arXiv cs.CL· Ofek I. Cohen·· 12 小时前AI 评分18
面向 Softmax 注意力的查询无关 coreset：更优界与高效构造
Query-Oblivious Coresets for Softmax Attention: Improved Bounds and Efficient Constructions
AI 导读
研究者为 softmax 注意力头构造出查询无关 coreset，规模为 O(e^ρ(√d_v+√(d_k log(1+ρ)))/ε)，在随机多项式时间内完成，将 Liberty、Andoni 与 Kleiner 的存在性上界改进到距其下界仅差 √log(1+ρ)。
正文 · 原文
Abstract:A query-oblivious coreset for a softmax-attention head is a subset of the key--value pairs whose attention output is within $\varepsilon$ of the full one for every query in a ball. With $\rho$ the query radius times the centred key radius, we build such coresets of size $O(e^{\rho}(\sqrt{d_v}+\sqrt{d_k\log(1+\rho)})/\varepsilon)$ in randomised polynomial time, improving the existential $O(\sqrt d\,e^{\rho+\frac12\log\rho+o(\log\log\rho)}/\varepsilon)$ of Liberty, Andoni and Kleiner to within $\sqrt{\log(1+\rho)}$ of their $\Omega(\sqrt d\,e^{\rho}/\varepsilon)$ lower bound: a spherical lift of both balls into one exponential-kernel instance admits the Bozzai--Rothvoss chaining bound, and Chevet's inequality splits key from value dimension. A sampling cap $O(e^{2\rho}/\varepsilon^{2})$ completes the envelope, and in fixed dimension Tai's diameter-free bound removes the logarithm. A census of every head of Qwen2.5-7B-Instruct and Llama-3.1-8B-Instruct finds $\rho\ge24.100$, so every whole-ball bound with a factor $e^{\rho}/\varepsilon$ prescribes a coreset larger than the cache: the algorithmic contribution is asymptotic on these models.
| Subjects: | Data Structures and Algorithms (cs.DS); Computation and Language (cs.CL) |
| Cite as: | arXiv:2609.06327 [cs.DS] |
| (or arXiv:2609.06327v3 [cs.DS] for this version) | |
| https://doi.org/10.48550/arXiv.2609.06327 arXiv-issued DOI via DataCite |
Submission history
From: Ofek I. Cohen [view email]
[v1]
Sun, 6 Sep 2026 01:23:58 UTC (28 KB)
[v2]
Sun, 13 Sep 2026 14:47:32 UTC (291 KB)
[v3]
Wed, 4 Nov 2026 09:20:34 UTC (286 KB)
来源：arXiv cs.CL · arxiv.org