Pith Number

pith:63Y3ZC4X

pith:2026:63Y3ZC4XSXQFYTLGXFRQXSCIXQ

not attested not anchored not stored refs resolved

On Kernel Eigen-alignments of KRR: Reconstruction and Generalization

Daniel Krutz, Ernest Fokoue, Richard Lange, Yang Liu

In kernel ridge regression, generalization performance depends on the alignment of kernel eigenvectors with the target vectors rather than just reconstruction accuracy.

arxiv:2605.15240 v1 · 2026-05-14 · stat.ML · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{63Y3ZC4XSXQFYTLGXFRQXSCIXQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

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.

C2weakest assumption

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 findings).

C3one line summary

Derives a finite-sample generalization bound for KRR by analyzing how perturbations in the kernel matrix affect eigenvector and eigenvalue estimates, concluding that reconstruction error has limited value for high-rank kernels.

References

300 extracted · 300 resolved · 0 Pith anchors

[1] Functional Analysis

[2] On regularization algorithms in learning theory

[3] Approximation theory and harmonic analysis on spheres and balls

[4] Aspects of Harmonic Analysis and Representation Theory

[5] Replica Method for the Machine Learning Theorist

Receipt and verification

First computed	2026-05-20T00:00:47.929077Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6f1bc8b9795e05c4d66b9630bc848bc3a4937a082c398bac259a676507b848f

Aliases

arxiv: 2605.15240 · arxiv_version: 2605.15240v1 · doi: 10.48550/arxiv.2605.15240 · pith_short_12: 63Y3ZC4XSXQF · pith_short_16: 63Y3ZC4XSXQFYTLG · pith_short_8: 63Y3ZC4X

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/63Y3ZC4XSXQFYTLGXFRQXSCIXQ \
  | 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: f6f1bc8b9795e05c4d66b9630bc848bc3a4937a082c398bac259a676507b848f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14b8241e23373358aed43cc9168fec1ad57d35d97bfa9942342c90d2da8ac3d2",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-14T05:46:31Z",
    "title_canon_sha256": "18624d13aadd5a9b7008d8464174ce45aa33879fe9804c98fa68adc4f04f4495"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15240",
    "kind": "arxiv",
    "version": 1
  }
}