Task Description:

The provided PyTorch neural network model, which integrates a Temporal Convolutional Network (TCN) encoder and a Transformer decoder, is experiencing performance degradation attributed to the curse of dimensionality. This phenomenon occurs in high-dimensional spaces where data becomes sparse, leading to challenges in modeling and generalization due to increased computational complexity and the risk of overfitting.

The model architecture includes several critical components:

Chomp1d Module: Adjusts the output of convolution layers to maintain causal relationships.
Residual Blocks with Causal Convolutions: Utilize weight normalization and dilation to capture temporal dependencies.
Temporal Convolutional Network (TCN) Encoder: Processes input sequences using stacked residual blocks.
Transformer Decoder: Generates output sequences with masked multi-head attention mechanisms.
Attention Layer: An additional fusion cross-attention layer to enhance the decoder's representations.
Fusion Strategies: Combines decoder outputs and attention outputs using different techniques.
Furthermore, the training function employs techniques such as gradient clipping, learning rate scheduling, and mixed-precision training to optimize the learning process.

Objective:

The primary objective is to analyze the given neural network model to identify and understand the impact of the curse of dimensionality on its performance. Based on this analysis, the task involves extracting actionable insights and proposing effective strategies to mitigate these issues, thereby enhancing the model's efficiency and accuracy.

Deliverables:

Comprehensive Analysis Report:

Model Architecture Examination:

Provide a detailed analysis of each component within the model architecture.
Identify elements contributing to high dimensionality, such as the depth of the network, the number of features, and the complexity of layers.
Discuss how these components interact and the implications for the model's capacity and generalization.
Impact Assessment of the Curse of Dimensionality:

Explain the specific challenges posed by high-dimensional spaces in the context of this model.
Analyze issues such as overfitting, increased computational burden, difficulties in optimization, and any observed degradation in performance metrics.
Use mathematical formulations or visualizations where appropriate to illustrate these challenges.
Strategies for Mitigation:

Dimensionality Reduction Techniques:

Propose methods to reduce input and model dimensionality without significant loss of important information.
Consider techniques such as Principal Component Analysis (PCA), autoencoder-based compression, or feature selection mechanisms.
Evaluate the potential impact of these techniques on the model's ability to capture temporal dependencies.
Model Architecture Optimization:

Suggest architectural modifications aimed at simplifying the model.
Explore options like parameter sharing, bottleneck layers, or depth-wise separable convolutions.
Discuss the trade-offs between model complexity and performance.
Regularization and Generalization:

Recommend regularization methods to prevent overfitting caused by high dimensionality.
Options may include L1/L2 regularization, dropout enhancements, early stopping criteria, or data augmentation strategies.
Assess how these methods can improve the model's ability to generalize to unseen data.
Training Procedure Enhancements:

Propose improvements to the optimization process, such as advanced learning rate schedules, adaptive optimizers, or gradient normalization techniques.

Summary of Findings:

Summarize the key insights gained from the analysis and experimentation.
Highlight which strategies were most effective in addressing the curse of dimensionality.
Recommendations:

Provide actionable recommendations for further improvements or future work.
Discuss any limitations encountered during the analysis.


The model :

Weight normzlizatioin 2223, Layer 2425.
Chomp1d removes extra time steps from the end of the sequence
class Chomp1d(nn.Module):
def init(self, chomp_size):
super(Chomp1d, self).init()
self.chomp_size = chomp_size
def forward(self, x):
if self.chomp_size > 0:
return x[:, :, :-self.chomp_size]
else:
return x

