前馈神经网络 (Feedforward Neural Network, FNN)

import torch import torch.nn as nn import torch.optim as optim import numpy as np import matplotlib.pyplot as plt # 1. 定义前馈神经网络 class FeedforwardNN(nn.Module): def __init__(self, input_dim, hidden_dim, output_dim): super(FeedforwardNN, self).__init__() self.fc = nn.Sequential( nn.Linear(input_dim, hidden_dim), # 输入层到隐藏层 nn.ReLU(), # 激活函数 nn.Linear(hidden_dim, output_dim), # 隐藏层到输出层 nn.Sigmoid() # 输出层的激活函数（适用于二分类问题） ) def forward(self, x): return self.fc(x) # 2. 创建 XOR 数据集 def create_xor_data(): X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]], dtype=np.float32) y = np.array([[0], [1], [1], [0]], dtype=np.float32) return X, y # 3. 训练前馈神经网络 def train_fnn(): # 数据准备 X, y = create_xor_data() X = torch.tensor(X, dtype=torch.float32) y = torch.tensor(y, dtype=torch.float32) # 初始化网络、损失函数和优化器 input_dim = X.shape[1] hidden_dim = 10 output_dim = 1 model = FeedforwardNN(input_dim, hidden_dim, output_dim) criterion = nn.BCELoss() # 二分类交叉熵损失 optimizer = optim.Adam(model.parameters(), lr=0.01) # 训练网络 epochs = 1000 loss_history = [] for epoch in range(epochs): # 前向传播 outputs = model(X) loss = criterion(outputs, y) # 反向传播与优化 optimizer.zero_grad() loss.backward() optimizer.step() # 记录损失 loss_history.append(loss.item()) if (epoch + 1) % 100 == 0: print(f"Epoch [{epoch + 1}/{epochs}], Loss: {loss.item():.4f}") # 绘制损失曲线 plt.plot(loss_history) plt.xlabel('Epoch') plt.ylabel('Loss') plt.title('Training Loss Curve') plt.show() # 输出训练结果 with torch.no_grad(): predictions = model(X).round() print("Predictions:", predictions.numpy()) print("Ground Truth:", y.numpy()) # 运行训练 if __name__ == "__main__": train_fnn()