{"paper":{"title":"On Kernel Eigen-alignments of KRR: Reconstruction and Generalization","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"In kernel ridge regression, generalization performance depends on the alignment of kernel eigenvectors with the target vectors rather than just reconstruction accuracy.","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Daniel Krutz, Ernest Fokoue, Richard Lange, Yang Liu","submitted_at":"2026-05-14T05:46:31Z","abstract_excerpt":"This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalization in learning problems. We establish a direct connection between generalization performance in kernel methods and the estimation of eigenvectors and eigenvalues of matrices, offering a more intuitive understanding compared to prior work with minimal assumptions. We also show that, since the prediction task in KRR is essentially the weighted sum of eigenvectors/singular vectors, by analyzing how much error can be caused by perturbations to the kernel matri"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we establish a generalization bound from an eigenvalues/eigenvectors estimation perspective, showing that strong generalization requires increasing eigenvector alignment, eigenvalue magnitude, or gaps between consecutive eigenvalues.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis relies on finite-sample settings and the generalization error arising from a suboptimal finite training set, with the claim that near-zero reconstruction error is trivially obtained for high-rank kernels (abstract paragraph on 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