Residual Block with causal convolutions and Chomp1d
class ResidualBlock(nn.Module):
def init(self, in_channels, out_channels, kernel_size, dilation, dropout):
super(ResidualBlock, self).init()
padding = (kernel_size - 1) * dilation

    self.conv1 = nn.utils.weight_norm(
        nn.Conv1d(in_channels, out_channels, kernel_size,
                  padding=padding, dilation=dilation)
    )
    self.chomp1 = Chomp1d(padding)
    self.relu1 = nn.ReLU()
    self.dropout1 = nn.Dropout(dropout)
    self.conv2 = nn.utils.weight_norm(
        nn.Conv1d(out_channels, out_channels, kernel_size,
                  padding=padding, dilation=dilation)
    )
    self.chomp2 = Chomp1d(padding)
    self.relu2 = nn.ReLU()
    self.dropout2 = nn.Dropout(dropout)
    # If the input and output channels are not the same, adjust with a 1x1 convolution
    self.downsample = nn.Conv1d(in_channels, out_channels, kernel_size=1) \
        if in_channels != out_channels else None

    self.relu = nn.ReLU()
    self.init_weights()

def init_weights(self):
    nn.init.normal_(self.conv1.weight, std=0.01)
    nn.init.normal_(self.conv2.weight, std=0.01)
    if self.downsample is not None:
        nn.init.normal_(self.downsample.weight, std=0.01)

def forward(self, x):
    residual = x  # Save the input for the residual connection
    out = self.conv1(x)
    out = self.chomp1(out)  # Remove extra padding
    out = self.relu1(out)
    out = self.dropout1(out)
    out = self.conv2(out)
    out = self.chomp2(out)  # Remove extra padding
    out = self.relu2(out)
    out = self.dropout2(out)
    if self.downsample is not None:
        residual = self.downsample(residual)

    return self.relu(out + residual)  # Residual connection with addition
Updated TCN Encoder with Residual Blocks 0.4
class TCNEncoder(nn.Module):
def init(self, input_size, hidden_size, num_layers, kernel_size, dropout):
super(TCNEncoder, self).init()
layers = []
in_channels = input_size

    for i in range(num_layers):
        dilation = 2 ** i
        out_channels = hidden_size

        layers.append(ResidualBlock(in_channels, out_channels, kernel_size, dilation, dropout))

        in_channels = out_channels  # For next layer

    self.network = nn.Sequential(*layers)

def forward(self, x):
    # x shape: (batch_size, seq_length, input_size)
    x = x.transpose(1, 2)  # Change to (batch_size, input_size, seq_length)
    x = self.network(x)
    x = x.transpose(1, 2)  # Back to (batch_size, seq_length, hidden_size)
    return x
Transformer Decoder with masked multi-head attention
class TransformerDecoder(nn.Module):
def init(self, input_size, hidden_size, num_layers, num_heads, dropout):
super(TransformerDecoder, self).init()
self.embedding = nn.Linear(input_size, hidden_size)
self.positional_encoding = PositionalEncoding(hidden_size, dropout)
decoder_layer = nn.TransformerDecoderLayer(d_model=hidden_size, nhead=num_heads, dropout=dropout)
self.transformer_decoder = nn.TransformerDecoder(decoder_layer, num_layers=num_layers)
self.fc_out = nn.Linear(hidden_size, input_size)

def forward(self, tgt, memory, tgt_mask):
    # tgt: (batch_size, tgt_seq_length, input_size)
    tgt_emb = self.embedding(tgt)
    tgt_emb = self.positional_encoding(tgt_emb)
    memory = memory.transpose(0, 1)  # (src_seq_length, batch_size, hidden_size)
    tgt_emb = tgt_emb.transpose(0, 1)  # (tgt_seq_length, batch_size, hidden_size)
    output = self.transformer_decoder(tgt_emb, memory, tgt_mask=tgt_mask)
    output = output.transpose(0, 1)  # Back to (batch_size, tgt_seq_length, hidden_size)
    return output
TCN-Encoder-Transformer-Decoder Model
class TCNEncoderTransformerDecoder(nn.Module):
def init(self, input_size, hidden_size, num_layers, kernel_size, num_heads, dropout):
super(TCNEncoderTransformerDecoder, self).init()
self.encoder = TCNEncoder(input_size, hidden_size, num_layers, kernel_size, dropout)
# Additional Attention Layer (Fusion Cross-Attention) ver = 0.4
self.attention_layer = nn.MultiheadAttention(embed_dim=hidden_size, num_heads=num_heads, dropout=dropout)
self.decoder = TransformerDecoder(input_size, hidden_size, num_layers, num_heads, dropout)
self.positional_encoding = PositionalEncoding(hidden_size, dropout) # For encoder outputs

