VSA Math Benchmark Suite — MATH-003

Branch: ralph/math-framework Tech Tree Node: MATH-003 Level: 11.39

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Key Metrics

Metric	Value	Status
Operations benchmarked	6 (bind, unbind, bundle2, bundleN, similarity, permute)	Complete
Dimensions tested	1024, 4096, 10000	Complete
Memory compression vs float32	19.5-20.0x	Verified
Bundle-N recall curve	N=3..500	Complete
Convergence validation	3 tests (bind recovery, bundle3, orthogonality)	Complete
Proof verification	12 proofs timed	Complete
Comparison table	Ternary vs Float32 vs Int8 vs Binary	Complete

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What This Means

For Users

• 20x memory savings over float32 representations, validated across all tested dimensions
• Add-only compute for bind/unbind (no multiply), enabling efficient hardware implementations
• Quantified recall curves showing bundle capacity limits at every scale from N=3 to N=500

For Operators

• Benchmark suite runs via zig build bench-math with ReleaseFast optimization
• 7-section suite covers all critical VSA operations
• Results are reproducible with deterministic seeded vectors

For Researchers

• Information density: 1.585 bits/trit (log2(3)), 58.5% more than binary
• Convergence: Bind/unbind recovery > 0.60, bundle3 signal > 0.15, orthogonality < 0.10
• Recall curve: Empirical vs theoretical 1/sqrt(N) model comparison

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Technical Details

Architecture

The benchmark suite (benchmarks/bench_math.zig) imports the core VSA module and bundle optimizer:

• vsa module: bind, unbind, bundle2, bundle3, cosineSimilarity, permute
• bundle_opt module: BundleAccumulator, bundleN

Benchmark Sections

1. Operation Throughput: ops/sec and ns/op for each VSA primitive at 3 dimensions
2. Bundle-N Throughput: Accumulator performance scaling from N=3 to N=500
3. Memory Efficiency: Packed ternary (5 trits/byte) vs float32/binary/theoretical
4. Recall Curve: Bundle capacity analysis with theory comparison
5. Convergence Validation: Statistical validation over multiple trials
6. Proof Verification Time: 12 algebraic proofs timed at 1000 iterations each
7. Comparison Table: Multi-format information density comparison

Memory Comparison (dim=1024)

Format	Bytes	Bits/element	Compression
Ternary packed	205	1.60	1.0x (baseline)
Float32	4096	32.00	20.0x more
Int8	1024	8.00	5.0x more
Binary packed	128	1.00	0.6x less

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Conclusion

MATH-003 provides a comprehensive, reproducible benchmark suite that quantifies the ternary VSA advantage across all critical dimensions: throughput, memory, recall, and convergence. The 20x memory savings vs float32 and add-only compute model are validated with empirical data.

Next steps: Run benchmarks on target hardware platforms, compare with SIMD-optimized implementations (OPT-001).

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phi^2 + 1/phi^2 = 3 = TRINITY