On the (Generative) Linear Sketching Problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918389630369792 |
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| author | Yuan, Xinyu Qiao, Yan Wang, Zonghui Chen, Wenzhi |
| author_facet | Yuan, Xinyu Qiao, Yan Wang, Zonghui Chen, Wenzhi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14474 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the (Generative) Linear Sketching Problem Yuan, Xinyu Qiao, Yan Wang, Zonghui Chen, Wenzhi Machine Learning 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. |
| title | On the (Generative) Linear Sketching Problem |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.14474 |