    # Fusion Layer ver = 0.4 if Fusion startgy 1 then multiply hidden_size by 2
    self.final_fc_layer = nn.Linear(hidden_size, input_size)
    self.dropout = nn.Dropout(dropout)

    # Alpha parameter for weighted sum fusion ver = 0.4
    # Initialize alpha as a learnable parameter with value 0.5
    self.alpha = nn.Parameter(torch.full((hidden_size,), 0.5))

def forward(self, src, tgt):
    # src: (batch_size, src_seq_length, input_size)
    # tgt: (batch_size, tgt_seq_length, input_size)

    # Encoder
    memory = self.encoder(src)  # (batch_size, src_seq_length, hidden_size)
    memory = self.positional_encoding(memory)  # Add positional encoding to memory

    # Decoder
    tgt_mask = nn.Transformer.generate_square_subsequent_mask(tgt.size(1)).to(tgt.device)  # (tgt_seq_length, tgt_seq_length)
    decoder_output = self.decoder(tgt, memory, tgt_mask)  # (batch_size, tgt_seq_length, hidden_size)

    # Reshape for MultiheadAttention (seq_length, batch_size, embed_dim)
    decoder_output_t = decoder_output.transpose(0, 1)  # (tgt_seq_length, batch_size, hidden_size)
    memory_t = memory.transpose(0, 1)  # (src_seq_length, batch_size, hidden_size)

    # Additional Attention Layer
    attn_output, _ = self.attention_layer(decoder_output_t, memory_t, memory_t)
    attn_output = attn_output.transpose(0, 1)  # (batch_size, tgt_seq_length, hidden_size)

    # Fusion Strategy 1: Concatenate decoder output and attention output
    #combined = torch.cat((decoder_output, attn_output), dim=-1)  # (batch_size, tgt_seq_length, hidden_size * 2)
    #combined = self.dropout(combined)#

    # Fusion Strategy 2: Weighted Sum of decoder output and attention output
    # I must always ensure alpha is in [0,1] using sigmoid or similar functions
    # Tested scaler alpha and it perfromed worse than 4% worse than Strategy 1 so switched it to vector
    alpha = torch.sigmoid(self.alpha).to(decoder_output.device).view(1, 1, -1)  # Shape: (1, 1, hidden_size)
    combined = alpha * decoder_output + (1 - alpha) * attn_output  # (batch_size, tgt_seq_length, hidden_size)
    combined = self.dropout(combined)

    # Fusion Strategy 2: Multiplication
    #final_output = self.multi_scale_fusion(decoder_output, memory)
    
    # Final Output Layer
    final_output = self.final_fc_layer(combined)  # (batch_size, tgt_seq_length, input_size)

    return final_output
Positional Encoding class (unchanged)
class PositionalEncoding(nn.Module):
def init(self, d_model, dropout=0.1, max_len=5000):
super(PositionalEncoding, self).init()
self.dropout = nn.Dropout(p=dropout)

    pe = torch.zeros(max_len, d_model)  # Create positional encoding matrix
    position = torch.arange(0, max_len, dtype=torch.float).unsqueeze(1)
    div_term = torch.exp(torch.arange(0, d_model, 2).float() * (-np.log(10000.0) / d_model))
    pe[:, 0::2] = torch.sin(position * div_term)  # Apply sine to even indices
    pe[:, 1::2] = torch.cos(position * div_term)  # Apply cosine to odd indices
    pe = pe.unsqueeze(0)
    self.register_buffer('pe', pe)  # Save positional encoding matrix

