用智能体协作逐次剥离矩阵，无需预设阈值，效果接近传统算法。
A Preliminary Agentic Framework for Matrix Deflation
- 由LLM生成秩1更新，VLM判断是否接受并决定停止时机。
- 在合成噪声数据上，误差仅比理想目标高1.75 RMSE。
- 适合对可解释性与自适应性有要求的矩阵分解场景。
能否让一组智能体像剥洋葱一样，逐次剥离矩阵的秩-1成分？我们提出一种代理式矩阵去噪方法：由大语言模型（LLM）生成秩-1奇异值分解（SVD）更新，视觉语言模型（VLM）评估并决定是否采纳，同时自主决定终止时机，避免使用固定范数阈值。通过上下文学习（ICL）和行/列置换策略提升求解稳定性，以暴露视觉结构。我们在数字（8×8）、CIFAR-10（32×32灰度）及合成（16×16）矩阵上进行测试，含高斯噪声。在已知真实秩k的合成噪声情形下，数值去噪提供噪声目标，最优代理配置仅比目标高1.75 RMSE。对于Digits与CIFAR-10，目标为去噪至原始弗罗贝尼乌斯范数的10%。各场景下性能均具竞争力，表明完全自主、无阈值的去噪是经典数值算法的可行替代方案。
原文摘要 · Abstract (English)
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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