Abstract
Empirical validation of the Geodesic Trajectory Cache (GTC) proposed in Paper IV. On three model scales (135M–1.5B parameters), GTC achieves cache hit rates of 90.4–91.5% at a 25%-fraction coverage budget — scale-invariant within ±0.5%. Batch Jacobi evaluation reaches 97× speedup at B=10. GTC is 15.5× faster than disk-based RAG. Compressed trajectory records occupy 5.96 KB each. End-to-end speculative decode with GTC drafts achieves 76.5 tok/s (1.53× baseline).
1. Key Results
| Metric | Value |
|---|---|
| Cache coverage (3-model avg) | 91.0% at 25% budget |
| Batch Jacobi peak | 97.9× at B=10 |
| vs. disk-based RAG | 15.5× faster |
| Record size | 5.96 KB (rank-5 exact) |
| Query latency | 30.9 μs |
| OTT end-to-end | 76.5 tok/s (1.53× baseline) |
2. Scale Invariance
Cache coverage is independent of model size: 91.0% (135M), 90.4% (360M), 91.5% (1.5B) — within ±0.5% across a 33× parameter range. The manifold structure is scale-invariant, confirming the intrinsic dimension hypothesis from Paper IV.
References
- Stewart, W.K.O. Organic Training Theory. HyperTensor Paper IV, 2026.
- Stewart, W.K.O. GRC Attention Compression. HyperTensor Paper I, 2026.