Hyperdimensional Connections a Lossless, Queryable Semantic Reasoning Framework

Hyperdimensional Connection Method: A Lossless Framework Preserving Meaning, Structure, and Semantic Relationships across Modalities

This repository contains the complete implementation and experimental validation of a revolutionary dimensionality reduction method that achieves perfect reconstruction (1.000 accuracy) while discovering semantic patterns invisible to traditional approaches. Built upon the MatrixTransformer framework's 16-dimensional decision hypercube, this method represents a paradigm shift from lossy compression to lossless, interpretable, and universally applicable feature extraction.

Key Features

• Perfect Information Preservation: Zero reconstruction error across all domains (biological, textual, visual) vs. 0.1% loss in traditional methods
• Cross-Modal Pattern Discovery: Unique ability to identify relationships across different feature representation types (3,015 connections in MNIST vs. 0 for traditional methods)
• Semantic Coherence Quantification: Achieves 94.7% semantic coherence in text analysis with queryable connection structures
• Domain-Agnostic Performance: Consistent advantages across 784-dimensional visual data, high-dimensional biological matrices, and multi-modal text representations
• 100% Sparsity Preservation: Maintains complete matrix sparsity while traditional dense methods achieve 0%

Experimental Validation

Comprehensive benchmarking across three diverse domains:

1. Biological Data: Drug-gene interaction networks preserving clinically relevant patterns (NFE2L2, AR, CYP3A4)
2. Textual Data: NewsGroups dataset with 23 cross-matrix links enabling multi-modal semantic analysis
3. Visual Data: MNIST digit recognition with cross-digit relationship discovery and geometric pattern analysis

Technical Innovation

• Hyperdimensional Connection Discovery: Identifies meaningful relationships in 8-dimensional hyperdimensional space
• Hypersphere Projection: Constrains matrices to hypersphere surfaces while preserving structural properties
• Bidirectional Matrix Conversion: Enables lossless round-trip transformation between connection and matrix representations
• Query-Ready Architecture: Supports unlimited post-hoc analysis including similarity searches, anomaly detection, and relationship discovery

Applications

• Bioinformatics: Drug discovery with preserved biological network structure
• Natural Language Processing: Multi-modal text analysis with cross-representation relationship discovery
• Computer Vision: Visual pattern analysis with cross-pattern relationship discovery
• Financial Analysis: Anomaly detection preserving sparse transaction patterns
• Scientific Computing: Simulation embeddings maintaining physical constraints

Repository Contents

• Complete MatrixTransformer implementation with hyperdimensional extensions
• Experimental benchmarking code and datasets
• Comprehensive visualizations and analysis tools
• Domain-specific applications and examples
• Full reproducibility documentation

This work establishes a new standard for analytical methods that refuse to sacrifice information for computational convenience, opening new possibilities for scientific discovery where perfect information preservation enables insights impossible with traditional lossy approaches.

from matrixtransformer import MatrixTransformer import numpy as np # Initialize the transformer transformer = MatrixTransformer(dimensions=256) # Add some sample matrices to the transformer's storage sample_matrices = [ np.random.randn(28, 28), # Image-like matrix np.eye(10), # Identity matrix np.random.randn(15, 15), # Random square matrix np.random.randn(20, 30), # Rectangular matrix np.diag(np.random.randn(12)) # Diagonal matrix ] # Store matrices in the transformer transformer.matrices = sample_matrices # Optional: Add some metadata about the matrices transformer.layer_info = [ {'type': 'image', 'source': 'synthetic'}, {'type': 'identity', 'source': 'standard'}, {'type': 'random', 'source': 'synthetic'}, {'type': 'rectangular', 'source': 'synthetic'}, {'type': 'diagonal', 'source': 'synthetic'} ] # Find hyperdimensional connections print("Finding hyperdimensional connections...") connections = transformer.find_hyperdimensional_connections(num_dims=8) # Access stored matrices print(f"\nAccessing stored matrices:") print(f"Number of matrices stored: {len(transformer.matrices)}") for i, matrix in enumerate(transformer.matrices): print(f"Matrix {i}: shape {matrix.shape}, type: {transformer._detect_matrix_type(matrix)}") # Convert connections to matrix representation print("\nConverting connections to matrix format...") coords3d = [] for i, matrix in enumerate(transformer.matrices): coords = transformer._generate_matrix_coordinates(matrix, i) coords3d.append(coords) coords3d = np.array(coords3d) indices = list(range(len(transformer.matrices))) # Create connection matrix with metadata conn_matrix, metadata = transformer.connections_to_matrix( connections, coords3d, indices, matrix_type='general' ) print(f"Connection matrix shape: {conn_matrix.shape}") print(f"Matrix sparsity: {metadata.get('matrix_sparsity', 'N/A')}") print(f"Total connections found: {metadata.get('connection_count', 'N/A')}") # Reconstruct connections from matrix print("\nReconstructing connections from matrix...") reconstructed_connections = transformer.matrix_to_connections(conn_matrix, metadata) # Compare original vs reconstructed print(f"Original connections: {len(connections)} matrices") print(f"Reconstructed connections: {len(reconstructed_connections)} matrices") # Access specific matrix and its connections matrix_idx = 0 if matrix_idx in connections: print(f"\nMatrix {matrix_idx} connections:") print(f"Original matrix shape: {transformer.matrices[matrix_idx].shape}") print(f"Number of connections: {len(connections[matrix_idx])}") # Show first few connections for i, conn in enumerate(connections[matrix_idx][:3]): target_idx = conn['target_idx'] strength = conn.get('strength', 'N/A') print(f" -> Connected to matrix {target_idx} (shape: {transformer.matrices[target_idx].shape}) with strength: {strength}") # Example: Process a specific matrix through the transformer print("\nProcessing a matrix through transformer:") test_matrix = transformer.matrices[0] matrix_type = transformer._detect_matrix_type(test_matrix) print(f"Detected matrix type: {matrix_type}") # Transform the matrix transformed = transformer.process_rectangular_matrix(test_matrix, matrix_type) print(f"Transformed matrix shape: {transformed.shape}")

This snippet shows the complete workflow from storing matrices to finding their hyperdimensional relationships and accessing the results.

Citation

Hyperdimensional_Connection_Method__Experimental_Evaluation.pdf