pytorch_advanced.py

"""
Advanced PyTorch Practice Problems
==================================

This comprehensive problem set contains 15 challenging PyTorch exercises designed to develop
mastery of PyTorch's ecosystem. Each problem requires implementation of complex functionality
and deep understanding of PyTorch internals.

These exercises progress from fundamental concepts to advanced techniques used in
state-of-the-art deep learning research and production environments.

Topics Covered:
- Advanced Tensor Operations and Memory Management
- Custom Autograd Functions and Computational Graph Optimization
- Complex Loss Functions and Regularization Techniques
- Advanced Optimization Strategies
- Custom Neural Network Architectures
- Advanced CNN Architectures and Techniques
- Recurrent Neural Networks and Advanced Sequence Modeling
- Attention Mechanisms and Transformer Architectures
- Generative Models (GANs, VAEs, Diffusion Models)
- Transfer Learning and Fine-tuning
- Distributed Training and Model Parallelism
- Quantization and Model Optimization
- PyTorch JIT and TorchScript
- Model Deployment and Serving
- PyTorch Extensions and C++ Integration

Prerequisites:
- Strong understanding of Python
- Familiarity with deep learning concepts
- Basic experience with PyTorch
"""

import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torch.utils.data import DataLoader, Dataset, TensorDataset
from torch.nn.utils.rnn import pack_padded_sequence, pad_packed_sequence
import torchvision
import numpy as np
import matplotlib.pyplot as plt
from typing import List, Tuple, Dict, Optional, Union, Callable
import math
import time
import os
import io
import copy

#############################
# 1. ADVANCED TENSOR OPERATIONS
#############################

# Problem 1: Implement advanced tensor manipulation functions that:
# - Create tensors with specific memory layouts (contiguous, strided, etc.)
# - Perform efficient in-place operations to minimize memory usage
# - Implement custom tensor indexing and slicing operations
# - Demonstrate understanding of broadcasting rules with complex examples
# - Benchmark different tensor operations for performance comparison

def create_memory_efficient_tensor(shape: Tuple[int, ...], layout_type: str = "contiguous"):
    """
    Create a tensor with specific memory layout characteristics.
    
    Args:
        shape: The shape of the tensor to create
        layout_type: One of "contiguous", "strided", "transposed", "discontiguous"
        
    Returns:
        A tensor with the specified memory layout
    """
    pass  # Implement tensor creation with specific memory layouts

def tensor_memory_benchmarks(sizes: List[Tuple[int, ...]]):
    """
    Benchmark different tensor operations and memory layouts.
    
    Args:
        sizes: List of tensor shapes to benchmark
        
    Returns:
        Dictionary of operation names to timing results
    """
    pass  # Implement benchmarking for different tensor operations

def custom_tensor_ops():
    """
    Implement and demonstrate advanced tensor operations including:
    - Custom strided operations
    - Complex broadcasting scenarios
    - Memory-efficient in-place operations
    - Tensor views vs. copies
    - Sparse tensor operations
    
    Returns:
        Dictionary of results from different operations
    """
    pass  # Implement advanced tensor operations


#############################
# 2. CUSTOM AUTOGRAD FUNCTIONS
#############################

# Problem 2: Implement custom autograd functions that:
# - Define forward and backward passes for complex operations
# - Optimize memory usage during backpropagation
# - Handle multiple inputs and outputs
# - Support higher-order gradients
# - Benchmark against built-in PyTorch functions

class CustomReLU(torch.autograd.Function):
    """
    Custom implementation of ReLU with configurable backward behavior.
    """
    
    @staticmethod
    def forward(ctx, input_tensor, alpha=0.0):
        """
        Forward pass of custom ReLU.
        
        Args:
            ctx: Context to save information for backward pass
            input_tensor: Input tensor
            alpha: Leakage factor (0.0 for standard ReLU)
            
        Returns:
            Output tensor after applying ReLU
        """
        pass  # Implement forward pass
    
    @staticmethod
    def backward(ctx, grad_output):
        """
        Backward pass of custom ReLU.
        
        Args:
            ctx: Context with saved tensors from forward pass
            grad_output: Gradient from downstream layers
            
        Returns:
            Gradient with respect to input and alpha
        """
        pass  # Implement backward pass

class CustomBatchNorm(torch.autograd.Function):
    """
    Custom implementation of BatchNorm with memory-efficient backward pass.
    """
    
    @staticmethod
    def forward(ctx, input_tensor, weight, bias, running_mean, running_var, 
                training=True, momentum=0.1, eps=1e-5):
        """
        Forward pass of custom BatchNorm.
        
        Args:
            ctx: Context to save information for backward pass
            input_tensor: Input tensor
            weight: Scale parameter
            bias: Shift parameter
            running_mean: Running mean for inference
            running_var: Running variance for inference
            training: Whether in training mode
            momentum: Momentum for running stats
            eps: Small constant for numerical stability
            
        Returns:
            Normalized tensor
        """
        pass  # Implement forward pass
    
    @staticmethod
    def backward(ctx, grad_output):
        """
        Backward pass of custom BatchNorm.
        
        Args:
            ctx: Context with saved tensors from forward pass
            grad_output: Gradient from downstream layers
            
        Returns:
            Gradients with respect to all inputs
        """
        pass  # Implement backward pass

def benchmark_custom_autograd():
    """
    Benchmark custom autograd functions against PyTorch built-ins.
    
    Returns:
        Dictionary of timing results
    """
    pass  # Implement benchmarking code


#############################
# 3. ADVANCED LOSS FUNCTIONS
#############################

# Problem 3: Implement advanced loss functions that:
# - Support complex weighting schemes for imbalanced data
# - Combine multiple loss terms with learned weights
# - Implement recent research papers on loss functions
# - Support both classification and regression tasks
# - Handle edge cases and numerical stability

class FocalLoss(nn.Module):
    """
    Implementation of Focal Loss for handling class imbalance.
    
    Reference: https://arxiv.org/abs/1708.02002
    """
    
    def __init__(self, alpha=None, gamma=2.0, reduction='mean'):
        """
        Initialize Focal Loss.
        
        Args:
            alpha: Class weights (None or tensor of shape [num_classes])
            gamma: Focusing parameter
            reduction: Reduction method ('none', 'mean', 'sum')
        """
        super(FocalLoss, self).__init__()
        pass  # Complete initialization
    
    def forward(self, inputs, targets):
        """
        Compute Focal Loss.
        
