{"slug": "exact-dynamics-and-finite-sample-trajectory-recovery-of-linear-recursive-feature", "title": "Exact Dynamics and Finite-Sample Trajectory Recovery of Linear Recursive Feature Machines", "summary": "A new arXiv paper, arXiv:2610.09196v1, extends the known connection between linear recursive feature machines (RFMs) and iteratively reweighted least squares from the interpolating setting to ridge-regularized multi-output regression with noise. The authors prove that for n samples the learned feature matrix stays close to its infinite-data ideal at every iteration, with the feature-matrix error decaying as O(√(d/n)) with high probability, where d is the dimension of the low-rank teacher matrix. Experiments on real-world text and single-cell gene-expression data illustrate the features learned by the linear model.", "body_md": "arXiv:2610.09196v1 Announce Type: new \nAbstract: Recursive feature machines (RFMs) learn representations of data by alternating between fitting a predictor to a dataset and updating features of that predictor using the average gradient outer product (AGOP). Connections between AGOPs and feature learning in neural networks motivate linear RFMs as a simple setting for analyzing how representations evolve during training. Here, we study the dynamics and statistics of linear RFM in noisy multi-output regression with isotropic sub-Gaussian input data and targets generated by a low-rank teacher matrix of dimension $d$. We extend the known connection between linear RFM and iteratively reweighted least squares from the interpolating setting to ridge-regularized multi-output regression with noise. We show that the learned feature matrix remains close to its infinite-data ideal counterpart at every iteration. Namely, for $n$ samples, we show the error in the feature matrix decays as $O(\\sqrt{d/n})$ with high probability. Experiments on real-world text and single-cell gene-expression data illustrate the features learned by this simple linear model.", "url": "https://wpnews.pro/news/exact-dynamics-and-finite-sample-trajectory-recovery-of-linear-recursive-feature", "canonical_source": "https://www.machinebrief.com/news/exact-dynamics-and-finite-sample-trajectory-recovery-of-line-dx0o", "published_at": "2026-10-08 04:00:00+00:00", "updated_at": "2026-10-08 05:17:06.341190+00:00", "lang": "en", "topics": ["machine-learning", "ai-research", "neural-networks"], "entities": ["arXiv", "Recursive feature machines", "average gradient outer product", "iteratively reweighted least squares"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/exact-dynamics-and-finite-sample-trajectory-recovery-of-linear-recursive-feature", "markdown": "https://wpnews.pro/news/exact-dynamics-and-finite-sample-trajectory-recovery-of-linear-recursive-feature.md", "text": "https://wpnews.pro/news/exact-dynamics-and-finite-sample-trajectory-recovery-of-linear-recursive-feature.txt", "jsonld": "https://wpnews.pro/news/exact-dynamics-and-finite-sample-trajectory-recovery-of-linear-recursive-feature.jsonld"}}