作为一个练习，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。我推导了所有方程并将所有东西组合在一起，但看起来我的网络不学习。我花了一些时间试图找出错误，但没有成功。也许你能注意到我遗漏了什么？
X = [(0,0), (1,0), (0,1), (1,1)]Y = [0, 1, 1, 0]w1 = 2 * np.random.random(size=(2,3)) - 1w2 = 2 * np.random.random(size=(3,1)) - 1b1 = 2 * np.random.random(size=(1,3)) - 1b2 = 2 * np.random.random(size=(1,1)) - 1def sigmoid(x): return 1./(1 + np.exp(-x))def dsigmoid(y): return y*(1-y)N = 1000error = 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)
回答：
其中有一些小错误，希望这对你有帮助
import numpy as npimport matplotlib.pyplot as pltX = [(0, 0), (1, 0), (0, 1), (1, 1)]Y = [0, 1, 1, 0]eta = 0.7w1 = 2 * np.random.random(size=(2, 3)) - 1w2 = 2 * np.random.random(size=(3, 1)) - 1b1 = 2 * np.random.random(size=(1, 3)) - 1b2 = 2 * np.random.random(size=(1, 1)) - 1def sigmoid(x): return 1. / (1 + np.exp(-x))def dsigmoid(y): return y * (1 - y)N = 2000error = []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()
