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

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(√ d eρ+frac12logρ+o(loglogρ)/varepsilon) exist, ρ the query radius times the centred key radius, against a lower bound Omega(√ d eρ/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(eρ(√dv+√dklog(1+ρ))/varepsilon) in randomised polynomial time, the first constructive whole-ball guarantee within √log(1+ρ) of the lower bound. A sampling cap O(e2ρ/varepsilon2) 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 eρ/varepsilonprescribes a coreset larger than the cache: the algorithmic contribution is asymptotic on these models.