为什么我手工制作的numpy神经网络无法学习？

Question

作为练习，我从头开始用numpy构建了一个神经网络。

为了简单起见，我想用它来解决XOR问题。 我推导出所有方程式并将所有内容放在一起，但看来我的网络没有学习。 我花了一些时间试图找出错误，但没有成功。 也许您注意到我在这里想念的东西？

X = [(0,0), (1,0), (0,1), (1,1)]
Y = [0, 1, 1, 0]

w1 = 2 * np.random.random(size=(2,3)) - 1
w2 = 2 * np.random.random(size=(3,1)) - 1
b1 = 2 * np.random.random(size=(1,3)) - 1
b2 = 2 * np.random.random(size=(1,1)) - 1
def sigmoid(x):
    return 1./(1 + np.exp(-x))

def dsigmoid(y):
    return y*(1-y)

N = 1000
error = np.zeros((N,1))
for n in range(N):
    Dw_1 = np.zeros((2,3))
    Dw_2 = np.zeros((3,1))
    Db_1 = np.zeros((1,3))
    Db_2 = np.zeros((1,1))

    for i in range(len(X)): # iterate over all examples
        x = np.array(X[i])
        y = np.array(Y[i])
        # Forward pass, 1st layer
        act1 = np.dot(w1.T, x) + b1
        lay1 = sigmoid(act1)
        # Forward pass, 2nd layer
        act2 = np.dot(w2.T, lay1.T) + b2
        lay2 = sigmoid(act2)
        # Computing error
        E = 0.5*(lay2 - y)**2
        error[n] += E[0]
        # Backprop, 2nd layer
        delta_l2 = (y-lay2) * dsigmoid(lay2)
        corr_w2 = (delta_l2 * lay1).T
        corr_b2 = delta_l2 * 1
        # Backprop, 1st layer
        delta_l1 = np.dot(w2, delta_l2) * dsigmoid(lay1).T
        corr_w1 = np.outer(x, delta_l1)
        corr_b1 = (delta_l1 * 1).T
        Dw_2 += corr_w2
        Dw_1 += corr_w1
        Db_2 += corr_b2
        Db_1 += corr_b1
        if n % 1000 == 0:
            print y, lay2,
    if n % 1000 == 0:
        print
    w2 = w2 - eta * Dw_2
    b2 = b2 - eta * Db_2
    w1 = w1 - eta * Dw_1
    b1 = b1 - eta * Db_1
    error[n] /= len(X)

Answer 1

里面有一些小错误，希望对您有所帮助

import numpy as np
import matplotlib.pyplot as plt

X = [(0, 0), (1, 0), (0, 1), (1, 1)]
Y = [0, 1, 1, 0]

eta = 0.7

w1 = 2 * np.random.random(size=(2, 3)) - 1
w2 = 2 * np.random.random(size=(3, 1)) - 1
b1 = 2 * np.random.random(size=(1, 3)) - 1
b2 = 2 * np.random.random(size=(1, 1)) - 1


def sigmoid(x):
    return 1. / (1 + np.exp(-x))


def dsigmoid(y):
    return y * (1 - y)


N = 2000
error = []
for n in range(N):
    Dw_1 = np.zeros((2, 3))
    Dw_2 = np.zeros((3, 1))
    Db_1 = np.zeros((1, 3))
    Db_2 = np.zeros((1, 1))

    tmp_error = 0
    for i in range(len(X)):  # iterate over all examples
        x = np.array(X[i]).reshape(1, 2)
        y = np.array(Y[i])

        layer1 = sigmoid(np.dot(x, w1) + b1)
        output = sigmoid(np.dot(layer1, w2) + b2)

        tmp_error += np.mean(np.abs(output - y))

        d_w2 = np.dot(layer1.T, ((output - y) * dsigmoid(output)))
        d_b2 = np.dot(1, ((output - y) * dsigmoid(output)))

        d_w1 = np.dot(x.T, (np.dot((output - y) * dsigmoid(output), w2.T) * dsigmoid(layer1)))
        d_b1 = np.dot(1, (np.dot((output - y) * dsigmoid(output), w2.T) * dsigmoid(layer1)))

        Dw_2 += d_w2
        Dw_1 += d_w1
        Db_1 += d_b1
        Db_2 += d_b2

    w2 = w2 - eta * Dw_2
    w1 = w1 - eta * Dw_1
    b1 = b1 - eta * Db_1
    b2 = b2 - eta * Db_2

    error.append(tmp_error)

error = np.array(error)
print(error.shape)
plt.plot(error)
plt.show()