import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.jit import script, trace


class Attention(nn.Module):
def __init__(self, hidden_dim):
super(Attention, self).__init__()
self.hidden_dim = hidden_dim
self.attn = nn.Linear(self.hidden_dim * 2, hidden_dim)
self.v = nn.Parameter(torch.rand(hidden_dim))

def forward(self, hidden, encoder_outputs):
timestep = encoder_outputs.size(0)
h = hidden.repeat(timestep, 1)
attn_energies = self.score(h, encoder_outputs)
return F.softmax(attn_energies, dim=1).unsqueeze(1)

def score(self, hidden, encoder_outputs):
energy = F.relu(self.attn(torch.cat([hidden, encoder_outputs], 1)))
energy = energy.transpose(1, 0)
v = self.v.repeat(encoder_outputs.size(0), 1).transpose(1, 0)
energy = torch.sum(v * energy, dim=1)
return energy


class LSTMModel(nn.Module):
def __init__(self, input_dim, hidden_dim, layer_dim, output_dim):
super(LSTMModel, self).__init__()
self.hidden_dim = hidden_dim
self.layer_dim = layer_dim
self.lstm = nn.LSTM(input_dim, hidden_dim, layer_dim, batch_first=True)
self.fc = nn.Linear(hidden_dim*2, output_dim) # *2 for the attention concat
self.attention = Attention(hidden_dim)

def forward(self, x):
h0 = torch.zeros(self.layer_dim, x.size(0), self.hidden_dim).requires_grad_()
c0 = torch.zeros(self.layer_dim, x.size(0), self.hidden_dim).requires_grad_()
out, (hn, cn) = self.lstm(x, (h0.detach(), c0.detach()))
attn_weights = self.attention(hn[-1], out)
context = attn_weights.bmm(out.transpose(0, 1))
out = self.fc(torch.cat([hn[-1], context[:, 0]], 1))
return out


class MemoizationTable:
def __init__(self, rows=10, cols=10, device='cpu'):
self.table = torch.zeros((rows, cols)).to(device)

def clear(self):
self.table.fill_(0)

def fill(self):
self.table.fill_(1)

def update_table(self, new_data):
self.table = new_data


def train_model(model, optimizer, loss_fn, data, memo, epochs=100):
for epoch in range(epochs):
model.train()
optimizer.zero_grad()
outputs = model(data)
memo.update_table(outputs.detach())
loss = loss_fn(outputs, data)
loss.backward()
optimizer.step()

if epoch % 10 == 0:
decision = torch.randint(0, 3, (1,)).item()
if decision == 0:
memo.clear()
elif decision == 1:
memo.fill()

print(f'Epoch {epoch+1}/{epochs}, Loss: {loss.item()}')


# Check if GPU is available
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

# Instantiate the LSTM model with 1 hidden layer of 1 dimension
model = LSTMModel(1, 1, 1, 1).to(device)
memo = MemoizationTable(device=device)
loss_fn = nn.MSELoss()

optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
# Check if GPU is available
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

# Instantiate the LSTM model with 1 hidden layer of 1 dimension
model = LSTMModel(1, 1, 1, 1).to(device)
memo = MemoizationTable(device=device)
loss_fn = nn.MSELoss()
optimizer = torch.optim.Adam(model.parameters(), lr=0.01)

# Generate some dummy data
data = torch.rand((100, 1, 1)).to(device)

# Train the model
train_model(model, optimizer, loss_fn, data, memo, epochs=100)

# Convert the model into TorchScript
script_model = torch.jit.script(model)
script_model.save("LSTMModel.pt")

print("Model training complete and saved as LSTMModel.pt")
Documentation
The provided code constructs a PyTorch implementation of a Long Short-Term Memory (LSTM) network model enhanced with an Attention mechanism and Memoization.

Class Definitions:
Attention(nn.Module):
This class represents the attention mechanism that is utilized in the LSTM model. The attention mechanism helps the model focus on specific parts of the input data, which can be beneficial in tasks such as translation, where certain parts of the input sentence might be more relevant at a given time.

LSTMModel(nn.Module):
This class is an implementation of an LSTM model. LSTM networks are a type of recurrent neural network (RNN) that can learn and remember over long sequences and do not rely on a pre-specified window for input data like a feedforward network or CNN. The use of attention within the model can help it focus on specific inputs that are more relevant, providing a potentially superior performance on certain tasks.

MemoizationTable:
This class represents a simple table for memoization purposes. Memoization is an optimization technique used primarily to speed up programs by storing the results of expensive function calls and reusing them when the same inputs occur again.

Function Definitions:
train_model:
This function is responsible for the training process of the LSTM model. It iterates over a number of epochs, performs the forward pass of the model, computes the loss, performs backpropagation, and updates the model parameters.
Main Program:
The main program first checks if a GPU is available for computation. Then, it initializes the LSTM model, the memoization table, the loss function (Mean Squared Error), and the optimizer (Adam). Some random dummy data is created for the training process. The model is then trained, converted into TorchScript for later use, and saved as a .pt file.

Potential Applications:
Here are few potential use cases for the given code:

Incremental Learning: If new data comes in a sequential manner and the model has to learn continually from the incoming data, this model would shine because of its LSTM structure and memoization capabilities.

Real-Time Translation: In real-time translation where each output has to be generated as soon as the corresponding input comes in, this LSTM model with attention would be beneficial as it can selectively focus on parts of the input sentence which are most relevant for translating the next word.

Sequence-to-Sequence Mapping with Variable Lengths: For tasks like text summarization or machine translation, where the lengths of input and output sequences can vary greatly, this LSTM model with attention could be advantageous.

Remember, the effectiveness of the model will highly depend on the specific task, the quality and quantity of available data, and the model's training process and hyperparameters.