感知器的一个公式:
当 wx+b>0 , f(x)=1,否则f(x)=0
- x输入的向量
- w:是权重
- w*x是点积
- b是偏置(与权重类似,偏置可以认为是激励函数的偏移量，或者给神经元一个基础活跃等级。)
对权重的调整公式,此处使用了梯度下降的方法: w=w+i*(t-count)*x
- i是一个常数,i越小感知器学习越精确,当然耗费时间也最长
- t:本应该得到的值
- count:实际计算得到的值
- x:同上
对偏置调整的公式: b=b+i(t-count)*
这次我们使用python来实现与和或
#因为与和或计算需要输入两个数,所以这里设置两个权重global w1,w2w1=0.4w2=0.6#偏置随便设一个global bb=0.8#上面提到的常数global ii=0.01对感知器公式实现的函数:
def count(x,y): if w1*x+w2*y+b>0: return 1 else: return 0对权重和偏置不断矫正的函数:
def update_all(r,x,y): global w1,w2,b temp = count(x,y) w1=w1+i*(r-temp)*x w2=w2+i*(r-temp)*y b=b+i*(r-temp) print(w1,w2,b)最后就是输入学习的资料和确认计算结果:
def main(): for _ in range(1,50): update_all(1.0,1.0,1.0) update_all(0.0,1.0,0.0) update_all(0.0,0.0,1.0) update_all(0.0,0.0,0.0) print('1 and 1 =',count(1,1)) print('0 and 1 =',count(0,1)) print('1 and 0 =',count(1,0)) print('0 and 0 =',count(0,0))这里我们先进行与的计算:
这里我前面代码写错了,所以说下面所有的结果会不一样…
进行25次学习的结果:
(0.4, 0.6, 0.8)(0.39, 0.6, 0.79)(0.39, 0.59, 0.78)(0.39, 0.59, 0.77)(0.39, 0.59, 0.77).......省略........(0.1599999999999998, 0.35999999999999976, 0.08999999999999947)(0.1599999999999998, 0.35999999999999976, 0.07999999999999947)('1 and 1 =', 1)('0 and 1 =', 1)('1 and 0 =', 1)('0 and 0 =', 1)这里我们明显发现结果是错误的,提升到50次:
(0.4, 0.6, 0.8)(0.39, 0.6, 0.79)(0.39, 0.59, 0.78)(0.39, 0.59, 0.77)(0.39, 0.59, 0.77)(0.38, 0.59, 0.76)(0.38, 0.58, 0.75).......省略........(0.07999999999999981, 0.1799999999999996, -0.18000000000000055)(0.07999999999999981, 0.1799999999999996, -0.18000000000000055)(0.07999999999999981, 0.1799999999999996, -0.18000000000000055)('1 and 1 =', 1)('0 and 1 =', 0)('1 and 0 =', 0)('0 and 0 =', 0)结果正确了,并且权重和偏置都稳定到一个值,是不是感觉很神奇
或运算也是相同的,这里我们将偏置改为b=0.4:
25次:
(0.4, 0.6, 0.4)(0.4, 0.6, 0.4)(0.4, 0.6, 0.4)(0.4, 0.6, 0.39)(0.4, 0.6, 0.39)(0.4, 0.6, 0.39)(0.4, 0.6, 0.39)(0.4, 0.6, 0.38)(0.4, 0.6, 0.38)(0.4, 0.6, 0.38).......省略........(0.4, 0.6, 0.16999999999999982)(0.4, 0.6, 0.16999999999999982)(0.4, 0.6, 0.16999999999999982)(0.4, 0.6, 0.16999999999999982)(0.4, 0.6, 0.1599999999999998)('1 and 1 =', 1)('0 and 1 =', 1)('1 and 0 =', 1)('0 and 0 =', 1)50次:
(0.4, 0.6, 0.4)(0.4, 0.6, 0.4)(0.4, 0.6, 0.4)(0.4, 0.6, 0.39)(0.4, 0.6, 0.39)(0.4, 0.6, 0.39)(0.4, 0.6, 0.39)(0.4, 0.6, 0.38).......省略........(0.4, 0.6, -1.97758476261356e-16)(0.4, 0.6, -1.97758476261356e-16)(0.4, 0.6, -1.97758476261356e-16)(0.4, 0.6, -1.97758476261356e-16)(0.4, 0.6, -1.97758476261356e-16)('1 and 1 =', 1)('0 and 1 =', 1)('1 and 0 =', 1)('0 and 0 =', 0)
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