HDC/VSA/HRR Strategy Development

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Research Overview

Goal: Develop and compare hyperdimensional computing strategies optimized for formal reasoning tasks.

Current state: Multiple strategies implemented (Dense-Binary, Sparse-Polynomial, Metric-Affine, EMA, and EXACT). Dense-Binary is the classic baseline; Sparse-Polynomial and Metric-Affine are novel contributions; EMA and EXACT are extensions/explorations for large-KB behavior and lossless representations.

Related theme: see Dynamic Size Representations for why “elastic geometry” (growth under KB expansion) is a core research direction in this project.

1. Current Strategy Landscape

Strategy Type Representation Status
Dense-Binary Classic VSA Bit vectors (2048-4096 bits) Baseline
Sparse-Polynomial NOVEL BigInt exponent sets (k=2-4) Original
Metric-Affine NOVEL Byte channels (16-32 bytes) Original + Fastest
Metric-Affine Elastic EXTENSION Elastic byte channels (32+ bytes) Chunked bundling, large KBs
EXACT EXPLORATION Lossless bitset-polynomial (BigInt monomials) Upper bound for retrievability
Novel Contributions:

See HRR Comparison for theoretical analysis.

2. Research Direction: Hybrid Strategies

Combine strengths of existing strategies:

// Concept: Adaptive Hybrid Strategy

class HybridHDC {
  constructor() {
    this.dense = new DenseBinaryHDC(2048);
    this.metric = new MetricAffineHDC(32);
    this.sparse = new SparsePolynomialHDC(4);
  }

  bind(a, b) {
    // Use metric for speed
    return this.metric.bind(a, b);
  }

  similarity(a, b) {
    // Use dense for accuracy
    return this.dense.similarity(
      this.toDense(a),
      this.toDense(b)
    );
  }

  store(fact) {
    // Use sparse for memory efficiency
    return this.sparse.encode(fact);
  }
}

3. Research Direction: Adaptive Geometry

Dynamically adjust vector dimensions based on KB complexity:

KB Size Recommended Geometry Rationale
< 1,000 facts Metric-Affine 16 bytes Minimal memory, sufficient capacity
1,000 - 10,000 facts Metric-Affine 32 bytes Standard configuration
10,000 - 100,000 facts Dense-Binary 4096 bits More capacity needed
> 100,000 facts Sparse-Polynomial k=8 Scalable representation

4. Research Direction: Novel Similarity Measures

Challenge: Different strategies have different similarity semantics. A unified measure would enable better interoperability.
Strategy Current Measure Proposed Enhancement
Dense-Binary Hamming distance Weighted Hamming by position importance
Sparse-Polynomial Jaccard index Weighted Jaccard with exponent magnitude
Metric-Affine Channel overlap Cosine similarity on byte channels

5. Research Direction: Scalability Testing

Current tests use ~1,300 facts. Need to test at larger scales:

Scale Benchmark Current Status
10K facts Extended stress theories Not tested
100K facts ConceptNet subset Not tested
1M facts Wikidata extract Not tested

6. Theoretical Questions

7. Implementation Priorities

Priority Task Expected Outcome
P1 100K fact stress test Identify scaling limits
P1 Hybrid strategy prototype Combine best features
P2 Adaptive geometry Auto-tuning for KB size
P2 Novel similarity measures Better retrieval accuracy
P3 Formal capacity analysis Theoretical foundations

8. Related Resources

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