        Args:
            inputs: Predictions (B, C) or (B, C, ...)
            targets: Ground truth labels (B) or (B, ...)
            
        Returns:
            Loss value
        """
        pass  # Implement forward pass

class LabelSmoothingCrossEntropy(nn.Module):
    """
    Cross entropy loss with label smoothing.
    """
    
    def __init__(self, smoothing=0.1, reduction='mean'):
        """
        Initialize Label Smoothing Cross Entropy Loss.
        
        Args:
            smoothing: Label smoothing factor (0.0 to 1.0)
            reduction: Reduction method ('none', 'mean', 'sum')
        """
        super(LabelSmoothingCrossEntropy, self).__init__()
        pass  # Complete initialization
    
    def forward(self, inputs, targets):
        """
        Compute Label Smoothing Cross Entropy Loss.
        
        Args:
            inputs: Predictions (B, C)
            targets: Ground truth labels (B)
            
        Returns:
            Loss value
        """
        pass  # Implement forward pass

class MultiTaskLoss(nn.Module):
    """
    Multi-task loss with learnable weights.
    
    Reference: https://arxiv.org/abs/1705.07115
    """
    
    def __init__(self, num_tasks, reduction='mean'):
        """
        Initialize Multi-Task Loss.
        
        Args:
            num_tasks: Number of tasks/loss terms
            reduction: Reduction method ('none', 'mean', 'sum')
        """
        super(MultiTaskLoss, self).__init__()
        pass  # Complete initialization
    
    def forward(self, losses):
        """
        Compute weighted multi-task loss.
        
        Args:
            losses: List of individual loss tensors
            
        Returns:
            Combined loss value
        """
        pass  # Implement forward pass


#############################
# 4. ADVANCED OPTIMIZATION TECHNIQUES
#############################

# Problem 4: Implement advanced optimization techniques that:
# - Create custom optimizers with adaptive learning rates
# - Implement learning rate schedulers with warmup and decay
# - Support gradient accumulation for large batch training
# - Implement gradient clipping and normalization
# - Support mixed precision training

class LAMB(optim.Optimizer):
    """
    Implementation of LAMB optimizer (Layer-wise Adaptive Moments for Batch training).
    
    Reference: https://arxiv.org/abs/1904.00962
    """
    
    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, 
                 weight_decay=0, adam=False):
        """
        Initialize LAMB optimizer.
        
        Args:
            params: Iterable of parameters to optimize
            lr: Learning rate
            betas: Coefficients for computing running averages
            eps: Term added for numerical stability
            weight_decay: Weight decay factor
            adam: Whether to use the Adam variant
        """
        defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, adam=adam)
        super(LAMB, self).__init__(params, defaults)
        pass  # Complete initialization
    
    @torch.no_grad()
    def step(self, closure=None):
        """
        Perform a single optimization step.
        
        Args:
            closure: Closure that reevaluates the model and returns the loss
            
        Returns:
            Loss value if closure is provided
        """
        pass  # Implement optimization step

class CosineWarmupScheduler(optim.lr_scheduler._LRScheduler):
    """
    Cosine learning rate scheduler with warmup.
    """
    
    def __init__(self, optimizer, warmup_epochs, max_epochs, warmup_start_lr=0.0, 
                 eta_min=0.0, last_epoch=-1):
        """
        Initialize scheduler.
        
        Args:
            optimizer: Optimizer to schedule
            warmup_epochs: Number of warmup epochs
            max_epochs: Total number of epochs
            warmup_start_lr: Initial learning rate during warmup
            eta_min: Minimum learning rate
            last_epoch: The index of the last epoch
        """
        self.warmup_epochs = warmup_epochs
        self.max_epochs = max_epochs
        self.warmup_start_lr = warmup_start_lr
        self.eta_min = eta_min
        super(CosineWarmupScheduler, self).__init__(optimizer, last_epoch)
        pass  # Complete initialization
    
    def get_lr(self):
        """
        Compute learning rate according to current epoch.
        
        Returns:
            List of learning rates for each parameter group
        """
        pass  # Implement learning rate computation

class GradientAccumulator:
    """
    Helper class for gradient accumulation.
    """
    
    def __init__(self, model, accumulation_steps=1):
        """
        Initialize gradient accumulator.
        
        Args:
            model: PyTorch model
            accumulation_steps: Number of steps to accumulate gradients
        """
        self.model = model
        self.accumulation_steps = accumulation_steps
        pass  # Complete initialization
    
    def zero_grad(self):
        """
        Zero gradients at the beginning of accumulation cycle.
        """
        pass  # Implement gradient zeroing
    
    def backward(self, loss):
        """
        Backward pass with scaling.
        
        Args:
            loss: Loss tensor
        """
        pass  # Implement backward pass
    
    def step(self, optimizer):
        """
        Optimizer step after accumulation.
        
        Args:
            optimizer: PyTorch optimizer
        """
        pass  # Implement optimizer step

def train_with_mixed_precision(model, train_loader, optimizer, loss_fn, epochs=10, 
                              scaler=None, device='cuda'):
    """
    Train a model using mixed precision.
    
    Args:
        model: PyTorch model
        train_loader: DataLoader for training data
        optimizer: PyTorch optimizer
        loss_fn: Loss function
        epochs: Number of training epochs
        scaler: GradScaler for mixed precision
        device: Device to train on
        
    Returns:
        Trained model and training history
    """
    pass  # Implement mixed precision training


#############################
# 5. CUSTOM NEURAL NETWORK MODULES
#############################

# Problem 5: Implement custom neural network modules that:
# - Create parameterized layers with custom forward and backward behavior
# - Support complex weight initialization schemes
# - Implement recent research innovations in neural network design
# - Support dynamic computation graphs
# - Optimize for both training and inference

class MishActivation(nn.Module):
    """
    Implementation of Mish activation function.
    
    Reference: https://arxiv.org/abs/1908.08681
    """
    
    def __init__(self):
        super(MishActivation, self).__init__()
    
    def forward(self, x):
        """
        Compute Mish activation: x * tanh(softplus(x)).
        
        Args:
            x: Input tensor
            
        Returns:
            Activated tensor
        """
        pass  # Implement forward pass

class SEBlock(nn.Module):
    """
    Squeeze-and-Excitation block for channel attention.
    
    Reference: https://arxiv.org/abs/1709.01507
    """
    
    def __init__(self, channels, reduction_ratio=16):
        """
        Initialize SE Block.
        
