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.
{
"annotation_id": "cefeeb34-4b6a-40df-b6f8-8d4993e7f585",
"date_created": "2026-02-17T05:53:15.112000Z",
"date_modified": "2026-02-17T05:53:15.112000Z",
"file_hash": "06bfd0e5bc281284f75d1301995e108a3ff096bb3a4d6583ce6a4fcc1050f4a0",
"private": false,
"record": {
"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"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "214b08a2-fcbc-4c1e-838d-ffa98cb3655f",
"id": "arXiv Dataset",
"type": "Model",
"variant": "snapshot-2026-01-17",
"version": "0.1.0"
},
"user_id": 1000002
}