# A Preliminary Agentic Framework for Matrix Deflation

arXiv: https://arxiv.org/abs/2601.08219 · HTML: https://mlsanity.com/paper/2601.08219/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal and embodied agents, one of 16 directions in LLM agents and tool use.
- Builds on 3 of its 8 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Placed in

- LLM agents and tool use / [Multimodal and embodied agents](https://mlsanity.com/agents/multimodal-and-embodied-agents/)

## Builds on (most cited first, 3 of 3)

- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)

## Abstract (arXiv)

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 (8×8), CIFAR-10 (32×32 grayscale), and synthetic (16×16) 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.