        Args:
            channels: Number of input channels
            reduction_ratio: Reduction ratio for bottleneck
        """
        super(SEBlock, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass of SE Block.
        
        Args:
            x: Input tensor of shape [B, C, H, W]
            
        Returns:
            Tensor with same shape as input, but with channel attention applied
        """
        pass  # Implement forward pass

class DynamicConv2d(nn.Module):
    """
    Dynamic convolution with attention over filters.
    
    Reference: https://arxiv.org/abs/1912.03458
    """
    
    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0, 
                 dilation=1, groups=1, bias=True, K=4):
        """
        Initialize Dynamic Convolution.
        
        Args:
            in_channels: Number of input channels
            out_channels: Number of output channels
            kernel_size: Size of convolution kernel
            stride: Stride of convolution
            padding: Padding added to input
            dilation: Dilation of convolution
            groups: Number of groups for grouped convolution
            bias: Whether to include bias
            K: Number of parallel convolutions
        """
        super(DynamicConv2d, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass of Dynamic Convolution.
        
        Args:
            x: Input tensor of shape [B, C_in, H, W]
            
        Returns:
            Output tensor of shape [B, C_out, H', W']
        """
        pass  # Implement forward pass

class WeightStandardizedConv2d(nn.Conv2d):
    """
    Convolution with weight standardization.
    
    Reference: https://arxiv.org/abs/1903.10520
    """
    
    def __init__(self, in_channels, out_channels, kernel_size, stride=1, padding=0, 
                 dilation=1, groups=1, bias=True, eps=1e-5):
        """
        Initialize Weight Standardized Convolution.
        
        Args:
            Standard Conv2d parameters
            eps: Small constant for numerical stability
        """
        super(WeightStandardizedConv2d, self).__init__(
            in_channels, out_channels, kernel_size, stride, padding, 
            dilation, groups, bias)
        self.eps = eps
    
    def forward(self, x):
        """
        Forward pass with weight standardization.
        
        Args:
            x: Input tensor
            
        Returns:
            Output tensor after convolution with standardized weights
        """
        pass  # Implement forward pass

def initialize_weights(module, method='kaiming_normal'):
    """
    Initialize weights of a module using various methods.
    
    Args:
        module: PyTorch module
        method: Initialization method
        
    Returns:
        Module with initialized weights
    """
    pass  # Implement weight initialization


#############################
# 6. ADVANCED CNN ARCHITECTURES
#############################

# Problem 6: Implement advanced CNN architectures that:
# - Create modern CNN building blocks (ResNet, EfficientNet, etc.)
# - Support feature pyramid networks and multi-scale processing
# - Implement attention mechanisms in CNNs
# - Support various normalization techniques
# - Optimize for both accuracy and efficiency

class ResidualBlock(nn.Module):
    """
    Residual block with bottleneck design.
    """
    
    def __init__(self, in_channels, out_channels, stride=1, expansion=4, 
                 downsample=None, norm_layer=nn.BatchNorm2d):
        """
        Initialize Residual Block.
        
        Args:
            in_channels: Number of input channels
            out_channels: Number of output channels
            stride: Stride for convolution
            expansion: Expansion factor for bottleneck
            downsample: Downsample function for skip connection
            norm_layer: Normalization layer
        """
        super(ResidualBlock, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass of Residual Block.
        
        Args:
            x: Input tensor
            
        Returns:
            Output tensor after residual block
        """
        pass  # Implement forward pass

class InvertedResidualBlock(nn.Module):
    """
    Inverted residual block from MobileNetV2/EfficientNet.
    """
    
    def __init__(self, in_channels, out_channels, stride=1, expand_ratio=6, 
                 norm_layer=nn.BatchNorm2d):
        """
        Initialize Inverted Residual Block.
        
        Args:
            in_channels: Number of input channels
            out_channels: Number of output channels
            stride: Stride for depthwise convolution
            expand_ratio: Expansion ratio for inverted bottleneck
            norm_layer: Normalization layer
        """
        super(InvertedResidualBlock, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass of Inverted Residual Block.
        
        Args:
            x: Input tensor
            
        Returns:
            Output tensor after inverted residual block
        """
        pass  # Implement forward pass

class FeaturePyramidNetwork(nn.Module):
    """
    Feature Pyramid Network for multi-scale feature extraction.
    
    Reference: https://arxiv.org/abs/1612.03144
    """
    
    def __init__(self, in_channels_list, out_channels):
        """
        Initialize Feature Pyramid Network.
        
        Args:
            in_channels_list: List of input channels for each level
            out_channels: Number of output channels for each level
        """
        super(FeaturePyramidNetwork, self).__init__()
        pass  # Complete initialization
    
    def forward(self, features):
        """
        Forward pass of Feature Pyramid Network.
        
        Args:
            features: List of feature maps from backbone
            
        Returns:
            List of feature maps with lateral connections
        """
        pass  # Implement forward pass

class EfficientNet(nn.Module):
    """
    Simplified implementation of EfficientNet.
    
    Reference: https://arxiv.org/abs/1905.11946
    """
    
    def __init__(self, width_multiplier=1.0, depth_multiplier=1.0, 
                 dropout_rate=0.2, num_classes=1000):
        """
        Initialize EfficientNet.
        
        Args:
            width_multiplier: Multiplier for channel dimensions
            depth_multiplier: Multiplier for layer depth
            dropout_rate: Dropout rate
            num_classes: Number of output classes
        """
        super(EfficientNet, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass of EfficientNet.
        
        Args:
            x: Input tensor
            
        Returns:
            Class logits
        """
        pass  # Implement forward pass

class GroupNorm1d(nn.Module):
    """
    Custom implementation of GroupNorm for 1D data.
    """
    
    def __init__(self, num_channels, num_groups=32, eps=1e-5):
        """
        Initialize GroupNorm1d.
        
        Args:
            num_channels: Number of channels
            num_groups: Number of groups
            eps: Small constant for numerical stability
        """
        super(GroupNorm1d, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass of GroupNorm1d.
        
        Args:
            x: Input tensor of shape [B, C, L]
            
        Returns:
            Normalized tensor
        """
        pass  # Implement forward pass


#############################
# 7. ADVANCED RNNs AND SEQUENCE MODELING
#############################

# Problem 7: Implement advanced RNN architectures that:
# - Create custom RNN cells with complex gating mechanisms
# - Support bidirectional and multi-layer configurations
# - Implement attention mechanisms for sequence data
# - Handle variable-length sequences efficiently
# - Optimize for both training and inference speed

class GRUCell(nn.Module):
    """
    Custom implementation of GRU cell.
    """
    
    def __init__(self, input_size, hidden_size, bias=True):
        """
        Initialize GRU cell.
        
