循环神经网络 RNN

隐状态（Hidden State）：RNN 通过隐状态来记住序列中的信息。

\[ h_t=f(W_{hh}h_{t-1}+W_{xh}x_t+b_h) \]

Output：RNN 的输出不仅依赖当前的输入，还依赖于隐状态的历史信息。

\[ y_t=W_{hy}h_t+b_y \]

PyTorch 中的 RNN

• torch.nn.RNN：基本的RNN单元。
• torch.nn.LSTM：长短期记忆单元，能够学习长期依赖关系。
• torch.nn.GRU：门控循环单元，是LSTM的简化版本，但通常更容易训练。

PyTorch 实现 RNN

import torch
import torch.nn as nn
import torch.optim as optim
import matplotlib.pyplot as plt
import numpy as np

# 数据集：字符序列预测（Hello -> Elloh）
char_set = list("hello")
char_to_idx = {c: i for i, c in enumerate(char_set)}
idx_to_char = {i: c for i, c in enumerate(char_set)}

# 数据准备
input_str = "hello"
target_str = "elloh"
input_data = [char_to_idx[c] for c in input_str]
target_data = [char_to_idx[c] for c in target_str]

# 转换为独热编码
input_one_hot = np.eye(len(char_set))[input_data]

# 转换为 PyTorch Tensor
inputs = torch.tensor(input_one_hot, dtype=torch.float32)
targets = torch.tensor(target_data, dtype=torch.long)

# 模型超参数
input_size = len(char_set)
hidden_size = 8
output_size = len(char_set)
num_epochs = 200
learning_rate = 0.1

# 定义 RNN 模型
class RNNModel(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(RNNModel, self).__init__()
        self.rnn = nn.RNN(input_size, hidden_size, batch_first=True)
        self.fc = nn.Linear(hidden_size, output_size)

    def forward(self, x, hidden):
        out, hidden = self.rnn(x, hidden)
        out = self.fc(out)  # 应用全连接层
        return out, hidden

model = RNNModel(input_size, hidden_size, output_size)

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

# 训练 RNN
losses = []
hidden = None  # 初始隐藏状态为 None
for epoch in range(num_epochs):
    optimizer.zero_grad()

    # 前向传播
    outputs, hidden = model(inputs.unsqueeze(0), hidden)
    hidden = hidden.detach()  # 防止梯度爆炸

    # 计算损失
    loss = criterion(outputs.view(-1, output_size), targets)
    loss.backward()
    optimizer.step()
    losses.append(loss.item())

    if (epoch + 1) % 20 == 0:
        print(f"Epoch [{epoch + 1}/{num_epochs}], Loss: {loss.item():.4f}")

# 测试 RNN
with torch.no_grad():
    test_hidden = None
    test_output, _ = model(inputs.unsqueeze(0), test_hidden)
    predicted = torch.argmax(test_output, dim=2).squeeze().numpy()

    print("Input sequence: ", ''.join([idx_to_char[i] for i in input_data]))
    print("Predicted sequence: ", ''.join([idx_to_char[i] for i in predicted]))