[人工智能]全连接神经网络面向向量编程实现

第一层 l0 输入层 3个节点
第二层 l1 隐藏层 4个节点
第三层 l2 输出层 2个节点
全连接网络，所以可以看到每个节点都和上一层的所有节点有连接
输入层有三个节点，我们将其依次编号为1、2、3；隐藏层的4个节点，编号依次为4、5、6、7；最后输出层的两个节点编号为8、9

前向算法的作用是计算计算每个结点对其下一层结点的影响，也就是说，把网络正向的走一遍：输入层—->隐藏层—->输出层
节点1、2、3是输入层的节点，所以，他们的输出值就是输入向量本身
隐藏层的输入 例如a4

输出层的输入是输入层的

import numpy as np
from numpy import random, dot, exp, array


# 前向算法
def forward(input):
    l1_out = 1 / (1 + exp(-(dot(w0, input.T))))  # l1_out.shape = (4,)
    l2_out = 1 / (1 + exp(-dot(w1, l1_out)))  # l2_out.shape = (2,)
    return l1_out, l2_out


# 后向算法
def backward(l1_out, l2_out, y1):
    l2_delta = l2_out * (1 - l2_out) * (y1 - l2_out)  # l2_delta.shape =(2,)
    l1_delta = l1_out * (1 - l1_out) * (l2_delta.dot(w1))  # l1_delta.shape =(4,)
    return l1_delta, l2_delta


x = array([[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]])
y = array([[0, 0], [1, 1], [1, 1], [0, 0]])
random.seed(20211016)
w0 = random.random((4, 3))
w1 = random.random((2, 4))
b0 = random.random((4, 1))
b1 = random.random((2, 1))

alpha = 0.01
j = 0
for i in range(100000):
    l0 = x[j, :]
    l1_out, l2_out = forward(l0)
    y1 = y[j, :]
    l1_delta, l2_delta = backward(l1_out, l2_out, y1)
    l1_delta = l1_delta.reshape(4, 1)
    l0 = l0.reshape(1, 3)
    w0 = w0 - alpha * dot(l1_delta, l0)
    l2_delta = l2_delta.reshape(2, 1)
    l1_out = l1_out.reshape(1, 4)
    w1 = w1 - alpha * dot(l2_delta, l1_out)
    if j < 3:
        j += 1
    else:
        j = 0

print(sum(l1_delta), sum(l2_delta))

运行结果 [-0.00029686] [-0.00061398]