        Args:
            input_size: Size of input features
            hidden_size: Size of hidden state
            bias: Whether to use bias
        """
        super(GRUCell, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x, hidden):
        """
        Forward pass of GRU cell.
        
        Args:
            x: Input tensor of shape [B, input_size]
            hidden: Hidden state of shape [B, hidden_size]
            
        Returns:
            New hidden state
        """
        pass  # Implement forward pass

class BidirectionalLSTM(nn.Module):
    """
    Custom implementation of bidirectional LSTM.
    """
    
    def __init__(self, input_size, hidden_size, num_layers=1, dropout=0.0, 
                 batch_first=True):
        """
        Initialize Bidirectional LSTM.
        
        Args:
            input_size: Size of input features
            hidden_size: Size of hidden state
            num_layers: Number of LSTM layers
            dropout: Dropout probability
            batch_first: Whether input is batch-first
        """
        super(BidirectionalLSTM, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x, lengths=None):
        """
        Forward pass of Bidirectional LSTM.
        
        Args:
            x: Input tensor of shape [B, L, input_size] if batch_first
            lengths: Sequence lengths for packing
            
        Returns:
            Output tensor and final hidden states
        """
        pass  # Implement forward pass

class BahdanauAttention(nn.Module):
    """
    Bahdanau (additive) attention mechanism.
    
    Reference: https://arxiv.org/abs/1409.0473
    """
    
    def __init__(self, hidden_size):
        """
        Initialize Bahdanau Attention.
        
        Args:
            hidden_size: Size of hidden states
        """
        super(BahdanauAttention, self).__init__()
        pass  # Complete initialization
    
    def forward(self, query, keys, values, mask=None):
        """
        Forward pass of Bahdanau Attention.
        
        Args:
            query: Query tensor of shape [B, hidden_size]
            keys: Key tensor of shape [B, L, hidden_size]
            values: Value tensor of shape [B, L, hidden_size]
            mask: Optional mask of shape [B, L]
            
        Returns:
            Context vector and attention weights
        """
        pass  # Implement forward pass

class LuongAttention(nn.Module):
    """
    Luong (multiplicative) attention mechanism.
    
    Reference: https://arxiv.org/abs/1508.04025
    """
    
    def __init__(self, hidden_size, method='general'):
        """
        Initialize Luong Attention.
        
        Args:
            hidden_size: Size of hidden states
            method: Attention method ('dot', 'general', 'concat')
        """
        super(LuongAttention, self).__init__()
        pass  # Complete initialization
    
    def forward(self, query, keys, values, mask=None):
        """
        Forward pass of Luong Attention.
        
        Args:
            query: Query tensor of shape [B, hidden_size]
            keys: Key tensor of shape [B, L, hidden_size]
            values: Value tensor of shape [B, L, hidden_size]
            mask: Optional mask of shape [B, L]
            
        Returns:
            Context vector and attention weights
        """
        pass  # Implement forward pass

class Seq2SeqModel(nn.Module):
    """
    Sequence-to-sequence model with attention.
    """
    
    def __init__(self, input_size, hidden_size, output_size, 
                 num_layers=1, dropout=0.0, attention_type='bahdanau'):
        """
        Initialize Seq2Seq Model.
        
        Args:
            input_size: Size of input features
            hidden_size: Size of hidden state
            output_size: Size of output features
            num_layers: Number of RNN layers
            dropout: Dropout probability
            attention_type: Type of attention ('bahdanau', 'luong')
        """
        super(Seq2SeqModel, self).__init__()
        pass  # Complete initialization
    
    def forward(self, source, target, source_lengths, target_lengths, 
                teacher_forcing_ratio=0.5):
        """
        Forward pass of Seq2Seq Model.
        
        Args:
            source: Source sequence of shape [B, L_src, input_size]
            target: Target sequence of shape [B, L_tgt, input_size]
            source_lengths: Lengths of source sequences
            target_lengths: Lengths of target sequences
            teacher_forcing_ratio: Probability of using teacher forcing
            
        Returns:
            Output sequence and attention weights
        """
        pass  # Implement forward pass


#############################
# 8. TRANSFORMER ARCHITECTURES
#############################

# Problem 8: Implement transformer architectures that:
# - Create multi-head self-attention mechanisms
# - Support positional encodings and embeddings
# - Implement transformer encoder and decoder blocks
# - Support various attention masking techniques
# - Optimize for both training and inference

class MultiHeadAttention(nn.Module):
    """
    Multi-head attention mechanism.
    """
    
    def __init__(self, embed_dim, num_heads, dropout=0.0):
        """
        Initialize Multi-Head Attention.
        
        Args:
            embed_dim: Dimension of embeddings
            num_heads: Number of attention heads
            dropout: Dropout probability
        """
        super(MultiHeadAttention, self).__init__()
        pass  # Complete initialization
    
    def forward(self, query, key, value, key_padding_mask=None, 
                attn_mask=None, need_weights=False):
        """
        Forward pass of Multi-Head Attention.
        
        Args:
            query: Query tensor of shape [B, L_q, embed_dim]
            key: Key tensor of shape [B, L_k, embed_dim]
            value: Value tensor of shape [B, L_v, embed_dim]
            key_padding_mask: Mask for padded elements in key
            attn_mask: Mask to prevent attention to certain positions
            need_weights: Whether to return attention weights
            
        Returns:
            Output tensor and attention weights (if needed)
        """
        pass  # Implement forward pass

class PositionalEncoding(nn.Module):
    """
    Sinusoidal positional encoding.
    """
    
    def __init__(self, embed_dim, max_len=5000, dropout=0.0):
        """
        Initialize Positional Encoding.
        
        Args:
            embed_dim: Dimension of embeddings
            max_len: Maximum sequence length
            dropout: Dropout probability
        """
        super(PositionalEncoding, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass of Positional Encoding.
        
        Args:
            x: Input tensor of shape [B, L, embed_dim]
            
        Returns:
            Tensor with positional encodings added
        """
        pass  # Implement forward pass

class TransformerEncoderLayer(nn.Module):
    """
    Transformer encoder layer.
    """
    
    def __init__(self, embed_dim, num_heads, ff_dim, dropout=0.0):
        """
        Initialize Transformer Encoder Layer.
        
