On the (Generative) Linear Sketching Problem

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 boldsymbolPhif 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.