我一直在尝试实现自己的玩具神经网络库来进行学习。我已经尝试在逻辑门操作如或门(Or)、与门(And)和异或门(XOR)上对其进行测试。
虽然它可以正常地处理或门操作,但在处理与门和异或门操作时失败了。它很少能够正确输出与门和异或门操作的结果。
我已经尝试过不同范围的学习率,并尝试了不同的学习曲线来找到随着时代数成本模式的变化。
import numpy as np
class myNeuralNet:
def __init__(self, layers = [2, 2, 1], learningRate = 0.09):
self.layers = layers
self.learningRate = learningRate
self.biasses = [np.random.randn(l, 1) for l in self.layers[1:]]
self.weights = [np.random.randn(i, o) for o, i in zip(self.layers[:-1], self.layers[1:])]
self.cost = []
def sigmoid(self, z):
return (1.0 / (1.0 + np.exp(-z)))
def sigmoidPrime(self, z):
return (self.sigmoid(z) * (1 - self.sigmoid(z)))
def feedForward(self, z, predict = False):
activations = [z]
for w, b in zip(self.weights, self.biasses): activations.append(self.sigmoid(np.dot(w, activations[-1]) + b))
# for activation in activations: print(activation)
if predict: return np.round(activations[-1])
return np.array(activations)
def drawLearningRate(self):
import matplotlib.pyplot as plt
plt.xlim(0, len(self.cost))
plt.ylim(0, 5)
plt.plot(np.array(self.cost).reshape(-1, 1))
plt.show()
def backPropogate(self, x, y):
bigDW = [np.zeros(w.shape) for w in self.weights]
bigDB = [np.zeros(b.shape) for b in self.biasses]
activations = self.feedForward(x)
delta = activations[-1] - y
# print(activations[-1])
# quit()
self.cost.append(np.sum([- y * np.log(activations[-1]) - (1 - y) * np.log(1 - activations[-1])]))
for l in range(2, len(self.layers) + 1):
bigDW[-l + 1] = (1 / len(x)) * np.dot(delta, activations[-l].T)
bigDB[-l + 1] = (1 / len(x)) * np.sum(delta, axis = 1)
delta = np.dot(self.weights[-l + 1].T, delta) * self.sigmoidPrime(activations[-l])
for w, dw in zip(self.weights, bigDW): w -= self.learningRate * dw
for b, db in zip(self.biasses, bigDB): b -= self.learningRate *db.reshape(-1, 1)
return np.sum(- y * np.log(activations[-1]) - (1 - y) * np.log(1 - activations[-1])) / 2
if __name__ == '__main__':
nn = myNeuralNet(layers = [2, 2, 1], learningRate = 0.35)
datasetX = np.array([[1, 1], [0, 1], [1, 0], [0, 0]]).transpose()
datasetY = np.array([[x ^ y] for x, y in datasetX.T]).reshape(1, -1)
print(datasetY)
# print(nn.feedForward(datasetX, predict = True))
for _ in range(60000): nn.backPropogate(datasetX, datasetY)
# print(nn.cost)
print(nn.feedForward(datasetX, predict = True))
nn.drawLearningRate()
有时会出现“RuntimeWarning: overflow encountered in exp”的警告,有时会导致收敛失败。