1))
    print ("Result of (0, 1) = %f" % result_of(0, 1))
    print ("Result of (1, 0) = %f" % result_of(1, 0))
if __name__ == '__main__':
    make_data()
    train()