# UHG Library Improvements

## Completed Improvements

1. ✅ Feature Extraction
- Implemented UHG-based feature extraction
- Added geometric pattern recognition
- Optimized for cybersecurity use cases

2. ✅ Anomaly Detection
- Added UHG anomaly scoring
- Implemented geometric distance metrics
- Optimized for outlier detection

3. ✅ Metric Learning
- Implemented UHG metric learning
- Added similarity preservation
- Optimized for pattern matching

4. ✅ Attention Mechanisms
- Implemented UHG attention
- Added multi-head attention
- Preserved geometric invariants

5. ✅ Threat Correlation
- Added indicator correlation
- Implemented relationship analysis
- Added cross-type pattern recognition

## Current Work: Hierarchical Graph Neural Networks

### Implementation Approaches

1. Cross-Ratio Preservation
- Direct computation in projective space
- Log-space calculations for numerical stability
- Iterative refinement for better preservation
- Batch-aware cross-ratio handling

2. Layer Architecture
- ProjectiveHierarchicalLayer
  - Level-aware transformations
  - Cross-ratio preserving weights
  - Parent-child relationship handling
  - Multi-level feature aggregation

3. Model Structure
- ProjectiveHierarchicalGNN
  - Cross-ratio preserving dropout
  - Level-based message passing
  - Hierarchical attention mechanism
  - Projective feature normalization

### Key Components

1. Projective Operations
- Pure UHG-based transformations
- Cross-ratio preservation utilities
- Geometric distance metrics
- Projective averaging methods

2. Hierarchical Structure
- Level encodings
- Parent-child relationships
- Level-based attention
- Hierarchical message passing

3. Batch Processing
- Cross-ratio preservation across batches
- Variable-sized graph handling
- Efficient batch operations
- Level-aware batching

### Technical Challenges

1. Cross-Ratio Preservation
- Numerical stability in computations
- Preservation during normalization
- Batch-level preservation
- Feature transformation effects

2. Hierarchical Operations
- Level-based weight computation
- Parent-child message passing
- Cross-level feature aggregation
- Level-aware attention

3. Performance Optimization
- Efficient batch processing
- Memory usage optimization
- Numerical precision
- Computational complexity

### Next Steps

1. Robustness Improvements
- Enhanced numerical stability
- Better cross-ratio preservation
- More efficient batch processing
- Improved level handling

2. Additional Features
- Dynamic level adaptation
- Adaptive message passing
- Multi-scale feature learning
- Hierarchical pooling

3. Testing and Validation
- Cross-ratio preservation tests
- Hierarchical structure tests
- Batch processing tests
- Performance benchmarks

## Planned Improvements

6. 🔄 Graph Neural Networks (Next Priority)
- Complete hierarchical GNN implementation
- Add more robust cross-ratio preservation
- Enhance batch processing capabilities
- Improve numerical stability

7. 📋 Visualization Tools
- Add UHG space visualization
- Implement pattern visualization
- Support relationship graphs
- Interactive exploration tools

8. 📋 Performance Optimization
- GPU acceleration
- Batch processing
- Memory optimization
- Sparse operations

9. 📋 Integration Tools
- STIX/TAXII support
- MISP integration
- Elastic integration
- Splunk integration

10. 📋 Documentation
- API documentation
- Usage examples
- Best practices
- Performance guide