HCC+: Hyperbolic Guarding for Certified Attention Retrieval
We study the Lipschitz stability of attention retrieval in hyperbolic spaces. Existing methods lack deterministic guarantees on attention-weight preservation under finite-precision representations. We introduce HCC+, a theoretical framework exploiting three properties of the Poincaré ball: exponential volume growth enabling query-independent boundary truncation; logarithmic covering radius of hyperbolic 1-centers enabling dimension-independent critical-key identification; and a packing bound with constants independent of the embedding dimension. We prove two deterministic guarantees: for exact retrieval, the per-layer attention deviation is bounded by 10\% of its ideal value; for soft att...
| Authors | Liangchen Ge |
|---|---|
| Primary category | cs.DS |
| Published | 25 August 2026 |
| Last updated at source | 25 August 2026 |
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