{"paper":{"title":"Large Dimensional Kernel Ridge Regression: Extending to Product Kernels","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A broad family of large-dimensional product kernels recovers the same saturation effects, minimax rates, and multiple-descent behavior previously known only for inner-product kernels on the sphere.","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Qian Lin, Yang Zhou, Yicheng Li, Yuqian Cheng","submitted_at":"2026-05-14T08:08:09Z","abstract_excerpt":"Recent studies have reported $\\textit{saturation effects}$ and $\\textit{multiple descent behavior}$ in large dimensional kernel ridge regression (KRR). However, these findings are predominantly derived under restrictive settings, such as inner product kernels on sphere or strong eigenfunction assumptions like hypercontractivity. Whether such behaviors hold for other kernels remains an open question. In this paper, we establish a broad, new family of large dimensional kernels and derive the corresponding convergence rates of the generalization error. As a result, we recover key phenomena previo"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we establish a broad, new family of large dimensional kernels and derive the corresponding convergence rates of the generalization error. As a result, we recover key phenomena previously associated with inner product kernels on sphere, including: i) the minimax optimality when the source condition s≤1; ii) the saturation effect when s>1; iii) a periodic plateau phenomenon in the convergence rate and a multiple-descent behavior with respect to the sample size n.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The new kernels belong to the defined broad family and satisfy the high-dimensional regime conditions that allow the eigenfunction and source-condition analysis to go through; without the full text these conditions remain unspecified.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A broad family of large-dimensional product kernels recovers the same saturation effects, minimax rates, and multiple-descent behavior previously known only for inner-product kernels on the sphere.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c32c1d2ab8682e60515a2e3a7434a32968a62019acfa81855499817916df3ee3"},"source":{"id":"2605.14524","kind":"arxiv","version":1},"verdict":{"id":"b3ed1ac3-52c8-45e4-8e41-7729c6fef7df","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:40:23.824960Z","strongest_claim":"we establish a broad, new family of large dimensional kernels and derive the corresponding convergence rates of the generalization error. As a result, we recover key phenomena previously associated with inner product kernels on sphere, including: i) the minimax optimality when the source condition s≤1; ii) the saturation effect when s>1; iii) a periodic plateau phenomenon in the convergence rate and a multiple-descent behavior with respect to the sample size n.","one_line_summary":"Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The new kernels belong to the defined broad family and satisfy the high-dimensional regime conditions that allow the eigenfunction and source-condition analysis to go through; without the full text these conditions remain unspecified.","pith_extraction_headline":"A broad family of large-dimensional product kernels recovers the same saturation effects, minimax rates, and multiple-descent behavior previously known only for inner-product kernels on the sphere."},"references":{"count":149,"sample":[{"doi":"","year":null,"title":"Nonparametric regression estimation using penalized least squares , author=. 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