Bi-directional Long Short-Term Memory，双向LSTM网络。

       有些时候预测可能需要由前面若干输入和后面若干输入共同决定，这样会更加准确。因此提出了双向循环神经网络，网络结构如上图。

       构建LSTM模型时，在参数中添加bidirectional=True，这样就构建了一个双向的LSTM模型。初始化参数时，全连接层的隐藏层特征数量x2，h0和c0参数也要相应改变。

import torch 
import torch.nn as nn
import torchvision
import torchvision.transforms as transforms

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

sequence_length = 28
input_size = 28
hidden_size = 128
num_layers = 2
num_classes = 10
batch_size = 100
num_epochs = 2
learning_rate = 0.003

# MNIST dataset
train_dataset = torchvision.datasets.MNIST(root='./data/',
                                           train=True, 
                                           transform=transforms.ToTensor(),
                                           download=True)

test_dataset = torchvision.datasets.MNIST(root='./data/',
                                          train=False, 
                                          transform=transforms.ToTensor())

# Data loader
train_loader = torch.utils.data.DataLoader(dataset=train_dataset,
                                           batch_size=batch_size, 
                                           shuffle=True)

test_loader = torch.utils.data.DataLoader(dataset=test_dataset,
                                          batch_size=batch_size, 
                                          shuffle=False)

class BiRNN(nn.Module):
    def __init__(self, input_size, hidden_size, num_layers, num_classes):
        super(BiRNN, self).__init__()
        self.hidden_size = hidden_size
        self.num_layers = num_layers
        self.lstm = nn.LSTM(input_size, hidden_size, num_layers, batch_first=True, bidirectional=True)
        self.fc = nn.Linear(hidden_size*2, num_classes)  # 2 for bidirection
    
    def forward(self, x):
        # Set initial states
        h0 = torch.zeros(self.num_layers*2, x.size(0), self.hidden_size).to(device) # 2 for bidirection 
        c0 = torch.zeros(self.num_layers*2, x.size(0), self.hidden_size).to(device)
        
        # Forward propagate LSTM
        out, _ = self.lstm(x, (h0, c0))  # out: tensor of shape (batch_size, seq_length, hidden_size*2)
        
        # Decode the hidden state of the last time step
        out = self.fc(out[:, -1, :])
        return out

model = BiRNN(input_size, hidden_size, num_layers, num_classes).to(device)

criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)

total_step = len(train_loader)
for epoch in range(num_epochs):
    for i, (images, labels) in enumerate(train_loader):
        images = images.reshape(-1, sequence_length, input_size).to(device)
        labels = labels.to(device)
        
        # Forward pass
        outputs = model(images)
        loss = criterion(outputs, labels)
        
        # Backward and optimize
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        
        if (i+1) % 100 == 0:
            print ('Epoch [{}/{}], Step [{}/{}], Loss: {:.4f}' 
                   .format(epoch+1, num_epochs, i+1, total_step, loss.item()))