Pith Number

pith:CPXHTH76

pith:2026:CPXHTH763SXNVGOXQ4RFQLNOS4

not attested not anchored not stored refs resolved

Large Dimensional Kernel Ridge Regression: Extending to Product Kernels

Qian Lin, Yang Zhou, Yicheng Li, Yuqian Cheng

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.

arxiv:2605.14524 v1 · 2026-05-14 · stat.ML · cs.LG

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

149 extracted · 149 resolved · 1 Pith anchors

[1] Nonparametric regression estimation using penalized least squares , author=. IEEE Trans. Inf. Theory , year=

[2] Bulletin of the American Mathematical Society , year=

[3] Annual Conference Computational Learning Theory , year=

[4] 2020 , journal = 2020

[5] 2017 , journal = 2017

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:06.032833Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13ee799ffedcaeda99d78722582dae972e29fb94d35bca4d4d40f53b334878a2

Aliases

arxiv: 2605.14524 · arxiv_version: 2605.14524v1 · doi: 10.48550/arxiv.2605.14524 · pith_short_12: CPXHTH763SXN · pith_short_16: CPXHTH763SXNVGOX · pith_short_8: CPXHTH76

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CPXHTH763SXNVGOXQ4RFQLNOS4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 13ee799ffedcaeda99d78722582dae972e29fb94d35bca4d4d40f53b334878a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b19808f4825ce4a24e5546bc279fe39dca0cbe93ae54a3a25ca924eac558aa6",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-14T08:08:09Z",
    "title_canon_sha256": "2e1b53b0a9004e340eb42270fb7bbcc0c0c069ef6d962f61974378c83ade1b1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14524",
    "kind": "arxiv",
    "version": 1
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}