Query-Oblivious Coresets for Softmax Attention: Improved Bounds and Efficient Constructions

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. Liberty, Andoni and Kleiner proved that unweighted coresets of size $O(\sqrt d e^{ρ+\frac12\logρ+o(\log\logρ)}/\varepsilon)$ exist, $ρ$ the query radius times the centred key radius, against a lower bound $Ω(\sqrt d e^ρ/\varepsilon)$, and conjectured that closing the gap needs new techniques. It does not: a spherical lift of both balls into one exponential-kernel instance lets the Bozzai-Rothvoss chaining bound apply, and Chevet's inequality splits key from value dimension, giving coresets of size $O(e^ρ(\sqrt{d_v}+\sqrt{d_k\log(1+ρ)})/\varepsilon)$ in randomised polynomial time, the first constructive whole-ball guarantee within $\sqrt{\log(1+ρ)}$ of the lower bound. A sampling cap $O(e^{2ρ}/\varepsilon^{2})$ completes the envelope; in fixed dimension Tai's diameter-free bound removes the logarithm, settling the Gaussian-restriction case of a Bozzai-Rothvoss question for the kernels. We give theLiberty-Andoni-Kleiner lower boud transfer the one-waycommunication bounds of Chen et r is the price of one signing forall queries. A census of every head of Qwen2.5-7B-Instruct and Llama-3-8B-Instruct finds $ρ$ at least 23.877, so everyactor $e^ρ/\varepsilon$prescribes a coreset larger than the cache: the algorithmic contribution is asymptotic on these models.