Pith Number

pith:RPHRCEJL

pith:2026:RPHRCEJLBY3GAW7NH2G7OJ2XDQ

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Average Gradient Outer Product in kernel regression provably recovers the central subspace for multi-index models

Damek Davis, Dmitriy Drusvyatskiy, Libin Zhu, Maryam Fazel

The average gradient outer product from kernel ridge regression recovers the central subspace of multi-index models in sample regimes too small for accurate prediction.

arxiv:2605.15082 v1 · 2026-05-14 · stat.ML · cs.LG · math.ST · stat.TH

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Claims

C1strongest claim

the top r-dimensional eigenspace of AGOP provably recovers the central subspace, even in regimes when the prediction error remains large. Specifically, if the target function f* has degree p*, ... subspace recovery occurs in the much lower sample regime n ≍ d^{p+δ} for any δ ∈ (0,1).

C2weakest assumption

a low degree p component of f* already carries all relevant directions for prediction, together with unspecified 'reasonable assumptions' on the kernel and the multi-index structure (abstract only).

C3one line summary

For multi-index polynomials, the top r eigenspace of the AGOP matrix from KRR recovers the central subspace at sample complexity n ~ d^{p+δ} where p is the degree of the informative component.

References

64 extracted · 64 resolved · 0 Pith anchors

[1] Sgd learning on neural networks: leap complexity and saddle-to-saddle dynamics 2023

[2] The merged-staircase property: a necessary and nearly sufficient condition for sgd learning of sparse functions on two-layer neural networks 2022

[3] Classical orthogonal polynomials

[4] Springer. 2006, pp. 36–62 2006

[5] Online learning and information exponents: On the importance of batch size, and time/complexity tradeoffs 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T21:40:25.977506Z
Last reissued	2026-05-17T21:57:19.284907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

8bcf11112b0e36605bed3e8df727571c35cd04e23f6389a3e1f08a728a002ff2

Aliases

arxiv: 2605.15082 · arxiv_version: 2605.15082v1 · pith_short_12: RPHRCEJLBY3G · pith_short_16: RPHRCEJLBY3GAW7N · pith_short_8: RPHRCEJL

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/RPHRCEJLBY3GAW7NH2G7OJ2XDQ \
  | 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: 8bcf11112b0e36605bed3e8df727571c35cd04e23f6389a3e1f08a728a002ff2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7e660042d30ada8fb1589a6ead7239b370037ac9f2b5b5f55d84fde3c2260bc",
    "cross_cats_sorted": [
      "cs.LG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-14T17:05:30Z",
    "title_canon_sha256": "45e919745effab06b7d8d5c9d9a01da6c72fc48e270ca2edebcc81d9bce79670"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15082",
    "kind": "arxiv",
    "version": 1
  }
}