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

Abstract:A query-oblivious coreset for a softmax-attention head is a subset $S$ of the key--value pairs such that attention computed from $S$ alone is within $\varepsilon$ of the full output, in $\ell_2$, simultaneously for every query in a ball. Liberty, Andoni and Kleiner proved that unweighted coresets of size $O(\sqrt d\,e^{\rho+\frac12\log\rho+o(\log\log\rho)}/\varepsilon)$ exist, $\rho$ being the query radius times the centred key radius, against a lower bound $\Omega(\sqrt d\,e^{\rho}/\varepsilon)$, and conjectured that closing the gap needs new techniques. We show it does not. A spherical lift of both balls into one exponential-kernel instance lets the chaining bound of Bozzai and Rothvoss apply directly, and Chevet's inequality splits key from value dimension: unweighted coresets of size $O(e^{\rho}(\sqrt{d_v}+\sqrt{d_k\log(1+\rho)})/\varepsilon)$ exist and are computable in randomised polynomial time, the first with a whole-ball guarantee at the existential size up to $\sqrt{\log(1+\rho)}$. A dimension-free sampling cap $O(e^{2\rho}/\varepsilon^{2})$ completes the envelope. In fixed dimension the logarithm disappears: completing the key ball to a sphere makes the kernel an unweighted Gaussian one, so Tai's diameter-free bound gives $O_{d_k,d_v}(e^{\rho}/\varepsilon)$, ruling out a matching logarithmic lower bound there and answering the Gaussian-restriction case of a question of Bozzai and Rothvoss for the exponential and Hellinger kernels. We restate the Liberty--Andoni--Kleiner bound in the centred convention with a full proof, and show that the one-way communication bounds of Chen et al.\ transfer to query-oblivious coresets, where for $\varepsilon\ll e^{-\rho}$ they are the strongest floors known. The dimensional factor is the price of one signing for all queries: for a single query the discrepancy is $O(e^{\rho})$, dimension-free.

Data Structures and Algorithms (cs.DS); Computation and Language (cs.CL)

arXiv:2609.06327 [cs.DS]

(or arXiv:2609.06327v1 [cs.DS] for this version)

https://doi.org/10.48550/arXiv.2609.06327 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.