        Args:
            embed_dim: Dimension of embeddings
            num_heads: Number of attention heads
            ff_dim: Dimension of feed-forward network
            dropout: Dropout probability
        """
        super(TransformerEncoderLayer, self).__init__()
        pass  # Complete initialization
    
    def forward(self, src, src_mask=None, src_key_padding_mask=None):
        """
        Forward pass of Transformer Encoder Layer.
        
        Args:
            src: Source tensor of shape [B, L, embed_dim]
            src_mask: Mask to prevent attention to certain positions
            src_key_padding_mask: Mask for padded elements
            
        Returns:
            Output tensor after encoder layer
        """
        pass  # Implement forward pass

class TransformerDecoderLayer(nn.Module):
    """
    Transformer decoder layer.
    """
    
    def __init__(self, embed_dim, num_heads, ff_dim, dropout=0.0):
        """
        Initialize Transformer Decoder Layer.
        
        Args:
            embed_dim: Dimension of embeddings
            num_heads: Number of attention heads
            ff_dim: Dimension of feed-forward network
            dropout: Dropout probability
        """
        super(TransformerDecoderLayer, self).__init__()
        pass  # Complete initialization
    
    def forward(self, tgt, memory, tgt_mask=None, memory_mask=None,
                tgt_key_padding_mask=None, memory_key_padding_mask=None):
        """
        Forward pass of Transformer Decoder Layer.
        
        Args:
            tgt: Target tensor of shape [B, L, embed_dim]
            memory: Memory tensor from encoder of shape [B, L_src, embed_dim]
            tgt_mask: Mask to prevent attention to certain positions in target
            memory_mask: Mask to prevent attention to certain positions in memory
            tgt_key_padding_mask: Mask for padded elements in target
            memory_key_padding_mask: Mask for padded elements in memory
            
        Returns:
            Output tensor after decoder layer
        """
        pass  # Implement forward pass

class Transformer(nn.Module):
    """
    Complete transformer model with encoder and decoder.
    """
    
    def __init__(self, src_vocab_size, tgt_vocab_size, embed_dim, num_heads,
                 ff_dim, num_encoder_layers, num_decoder_layers, dropout=0.1):
        """
        Initialize Transformer.
        
        Args:
            src_vocab_size: Size of source vocabulary
            tgt_vocab_size: Size of target vocabulary
            embed_dim: Dimension of embeddings
            num_heads: Number of attention heads
            ff_dim: Dimension of feed-forward network
            num_encoder_layers: Number of encoder layers
            num_decoder_layers: Number of decoder layers
            dropout: Dropout probability
        """
        super(Transformer, self).__init__()
        pass  # Complete initialization
    
    def forward(self, src, tgt, src_key_padding_mask=None, tgt_key_padding_mask=None,
                memory_key_padding_mask=None, tgt_mask=None):
        """
        Forward pass of Transformer.
        
        Args:
            src: Source tensor of shape [B, L_src]
            tgt: Target tensor of shape [B, L_tgt]
            src_key_padding_mask: Mask for padded elements in source
            tgt_key_padding_mask: Mask for padded elements in target
            memory_key_padding_mask: Mask for padded elements in memory
            tgt_mask: Mask to prevent attention to future positions in target
            
        Returns:
            Output logits of shape [B, L_tgt, tgt_vocab_size]
        """
        pass  # Implement forward pass


#############################
# 9. GENERATIVE MODELS
#############################

# Problem 9: Implement generative models that:
# - Create GAN architectures with various loss functions
# - Implement VAE with different prior distributions
# - Support conditional generation
# - Implement diffusion models
# - Optimize for both sample quality and training stability

class Generator(nn.Module):
    """
    Generator network for GAN.
    """
    
    def __init__(self, latent_dim, output_channels=3, img_size=64):
        """
        Initialize Generator.
        
        Args:
            latent_dim: Dimension of latent space
            output_channels: Number of output channels
            img_size: Size of output image
        """
        super(Generator, self).__init__()
        pass  # Complete initialization
    
    def forward(self, z):
        """
        Forward pass of Generator.
        
        Args:
            z: Latent vector of shape [B, latent_dim]
            
        Returns:
            Generated images of shape [B, output_channels, img_size, img_size]
        """
        pass  # Implement forward pass

class Discriminator(nn.Module):
    """
    Discriminator network for GAN.
    """
    
    def __init__(self, input_channels=3, img_size=64):
        """
        Initialize Discriminator.
        
        Args:
            input_channels: Number of input channels
            img_size: Size of input image
        """
        super(Discriminator, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass of Discriminator.
        
        Args:
            x: Input images of shape [B, input_channels, img_size, img_size]
            
        Returns:
            Discrimination scores of shape [B, 1]
        """
        pass  # Implement forward pass

class WGAN_GP(nn.Module):
    """
    Wasserstein GAN with gradient penalty.
    
    Reference: https://arxiv.org/abs/1704.00028
    """
    
    def __init__(self, latent_dim, img_channels=3, img_size=64):
        """
        Initialize WGAN-GP.
        
        Args:
            latent_dim: Dimension of latent space
            img_channels: Number of image channels
            img_size: Size of images
        """
        super(WGAN_GP, self).__init__()
        pass  # Complete initialization
    
    def gradient_penalty(self, real_samples, fake_samples):
        """
        Compute gradient penalty for WGAN-GP.
        
        Args:
            real_samples: Real images
            fake_samples: Generated images
            
        Returns:
            Gradient penalty term
        """
        pass  # Implement gradient penalty
    
    def train_step(self, real_samples, optimizer_G, optimizer_D, n_critic=5):
        """
        Perform a single training step.
        
        Args:
            real_samples: Batch of real images
            optimizer_G: Generator optimizer
            optimizer_D: Discriminator optimizer
            n_critic: Number of discriminator updates per generator update
            
        Returns:
            Dictionary of losses
        """
        pass  # Implement training step

class VAE(nn.Module):
    """
    Variational Autoencoder.
    
    Reference: https://arxiv.org/abs/1312.6114
    """
    
    def __init__(self, input_dim, hidden_dim, latent_dim):
        """
        Initialize VAE.
        
        Args:
            input_dim: Dimension of input data
            hidden_dim: Dimension of hidden layers
            latent_dim: Dimension of latent space
        """
        super(VAE, self).__init__()
        pass  # Complete initialization
    
    def encode(self, x):
        """
        Encode input to latent distribution parameters.
        
