dorsal/arxiv
View SchemaA Preliminary Agentic Framework for Matrix Deflation
| Authors | Paimon Goulart, Evangelos E. Papalexakis |
|---|---|
| Categories | |
| ArXiv ID | 2601.08219vv1 |
| URL | https://arxiv.org/abs/2601.08219 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
Can a small team of agents peel a matrix apart, one rank-1 slice at a time? We propose an agentic approach to matrix deflation in which a solver Large Language Model (LLM) generates rank-1 Singular Value Decomposition (SVD) updates and a Vision Language Model (VLM) accepts or rejects each update and decides when to stop, eliminating fixed norm thresholds. Solver stability is improved through in-context learning (ICL) and types of row/column permutations that expose visually coherent structure. We evaluate on Digits ($8{\times}8$), CIFAR-10 ($32{\times}32$ grayscale), and synthetic ($16{\times}16$) matrices with and without Gaussian noise. In the synthetic noisy case, where the true construction rank $k$ is known, numerical deflation provides the noise target and our best agentic configuration differs by only $1.75$ RMSE of the target. For Digits and CIFAR-10, targets are defined by deflating until the Frobenius norm reaches $10\%$ of the original. Across all settings, our agent achieves competitive results, suggesting that fully agentic, threshold-free deflation is a viable alternative to classical numerical algorithms.
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"abstract": "Can a small team of agents peel a matrix apart, one rank-1 slice at a time? We propose an agentic approach to matrix deflation in which a solver Large Language Model (LLM) generates rank-1 Singular Value Decomposition (SVD) updates and a Vision Language Model (VLM) accepts or rejects each update and decides when to stop, eliminating fixed norm thresholds. Solver stability is improved through in-context learning (ICL) and types of row/column permutations that expose visually coherent structure. We evaluate on Digits ($8{\\times}8$), CIFAR-10 ($32{\\times}32$ grayscale), and synthetic ($16{\\times}16$) matrices with and without Gaussian noise. In the synthetic noisy case, where the true construction rank $k$ is known, numerical deflation provides the noise target and our best agentic configuration differs by only $1.75$ RMSE of the target. For Digits and CIFAR-10, targets are defined by deflating until the Frobenius norm reaches $10\\%$ of the original. Across all settings, our agent achieves competitive results, suggesting that fully agentic, threshold-free deflation is a viable alternative to classical numerical algorithms.",
"arxiv_id": "2601.08219",
"authors": [
"Paimon Goulart",
"Evangelos E. Papalexakis"
],
"categories": [
"cs.LG"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "A Preliminary Agentic Framework for Matrix Deflation",
"url": "https://arxiv.org/abs/2601.08219",
"version": "v1"
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