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

תקציר מקורי באנגליתarXiv:2609.06327v2 Announce Type: replace-cross 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 $O(\sqrt d e^{\rho+\frac12\log\rho+o(\log\log\rho)}/\varepsilon)$ exist, $\rho$ 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. 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^{\rho}(\sqrt{d_v}+\sqrt{d_k\log(