        Args:
            x: Input data
            
        Returns:
            Mean and log variance of latent distribution
        """
        pass  # Implement encoding
    
    def reparameterize(self, mu, logvar):
        """
        Reparameterization trick.
        
        Args:
            mu: Mean of latent distribution
            logvar: Log variance of latent distribution
            
        Returns:
            Sampled latent vector
        """
        pass  # Implement reparameterization
    
    def decode(self, z):
        """
        Decode latent vector to reconstruction.
        
        Args:
            z: Latent vector
            
        Returns:
            Reconstructed data
        """
        pass  # Implement decoding
    
    def forward(self, x):
        """
        Forward pass of VAE.
        
        Args:
            x: Input data
            
        Returns:
            Reconstructed data, mean, and log variance
        """
        pass  # Implement forward pass

class DiffusionModel(nn.Module):
    """
    Denoising diffusion probabilistic model.
    
    Reference: https://arxiv.org/abs/2006.11239
    """
    
    def __init__(self, unet, beta_start=1e-4, beta_end=0.02, timesteps=1000):
        """
        Initialize Diffusion Model.
        
        Args:
            unet: U-Net model for denoising
            beta_start: Start value for noise schedule
            beta_end: End value for noise schedule
            timesteps: Number of diffusion steps
        """
        super(DiffusionModel, self).__init__()
        pass  # Complete initialization
    
    def forward_diffusion(self, x_0, t):
        """
        Forward diffusion process.
        
        Args:
            x_0: Original clean data
            t: Timestep
            
        Returns:
            Noisy data and noise
        """
        pass  # Implement forward diffusion
    
    def reverse_diffusion(self, x_T, timesteps=None):
        """
        Reverse diffusion process (sampling).
        
        Args:
            x_T: Pure noise
            timesteps: Number of sampling steps (default: same as training)
            
        Returns:
            Generated samples
        """
        pass  # Implement reverse diffusion
    
    def train_step(self, x_0, optimizer):
        """
        Perform a single training step.
        
        Args:
            x_0: Batch of training data
            optimizer: Optimizer
            
        Returns:
            Loss value
        """
        pass  # Implement training step


#############################
# 10. TRANSFER LEARNING AND FINE-TUNING
#############################

# Problem 10: Implement transfer learning techniques that:
# - Support loading and adapting pre-trained models
# - Implement various fine-tuning strategies
# - Support domain adaptation techniques
# - Implement knowledge distillation
# - Optimize for both performance and efficiency

class FeatureExtractor(nn.Module):
    """
    Extract features from pre-trained models.
    """
    
    def __init__(self, model_name='resnet50', layers=None, requires_grad=False):
        """
        Initialize Feature Extractor.
        
        Args:
            model_name: Name of pre-trained model
            layers: List of layer names to extract features from
            requires_grad: Whether to compute gradients for pre-trained weights
        """
        super(FeatureExtractor, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass of Feature Extractor.
        
        Args:
            x: Input tensor
            
        Returns:
            Dictionary of features from specified layers
        """
        pass  # Implement forward pass

class GradualUnfreezing(nn.Module):
    """
    Wrapper for gradual unfreezing of layers during fine-tuning.
    """
    
    def __init__(self, model, layer_groups=None):
        """
        Initialize Gradual Unfreezing.
        
        Args:
            model: Pre-trained model
            layer_groups: List of layer groups for unfreezing
        """
        super(GradualUnfreezing, self).__init__()
        pass  # Complete initialization
    
    def freeze_all(self):
        """
        Freeze all parameters.
        """
        pass  # Implement freezing
    
    def unfreeze_group(self, group_idx):
        """
        Unfreeze a specific layer group.
        
        Args:
            group_idx: Index of layer group to unfreeze
        """
        pass  # Implement unfreezing
    
    def forward(self, x):
        """
        Forward pass.
        
        Args:
            x: Input tensor
            
        Returns:
            Model output
        """
        pass  # Implement forward pass

class DomainAdaptation(nn.Module):
    """
    Domain adaptation using adversarial training.
    
    Reference: https://arxiv.org/abs/1505.07818
    """
    
    def __init__(self, feature_extractor, task_classifier, domain_classifier):
        """
        Initialize Domain Adaptation.
        
        Args:
            feature_extractor: Feature extraction network
            task_classifier: Task-specific classifier
            domain_classifier: Domain classifier
        """
        super(DomainAdaptation, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x, alpha=1.0):
        """
        Forward pass with gradient reversal.
        
        Args:
            x: Input tensor
            alpha: Adaptation parameter
            
        Returns:
            Task predictions and domain predictions
        """
        pass  # Implement forward pass
    
    def train_step(self, source_data, source_labels, target_data, optimizer, alpha=1.0):
        """
        Perform a single training step.
        
        Args:
            source_data: Source domain data
            source_labels: Source domain labels
            target_data: Target domain data
            optimizer: Optimizer
            alpha: Adaptation parameter
            
        Returns:
            Dictionary of losses
        """
        pass  # Implement training step

class KnowledgeDistillation(nn.Module):
    """
    Knowledge distillation from teacher to student model.
    
    Reference: https://arxiv.org/abs/1503.02531
    """
    
    def __init__(self, teacher_model, student_model, temperature=1.0, alpha=0.5):
        """
        Initialize Knowledge Distillation.
        
        Args:
            teacher_model: Teacher model (pre-trained)
            student_model: Student model (to be trained)
            temperature: Temperature for softening distributions
            alpha: Weight for distillation loss
        """
        super(KnowledgeDistillation, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass through both teacher and student.
        
        Args:
            x: Input tensor
            
        Returns:
            Student outputs and teacher outputs
        """
        pass  # Implement forward pass
    
    def distillation_loss(self, student_logits, teacher_logits, labels):
        """
        Compute distillation loss.
        
        Args:
            student_logits: Logits from student model
            teacher_logits: Logits from teacher model
            labels: Ground truth labels
            
        Returns:
            Total loss combining distillation and standard loss
        """
        pass  # Implement distillation loss


#############################
# 11. DISTRIBUTED TRAINING AND MODEL PARALLELISM
#############################

# Problem 11: Implement distributed training techniques that:
# - Support data parallel training across multiple GPUs
# - Implement model parallel training for large models
# - Support distributed training across multiple nodes
# - Implement pipeline parallelism
# - Optimize communication patterns for efficiency

def setup_distributed_training(rank, world_size, backend='nccl'):
    """
    Set up distributed training environment.
    
