[
    {
        "id": "osp-16751",
        "type": "article-journal",
        "title": "Exact Dynamics and Finite-Sample Trajectory Recovery of Linear Recursive Feature Machines",
        "author": [
            {
                "family": "Cheng",
                "given": "Andrew"
            },
            {
                "family": "Kiani",
                "given": "Bobak T."
            },
            {
                "family": "Lu",
                "given": "Yue M."
            },
            {
                "family": "Radhakrishnan",
                "given": "Adityanarayanan"
            }
        ],
        "URL": "https://omanscience.com/en/articles/exact-dynamics-and-finite-sample-trajectory-recovery-of-linear-recursive-feature-machines",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "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."
    }
]