A Preliminary Agentic Framework for Matrix Deflation

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 $10\mathrm{\%}$ 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.