Pith Number

pith:5FJPKEKX

pith:2026:5FJPKEKXATQWBPTM53WR4F5EZ3

not attested not anchored not stored refs pending

Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimization

Chiheb Yaakoubi, Cosme Louart, Malik Tiomoko, Zhenyu Liao

In high-dimensional ERM with non-Gaussian data, the estimator's projection on a test point follows the convolution of a generally non-Gaussian distribution with an independent Gaussian whose variance is set by the trace of the estimator's 2

arxiv:2604.03146 v2 · 2026-04-03 · stat.ML · cs.LG

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\usepackage{pith}
\pithnumber{5FJPKEKXATQWBPTM53WR4F5EZ3}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

under a concentration assumption on the data matrix and standard regularity conditions on the loss and regularizer, we show that for a test covariate x independent of the training data, the projection θ̂⊤x approximately follows the convolution of the (generally non-Gaussian) distribution of μ_θ̂⊤x with an independent centered Gaussian variable of variance Tr(C_θ̂ E[xx⊤])

C2weakest assumption

the heuristic extension of the Convex Gaussian Min-Max Theorem to non-Gaussian settings under a concentration assumption on the data matrix

C3one line summary

In high-dimensional convex ERM with non-Gaussian data, the projection of the estimator onto a test covariate asymptotically follows the convolution of a generally non-Gaussian term with an independent centered Gaussian whose variance is the trace of the estimator covariance times the data second-mom

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

$\alpha$-TCAV: A Unified Framework for Testing with Concept Activation Vectors

Receipt and verification

First computed	2026-06-08T01:04:03.544438Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e952f5115704e160be6ceeed1e17a4ceec0c7ee1858c2b9372d0690375146bf3

Aliases

arxiv: 2604.03146 · arxiv_version: 2604.03146v2 · doi: 10.48550/arxiv.2604.03146 · pith_short_12: 5FJPKEKXATQW · pith_short_16: 5FJPKEKXATQWBPTM · pith_short_8: 5FJPKEKX

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5FJPKEKXATQWBPTM53WR4F5EZ3 \
  | 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: e952f5115704e160be6ceeed1e17a4ceec0c7ee1858c2b9372d0690375146bf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ecc7294798a8e729c1c0b7e0d087d728c415c1ba47a41e1c08afe86894a0d55",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-04-03T16:07:02Z",
    "title_canon_sha256": "0aead56dd7055962032b37ae151118c4662621e6e710fc613814556c293780eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.03146",
    "kind": "arxiv",
    "version": 2
  }
}