深度学习入门：神经网络原理与 PyTorch 实战

1. 神经网络基础

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神经网络结构：
├── 输入层：接收原始特征
├── 隐藏层：提取特征（可多层）
├── 输出层：产生预测结果
└── 激活函数：引入非线性

常见激活函数：
├── Sigmoid: σ(x) = 1/(1+e^(-x))，输出 (0,1)
├── Tanh: tanh(x)，输出 (-1,1)
├── ReLU: max(0,x)，最常用
├── LeakyReLU: max(0.01x, x)
└── Softmax: 多分类输出概率

2. PyTorch 基础

python 复制代码

import torch
import torch.nn as nn
import torch.optim as optim

# 创建张量
x = torch.randn(3, 4)           # 随机张量
y = torch.zeros(3, 4)           # 零张量
z = torch.ones(3, 4)            # 全 1 张量

# GPU 加速
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
x = x.to(device)

3. 构建神经网络

python 复制代码

import torch.nn as nn

class SimpleNN(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super().__init__()
        self.layers = nn.Sequential(
            nn.Linear(input_size, hidden_size),
            nn.ReLU(),
            nn.Dropout(0.2),
            nn.Linear(hidden_size, hidden_size),
            nn.ReLU(),
            nn.Dropout(0.2),
            nn.Linear(hidden_size, output_size)
        )
    
    def forward(self, x):
        return self.layers(x)

# 创建模型
model = SimpleNN(784, 256, 10).to(device)
print(model)

4. 训练循环

python 复制代码

import torch.optim as optim
from torch.utils.data import DataLoader, TensorDataset

# 数据准备
dataset = TensorDataset(X_train_tensor, y_train_tensor)
dataloader = DataLoader(dataset, batch_size=32, shuffle=True)

# 损失函数和优化器
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=0.001)

# 训练
for epoch in range(100):
    model.train()
    total_loss = 0
    
    for batch_X, batch_y in dataloader:
        batch_X, batch_y = batch_X.to(device), batch_y.to(device)
        
        # 前向传播
        outputs = model(batch_X)
        loss = criterion(outputs, batch_y)
        
        # 反向传播
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        
        total_loss += loss.item()
    
    if (epoch + 1) % 10 == 0:
        print(f"Epoch {epoch+1}, Loss: {total_loss/len(dataloader):.4f}")

5. 模型评估

python 复制代码

# 评估模式
model.eval()
with torch.no_grad():
    outputs = model(X_test_tensor.to(device))
    predictions = outputs.argmax(dim=1).cpu()
    accuracy = (predictions == y_test_tensor).float().mean()
    print(f"准确率: {accuracy:.4f}")

6. CNN 图像分类

python 复制代码

class SimpleCNN(nn.Module):
    def __init__(self, num_classes=10):
        super().__init__()
        self.features = nn.Sequential(
            nn.Conv2d(3, 32, 3, padding=1),
            nn.ReLU(),
            nn.MaxPool2d(2),
            nn.Conv2d(32, 64, 3, padding=1),
            nn.ReLU(),
            nn.MaxPool2d(2),
            nn.Conv2d(64, 128, 3, padding=1),
            nn.ReLU(),
            nn.MaxPool2d(2),
        )
        self.classifier = nn.Sequential(
            nn.Flatten(),
            nn.Linear(128 * 4 * 4, 256),
            nn.ReLU(),
            nn.Dropout(0.5),
            nn.Linear(256, num_classes)
        )
    
    def forward(self, x):
        x = self.features(x)
        x = self.classifier(x)
        return x

7. 模型保存与加载

python 复制代码

# 保存
torch.save(model.state_dict(), 'model.pth')

# 加载
model = SimpleNN(784, 256, 10)
model.load_state_dict(torch.load('model.pth'))
model.eval()

总结

概念	说明
前向传播	输入 → 输出
反向传播	计算梯度
优化器	SGD/Adam/AdamW
损失函数	CrossEntropy/MSE
正则化	Dropout/BatchNorm