使用sigmoid激活的python中从头开始的神经网络

import numpy as np

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

class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        
        # 初始化权重和偏置
        self.W1 = np.random.randn(self.input_size, self.hidden_size)
        self.b1 = np.zeros((1, self.hidden_size))
        self.W2 = np.random.randn(self.hidden_size, self.output_size)
        self.b2 = np.zeros((1, self.output_size))
        
    def forward(self, X):
        # 前向传播
        self.z1 = np.dot(X, self.W1) + self.b1
        self.a1 = sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.W2) + self.b2
        self.a2 = sigmoid(self.z2)
        return self.a2
    
    def backward(self, X, y, learning_rate):
        # 反向传播
        m = X.shape[0]
        
        # 计算输出层的误差
        self.delta2 = self.a2 - y
        
        # 计算隐藏层的误差
        self.delta1 = np.dot(self.delta2, self.W2.T) * (self.a1 * (1 - self.a1))
        
        # 更新权重和偏置
        self.W2 -= learning_rate * np.dot(self.a1.T, self.delta2) / m
        self.b2 -= learning_rate * np.sum(self.delta2, axis=0, keepdims=True) / m
        self.W1 -= learning_rate * np.dot(X.T, self.delta1) / m
        self.b1 -= learning_rate * np.sum(self.delta1, axis=0, keepdims=True) / m

# 创建神经网络对象
nn = NeuralNetwork(input_size=2, hidden_size=3, output_size=1)

# 定义输入和标签数据
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([[0], [1], [1], [0]])

# 训练神经网络
for i in range(10000):
    nn.forward(X)
    nn.backward(X, y, learning_rate=0.1)

# 预测新数据
new_data = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
predictions = nn.forward(new_data)
print(predictions)