# UHG Library Vectorization Project

This document outlines the approach, best practices, and implementation guidelines for improving vectorization across the Universal Hyperbolic Geometry (UHG) library.

## Objectives

1. **Performance Improvement**: Enhance computational efficiency for large-scale data processing
2. **Numerical Stability**: Improve precision in hyperbolic calculations
3. **Scalability**: Enable processing of larger graphs and datasets
4. **Hardware Utilization**: Better leverage GPU/CPU capabilities

## Vectorization Principles

When implementing vectorized operations, follow these principles:

### 1. Batch Dimension Handling

- Use ellipsis notation (`...`) to handle arbitrary batch dimensions
- Support broadcasting between tensors of different batch shapes
- Preserve batch dimensions in output tensors

Example:
```python
# Good: Handles arbitrary batch dimensions
def uhg_inner_product(a: torch.Tensor, b: torch.Tensor) -> torch.Tensor:
    return torch.sum(a[..., :-1] * b[..., :-1], dim=-1) - a[..., -1] * b[..., -1]

# Bad: Only handles specific batch dimensions
def uhg_inner_product(a: torch.Tensor, b: torch.Tensor) -> torch.Tensor:
    return torch.sum(a[:, :-1] * b[:, :-1], dim=1) - a[:, -1] * b[:, -1]
```

### 2. Memory Efficiency

- Avoid unnecessary tensor copies
- Use in-place operations where appropriate
- Implement chunking for very large tensors

Example:
```python
# Good: Avoids unnecessary copies
result = torch.zeros_like(a[..., 0])
result = torch.sum(a[..., :-1] * b[..., :-1], dim=-1) - a[..., -1] * b[..., -1]

# Bad: Creates unnecessary intermediate tensors
spatial = a[..., :-1].clone()
temporal = a[..., -1].clone()
result = torch.sum(spatial * b[..., :-1], dim=-1) - temporal * b[..., -1]
```

### 3. Numerical Stability

- Add small epsilon values to denominators
- Use `torch.clamp` to prevent division by zero
- Implement stable algorithms for complex operations

Example:
```python
# Good: Ensures numerical stability
denom = torch.clamp(a * b, min=1e-9)
result = x / denom

# Bad: Potential numerical instability
result = x / (a * b)
```

### 4. Testing Strategy

For each vectorized operation:

1. **Correctness Tests**: Compare against loop implementation
2. **Shape Tests**: Verify output shapes for various input shapes
3. **Broadcasting Tests**: Verify broadcasting behavior
4. **Performance Tests**: Measure speedup over loop implementation
5. **Numerical Stability Tests**: Test with edge cases

## Implementation Process

Follow this process for each vectorization task:

1. **Analyze Current Implementation**: Understand the mathematical operation and current implementation
2. **Identify Vectorization Opportunities**: Determine how to vectorize the operation
3. **Implement Vectorized Version**: Write the vectorized implementation
4. **Write Tests**: Create comprehensive tests for the vectorized operation
5. **Benchmark**: Measure performance improvement
6. **Document**: Update documentation with vectorization details

## Prioritization

The checklist in `vectorization_checklist.gitignore` prioritizes tasks based on:

1. **Foundation First**: Core operations that other components depend on
2. **Impact**: Operations that will benefit most from vectorization
3. **Complexity**: Starting with simpler operations before tackling complex ones
4. **Dependencies**: Ensuring dependencies are vectorized before dependent operations

## Benchmarking

For each vectorized operation, measure:

1. **Speedup Factor**: How much faster is the vectorized implementation?
2. **Memory Usage**: How does memory usage compare?
3. **Scaling Behavior**: How does performance scale with input size?
4. **GPU vs. CPU**: How does performance differ between GPU and CPU?

## Documentation

Document vectorization improvements in:

1. **Function Docstrings**: Note vectorization capabilities
2. **Implementation Notes**: Explain vectorization approach
3. **Performance Guidelines**: Provide guidance on batch sizes and memory usage

## Conclusion

Improving vectorization across the UHG library will significantly enhance its performance, scalability, and usability for large-scale cybersecurity applications. By following a systematic approach and adhering to best practices, we can ensure that the vectorized operations are correct, efficient, and maintainable. 