On the (Generative) Linear Sketching Problem

Abstract:Sketch techniques have been extensively studied in recent years and are especially well-suited to data streaming scenarios, where the sketch summary is updated quickly and compactly. However, it is challenging to recover the current state from these summaries in a way that is accurate, fast, and real. In this paper, we seek a solution that reconciles this tension, aiming for near-perfect recovery with lightweight computational procedures. Focusing on linear sketching problems of the form $\boldsymbol{\Phi}f \rightarrow f$, our study proceeds in three stages. First, we dissect existing techniques and show the root cause of the sketching dilemma: an orthogonal information loss. Second, we examine how generative priors can be leveraged to bridge the information gap. Third, we propose FLORE, a novel generative sketching framework that embraces these analyses to achieve the best of all worlds. More importantly, FLORE can be trained without access to ground-truth data. Comprehensive evaluations demonstrate FLORE's ability to provide high-quality recovery, and support summary with low computing overhead, outperforming previous methods by up to 1000 times in error reduction and 100 times in processing speed compared to learning-based solutions.

Machine Learning (cs.LG)

arXiv:2603.14474 [cs.LG]

(or arXiv:2603.14474v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2603.14474 Focus to learn more arXiv-issued DOI via DataCite

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