    Args:
        rank: Rank of current process
        world_size: Total number of processes
        backend: Backend for distributed communication
        
    Returns:
        Process group
    """
    pass  # Implement distributed setup

class DistributedTrainer:
    """
    Trainer for distributed data parallel training.
    """
    
    def __init__(self, model, optimizer, loss_fn, device, rank, world_size):
        """
        Initialize Distributed Trainer.
        
        Args:
            model: PyTorch model
            optimizer: Optimizer
            loss_fn: Loss function
            device: Device to train on
            rank: Rank of current process
            world_size: Total number of processes
        """
        pass  # Complete initialization
    
    def train_epoch(self, train_loader):
        """
        Train for one epoch.
        
        Args:
            train_loader: DataLoader for training data
            
        Returns:
            Average loss
        """
        pass  # Implement training epoch
    
    def validate(self, val_loader):
        """
        Validate model.
        
        Args:
            val_loader: DataLoader for validation data
            
        Returns:
            Validation metrics
        """
        pass  # Implement validation

class ModelParallelResNet50(nn.Module):
    """
    ResNet50 with model parallelism across multiple GPUs.
    """
    
    def __init__(self, num_classes=1000, devices=None):
        """
        Initialize Model Parallel ResNet50.
        
        Args:
            num_classes: Number of output classes
            devices: List of devices to distribute model across
        """
        super(ModelParallelResNet50, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass with cross-device communication.
        
        Args:
            x: Input tensor on first device
            
        Returns:
            Output tensor on last device
        """
        pass  # Implement forward pass

class PipelineParallelModel(nn.Module):
    """
    Pipeline parallelism implementation.
    
    Reference: https://arxiv.org/abs/1811.06965
    """
    
    def __init__(self, layers, devices, chunks=1):
        """
        Initialize Pipeline Parallel Model.
        
        Args:
            layers: List of model layers
            devices: List of devices to distribute layers across
            chunks: Number of micro-batches for pipelining
        """
        super(PipelineParallelModel, self).__init__()
        pass  # Complete initialization
    
    def forward(self, x):
        """
        Forward pass with pipeline parallelism.
        
        Args:
            x: Input tensor
            
        Returns:
            Output tensor
        """
        pass  # Implement forward pass


#############################
# 12. QUANTIZATION AND MODEL OPTIMIZATION
#############################

# Problem 12: Implement model optimization techniques that:
# - Support various quantization methods (post-training, QAT)
# - Implement pruning for model sparsity
# - Support knowledge distillation for model compression
# - Implement neural architecture search
# - Optimize models for inference on different hardware

def quantize_model_post_training(model, calibration_data_loader, backend='fbgemm'):
    """
    Perform post-training static quantization.
    
    Args:
        model: PyTorch model to quantize
        calibration_data_loader: DataLoader for calibration data
        backend: Backend for quantized operations
        
    Returns:
        Quantized model
    """
    pass  # Implement post-training quantization

class QuantizationAwareTraining:
    """
    Helper for quantization-aware training.
    """
    
    def __init__(self, model, optimizer, loss_fn, device):
        """
        Initialize Quantization-Aware Training.
        
        Args:
            model: PyTorch model
            optimizer: Optimizer
            loss_fn: Loss function
            device: Device to train on
        """
        pass  # Complete initialization
    
    def prepare_model(self):
        """
        Prepare model for quantization-aware training.
        
        Returns:
            Prepared model
        """
        pass  # Implement model preparation
    
    def train_epoch(self, train_loader):
        """
        Train for one epoch with quantization awareness.
        
        Args:
            train_loader: DataLoader for training data
            
        Returns:
            Average loss
        """
        pass  # Implement training epoch
    
    def convert_model(self):
        """
        Convert model to fully quantized version.
        
        Returns:
            Quantized model
        """
        pass  # Implement model conversion

class MagnitudePruning:
    """
    Magnitude-based weight pruning.
    """
    
    def __init__(self, model, prune_ratio=0.5, prune_schedule=None):
        """
        Initialize Magnitude Pruning.
        
        Args:
            model: PyTorch model
            prune_ratio: Target sparsity ratio
            prune_schedule: Schedule for gradual pruning
        """
        pass  # Complete initialization
    
    def prune_step(self, epoch=None):
        """
        Perform a pruning step.
        
        Args:
            epoch: Current epoch for scheduled pruning
            
        Returns:
            Current sparsity ratio
        """
        pass  # Implement pruning step
    
    def apply_mask(self):
        """
        Apply pruning masks to weights.
        """
        pass  # Implement mask application

class NeuralArchitectureSearch:
    """
    Simple neural architecture search implementation.
    """
    
    def __init__(self, search_space, evaluation_metric, max_trials=100):
        """
        Initialize Neural Architecture Search.
        
        Args:
            search_space: Definition of architecture search space
            evaluation_metric: Function to evaluate architectures
            max_trials: Maximum number of architectures to try
        """
        pass  # Complete initialization
    
    def sample_architecture(self):
        """
        Sample an architecture from the search space.
        
        Returns:
            Architecture specification
        """
        pass  # Implement architecture sampling
    
    def search(self, train_loader, val_loader, epochs_per_trial=10):
        """
        Perform architecture search.
        
        Args:
            train_loader: DataLoader for training data
            val_loader: DataLoader for validation data
            epochs_per_trial: Number of epochs to train each architecture
            
        Returns:
            Best architecture found
        """
        pass  # Implement search algorithm


#############################
# 13. PYTORCH JIT AND TORCHSCRIPT
#############################

# Problem 13: Implement TorchScript techniques that:
# - Convert models to TorchScript via tracing and scripting
# - Optimize TorchScript models for inference
# - Support custom TorchScript operators
# - Handle dynamic control flow in TorchScript
# - Benchmark TorchScript models against eager mode

def trace_model(model, example_inputs):
    """
    Trace a PyTorch model to TorchScript.
    
    Args:
        model: PyTorch model
        example_inputs: Example inputs for tracing
        
    Returns:
        Traced model
    """
    pass  # Implement model tracing

def script_model(model):
    """
    Script a PyTorch model to TorchScript.
    
    Args:
        model: PyTorch model
        
    Returns:
        Scripted model
    """
    pass  # Implement model scripting

class TorchScriptOptimizer:
    """
    Optimize TorchScript models for inference.
    """
    
    def __init__(self, ts_model):
        """
        Initialize TorchScript Optimizer.
        