def forward(self, x):
    x = x + self.pe[:, :x.size(1), :].to(x.device)  # Add positional encoding
    return self.dropout(x)
Learnable Positional Encoding class
class LearnablePositionalEncoding(nn.Module):
def init(self, d_model, max_len=5000):
super(LearnablePositionalEncoding, self).init()
self.pe = nn.Parameter(torch.randn(1, max_len, d_model))

def forward(self, x):
    x = x + self.pe[:, :x.size(1), :].to(x.device)
    return x
The training function:

Function to train the model with teacher forcing
def train_model(model, train_loader, val_loader, num_epochs, learning_rate, gradient_clip_val, train_only = False):
criterion = nn.MSELoss()
optimizer = torch.optim.Adam([
{'params': model.parameters(), 'lr': learning_rate}, # Lower learning rate for model parameters
#{'params': [criterion.scale], 'lr': 2}, # Higher learning rate for the scale parameter
])
processor_type= 'cuda' if torch.cuda.is_available() else 'cpu'
scaler = GradScaler()
device = torch.device(processor_type)
model.to(device)

scheduler = torch.optim.lr_scheduler.OneCycleLR(optimizer, max_lr=learning_rate*2, steps_per_epoch=len(train_loader), epochs=num_epochs)

# Track best validation loss for early stopping
best_val_loss = float('inf')
patience = 350
patience_counter = 0
pbar = tqdm(range(num_epochs), desc=f"Epochs", unit="epoch")
for epoch in pbar:
    model.train()
    train_loss = 0.0
    train_sMAPE = 0.0
    train_MASE = 0.0
    for batch_x, batch_y in train_loader:
        
        batch_x, batch_y = _prepare_batch(batch_x, batch_y, device)
        # Prepare decoder input by shifting targets (teacher forcing)
        decoder_input = _prepare_decoder_input(batch_x, batch_y)

        optimizer.zero_grad(set_to_none=True)
        
        with autocast(device_type= processor_type):
            output = model(batch_x, decoder_input)
            loss = criterion(output, batch_y)
            batch_sMAPE = smape(batch_y, output)
            batch_MASE = mase(batch_y, output, torch.tensor(train_data.values, dtype=torch.float32).to(device))
        # Scale the loss and call backward
        
        scaler.scale(loss).backward()
        scaler.unscale_(optimizer)
        torch.nn.utils.clip_grad_norm_(model.parameters(), gradient_clip_val)
        scaler.step(optimizer)
        scaler.update()
        train_loss += loss.item()
        train_sMAPE += batch_sMAPE
        train_MASE += batch_MASE
        scheduler.step()
        
    train_loss /= len(train_loader)
    train_sMAPE /= len(train_loader)
    train_MASE /= len(train_loader)

    if not(train_only):
        Flag, best_val_loss, losses = validate_model(model, val_loader, criterion, best_val_loss, processor_type, patience_counter, patience)
        val_loss, val_sMAPE, val_MASE = losses

        #break if patience runs out
        if not(Flag):
            break
        
    # Log to wandb
    wandb.log({"Epoch": epoch + 1, "Train Loss": train_loss, "Train sMAPE": train_sMAPE, "Train MASE": train_MASE, 
               "Validation Loss": val_loss, "Validation sMAPE": val_sMAPE, "Validation MASE": val_MASE,
               "Learning Rate": scheduler.get_last_lr()[0]
               #,"EXP Function Scale": criterion.scale.item()
              })
    # Update progress bar
    pbar.set_description(f"Epoch {epoch + 1}/{num_epochs}" 
    +f"- Average Loss: {val_loss:.4f}" 
    +f"- LR: {scheduler.get_last_lr()[0]:.6f}")

# Finalize wandb logging
#wandb.finish()
return model