# HCC+: Hyperbolic Guarding for Certified Attention Retrieval

arXiv: https://arxiv.org/abs/2608.24971 · HTML: https://mlsanity.com/paper/2608.24971/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 8 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [Riemann GeoResolver: A Non-Euclidean Attention Framework from Euclidean Resolver to Hyperbolic-Spherical Geometry](https://mlsanity.com/paper/2608.10416/) (2026)

## Abstract (arXiv)

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 Poincar'e 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 attention, the total variation distance decays as O(1/√n), the rate of finite-sample variance. As a consequence of the guarding mechanism, the framework achieves a storage reduction factor of 6.1× relative to FP16. We provide the first deterministic, query-independent retrieval certificate in non-Euclidean geometry.