A Preliminary Agentic Framework for Matrix Deflation

• URL: http://arxiv.org/abs/2601.08219v1
• Date: Tue, 06 Jan 2026 23:59:18 GMT
• Title: A Preliminary Agentic Framework for Matrix Deflation
• Abstract summary: We propose an agentic approach to matrix deflation in which a solver generates rank-1 updates and decides when to stop.<n>We evaluate on Digits ($8times8$), CIFAR-10 ($32times32$ grayscale), and synthetic ($16times16$) matrices with and without Gaussian noise.<n>Across all settings, our agent achieves competitive results, suggesting that fully agentic, threshold-free deflation is a viable alternative to classical numerical algorithms.
• Score: 2.6140509675507384
• 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.

Related papers

• Hidden-State Privacy Has an Empty Middle [51.56484100374058]
  We prove a complementary Fisher-ball lower bound: every full-rank Gaussian release at $O(1)$ Fisher utility admits a direction whose Mahalanobis signal grows linearly in hidden width.<n>A split-memory transformer trained from scratch reaches $G_mathrmMah in [20, 33]$ at 90M and maintains a $6$--$24times$ advantage over same-budget GPT baselines from 30M to 1B at a fixed-token language loss penalty.
  arXiv  Detail & Related papers  (2026-05-21T20:12:09Z)
• Beyond Accuracy: A Unified Random Matrix Theory Diagnostic Framework for Crash Classification Models [6.908972852063454]
  We introduce a diagnostic framework grounded in Random Matrix Theory (RMT) and Heavy-Tailed Self-Regularization (HTSR)<n>We evaluate nine model families on two Iowa DOT crash classification tasks (173,512 and 371,062 records respectively)<n>We find that the power-law exponent $$ provides a structural quality signal: well-regularized models consistently yield $$ within $[2, 4]$ (mean $2.87 pm 0.34$)<n>We propose an $$-based early stopping criterion and a spectral model selection protocol, and validate both against cross-validated F
  arXiv  Detail & Related papers  (2026-02-23T05:42:54Z)
• Optimal Unconstrained Self-Distillation in Ridge Regression: Strict Improvements, Precise Asymptotics, and One-Shot Tuning [61.07540493350384]
  Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth and the teacher's own predictions.<n>We show that for any prediction risk, the optimally mixed student improves upon the ridge teacher for every regularization level.<n>We propose a consistent one-shot tuning method to estimate $star$ without grid search, sample splitting, or refitting.
  arXiv  Detail & Related papers  (2026-02-19T17:21:15Z)
• Spectral Sentinel: Scalable Byzantine-Robust Decentralized Federated Learning via Sketched Random Matrix Theory on Blockchain [0.0]
  Byzantine clients poison gradients under heterogeneous (Non-IID) data.<n>We propose Spectral Sentinel, a Byzantine detection and aggregation framework.<n>We implement the full system with blockchain integration on Polygon networks.
  arXiv  Detail & Related papers  (2025-12-14T09:43:03Z)
• Evolution Strategies at the Hyperscale [57.75314521465674]
  We introduce EGGROLL, an evolution strategies (ES) algorithm designed to scale backprop-free optimization to large population sizes.<n>ES is a set of powerful blackbox optimisation methods that can handle non-differentiable or noisy objectives.<n>EGGROLL overcomes these bottlenecks by generating random matrices $Ain mathbbRmtimes r, Bin mathbbRntimes r$ with $rll min(m,n)$ to form a low-rank matrix perturbation $A Btop$
  arXiv  Detail & Related papers  (2025-11-20T18:56:05Z)
• FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA [68.44043212834204]
  Low-Rank Adaptation (LoRA) is widely used for efficient fine-tuning of language models in learning (FL)<n>Low-Rank Adaptation (LoRA) is widely used for efficient fine-tuning of language models in learning (FL)
  arXiv  Detail & Related papers  (2025-05-19T07:32:56Z)
• Near-Optimal Online Learning for Multi-Agent Submodular Coordination: Tight Approximation and Communication Efficiency [52.60557300927007]
  We present a $textbfMA-OSMA$ algorithm to transfer the discrete submodular problem into a continuous optimization.<n>We also introduce a projection-free $textbfMA-OSEA$ algorithm, which effectively utilizes the KL divergence by mixing a uniform distribution.<n>Our algorithms significantly improve the $(frac11+c)$-approximation provided by the state-of-the-art OSG algorithm.
  arXiv  Detail & Related papers  (2025-02-07T15:57:56Z)
• Fair Submodular Cover [18.37610521373708]
  We present the study of Fair Submodular Cover (FSC), where given a ground set $U$, a monotone submodular function $f:2UtomathbbR_ge 0$, a threshold $tau$. We first introduce discrete algorithms for FSC that achieve a bicriteria approximation ratio of $(frac1epsilon, 1-O(epsilon))$. We then present a continuous algorithm that achieves a $(frac1epsilon, 1-O(epsilon))$-
  arXiv  Detail & Related papers  (2024-07-05T18:37:09Z)
• Refined Sample Complexity for Markov Games with Independent Linear Function Approximation [49.5660193419984]
  Markov Games (MG) is an important model for Multi-Agent Reinforcement Learning (MARL) This paper first refines the AVLPR framework by Wang et al. (2023), with an insight of designing pessimistic estimation of the sub-optimality gap. We give the first algorithm that tackles the curse of multi-agents, attains the optimal $O(T-1/2) convergence rate, and avoids $textpoly(A_max)$ dependency simultaneously.
  arXiv  Detail & Related papers  (2024-02-11T01:51:15Z)
• Contextual Combinatorial Bandits with Probabilistically Triggered Arms [55.9237004478033]
  We study contextual bandits with probabilistically triggered arms (C$2$MAB-T) under a variety of smoothness conditions. Under the triggering modulated (TPM) condition, we devise the C$2$-UC-T algorithm and derive a regret bound $tildeO(dsqrtT)$.
  arXiv  Detail & Related papers  (2023-03-30T02:51:00Z)
• Majorization-minimization for Sparse Nonnegative Matrix Factorization with the $\beta$-divergence [2.3787352248749376]
  It is well known that the norm of the other factor (the dictionary matrix) needs to be controlled in order to avoid an ill-posed formulation. Standard practice consists in constraining the columns of the dictionary to have unit norm, which leads to a nontrivial optimization problem. We derive block-descent majorization-minimization algorithms that result in simple multiplicative updates for either $ell_1$-regularization or the more "aggressive" log-regularization.
  arXiv  Detail & Related papers  (2022-07-13T16:09:29Z)
• Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimation [58.24280149662003]
  We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. We develop new algorithms for list-decodable mean estimation, achieving nearly-optimal statistical guarantees.
  arXiv  Detail & Related papers  (2021-06-16T03:34:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.