        Args:
            ts_model: TorchScript model
        """
        pass  # Complete initialization
    
    def optimize(self, optimization_level=3):
        """
        Apply optimizations to TorchScript model.
        
        Args:
            optimization_level: Level of optimization (0-3)
            
        Returns:
            Optimized TorchScript model
        """
        pass  # Implement optimization
    
    def fuse_operations(self):
        """
        Fuse operations in TorchScript model.
        
        Returns:
            Model with fused operations
        """
        pass  # Implement operation fusion

@torch.jit.script
def custom_script_function(x, y):
    """
    Custom TorchScript function with control flow.
    
    Args:
        x: First input tensor
        y: Second input tensor
        
    Returns:
        Processed tensor
    """
    pass  # Implement custom script function

def benchmark_torchscript_vs_eager(model, scripted_model, inputs, num_iterations=1000):
    """
    Benchmark TorchScript model against eager mode.
    
    Args:
        model: PyTorch model in eager mode
        scripted_model: TorchScript version of the model
        inputs: Input tensors for benchmarking
        num_iterations: Number of iterations for benchmarking
        
    Returns:
        Dictionary of timing results
    """
    pass  # Implement benchmarking


#############################
# 14. MODEL DEPLOYMENT AND SERVING
#############################

# Problem 14: Implement model deployment techniques that:
# - Export models to different formats (ONNX, TorchScript, etc.)
# - Create model serving endpoints
# - Optimize models for different deployment targets
# - Implement batching and dynamic shapes
# - Benchmark deployed models for latency and throughput

def export_to_onnx(model, example_inputs, onnx_path, input_names=None, output_names=None, 
                  dynamic_axes=None, opset_version=12):
    """
    Export PyTorch model to ONNX format.
    
    Args:
        model: PyTorch model
        example_inputs: Example inputs for tracing
        onnx_path: Path to save ONNX model
        input_names: Names for input tensors
        output_names: Names for output tensors
        dynamic_axes: Dynamic axes specification
        opset_version: ONNX opset version
        
    Returns:
        Path to exported model
    """
    pass  # Implement ONNX export

class ModelServer:
    """
    Simple model serving implementation.
    """
    
    def __init__(self, model_path, model_type='torchscript', device='cpu', 
                batch_size=1, max_batch_size=16):
        """
        Initialize Model Server.
        
        Args:
            model_path: Path to saved model
            model_type: Type of model ('torchscript', 'onnx', 'pytorch')
            device: Device to run inference on
            batch_size: Default batch size
            max_batch_size: Maximum batch size for dynamic batching
        """
        pass  # Complete initialization
    
    def preprocess(self, inputs):
        """
        Preprocess inputs before inference.
        
        Args:
            inputs: Raw inputs
            
        Returns:
            Preprocessed inputs
        """
        pass  # Implement preprocessing
    
    def inference(self, inputs):
        """
        Run inference on inputs.
        
        Args:
            inputs: Preprocessed inputs
            
        Returns:
            Model outputs
        """
        pass  # Implement inference
    
    def postprocess(self, outputs):
        """
        Postprocess model outputs.
        
        Args:
            outputs: Raw model outputs
            
        Returns:
            Processed outputs
        """
        pass  # Implement postprocessing
    
    def predict(self, inputs):
        """
        End-to-end prediction pipeline.
        
        Args:
            inputs: Raw inputs
            
        Returns:
            Processed predictions
        """
        pass  # Implement prediction pipeline

def benchmark_model_serving(server, test_inputs, batch_sizes=None, num_iterations=100):
    """
    Benchmark model serving performance.
    
    Args:
        server: ModelServer instance
        test_inputs: Test inputs for benchmarking
        batch_sizes: List of batch sizes to test
        num_iterations: Number of iterations for each batch size
        
    Returns:
        Dictionary of latency and throughput metrics
    """
    pass  # Implement benchmarking


#############################
# 15. PYTORCH EXTENSIONS AND C++ INTEGRATION
#############################

# Problem 15: Implement PyTorch C++ extensions that:
# - Create custom C++ operators for PyTorch
# - Implement CUDA kernels for GPU acceleration
# - Integrate with existing C++ libraries
# - Optimize performance-critical operations
# - Benchmark against pure Python implementations

def create_cpp_extension_module():
    """
    Create a simple C++ extension module.
    
    Returns:
        Path to compiled extension
    """
    pass  # Implement extension creation

class CustomCppFunction(torch.autograd.Function):
    """
    PyTorch function using custom C++ implementation.
    """
    
    @staticmethod
    def forward(ctx, input):
        """
        Forward pass using C++ extension.
        
        Args:
            ctx: Context to save information for backward pass
            input: Input tensor
            
        Returns:
            Output tensor
        """
        pass  # Implement forward pass
    
    @staticmethod
    def backward(ctx, grad_output):
        """
        Backward pass using C++ extension.
        
        Args:
            ctx: Context with saved tensors from forward pass
            grad_output: Gradient from downstream layers
            
        Returns:
            Gradient with respect to input
        """
        pass  # Implement backward pass

class CustomCudaFunction(torch.autograd.Function):
    """
    PyTorch function using custom CUDA implementation.
    """
    
    @staticmethod
    def forward(ctx, input):
        """
        Forward pass using CUDA extension.
        
        Args:
            ctx: Context to save information for backward pass
            input: Input tensor
            
        Returns:
            Output tensor
        """
        pass  # Implement forward pass
    
    @staticmethod
    def backward(ctx, grad_output):
        """
        Backward pass using CUDA extension.
        
        Args:
            ctx: Context with saved tensors from forward pass
            grad_output: Gradient from downstream layers
            
        Returns:
            Gradient with respect to input
        """
        pass  # Implement backward pass

def benchmark_cpp_vs_python(input_tensor, num_iterations=1000):
    """
    Benchmark C++ extension against pure Python implementation.
    
    Args:
        input_tensor: Input tensor for benchmarking
        num_iterations: Number of iterations for benchmarking
        
    Returns:
        Dictionary of timing results
    """
    pass  # Implement benchmarking

def integrate_with_external_library(input_tensor):
    """
    Demonstrate integration with an external C++ library.
    
    Args:
        input_tensor: Input tensor
        
    Returns:
        Processed tensor
    """
    pass  # Implement external library integration