A Preliminary Agentic Framework for Matrix Deflation
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arXiv
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| Format: | Preprint |
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2026
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| author | Goulart, Paimon Papalexakis, Evangelos E. |
| author_facet | Goulart, Paimon Papalexakis, Evangelos E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08219 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Preliminary Agentic Framework for Matrix Deflation Goulart, Paimon Papalexakis, Evangelos E. Machine Learning 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. |
| title | A Preliminary Agentic Framework for Matrix Deflation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.08219 |