On the (Generative) Linear Sketching Problem

2026-03-15

AI Summary

This work addresses the fundamental limitations of conventional linear sketching methods in data stream scenarios, where achieving a balance among reconstruction accuracy, computational efficiency, and real-time performance remains challenging due to information gaps caused by loss of orthogonal components. To overcome this, we propose FLORE—the first unsupervised generative sketching framework that incorporates a generative prior, enabling high-fidelity signal recovery without requiring ground-truth training data. By synergistically integrating generative modeling, linear sketching, and a lightweight recovery algorithm, FLORE achieves high-quality reconstruction while reducing recovery error by up to three orders of magnitude and accelerating computation by up to 100× compared to existing learning-based approaches.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Natural Language Processing: Generation
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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 $\boldsymbolΦf \rightarrow f$, 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.

Problem

• linear sketching
• data streaming
• state recovery
• information loss
• generative priors

Innovation

• generative sketching
• linear sketching
• information loss
• FLORE
• data-free training