为什么我手工制作的numpy神经网络无法学习？

Question

As an exercise I was building a neural network in numpy from scratch.

For simplicity I wanted to use it to solve XOR problem. I derived all the equation and put everything together, but it looks like my network doesn't learn. I've spent some time trying to spot the mistake, but without success. Maybe you notice something I'm missing here?

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

There were small mistakes in it, I hope this helps you

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()