Pith Number

pith:DFAT3OH2

pith:2026:DFAT3OH26N7LOJDOLD62I6SFPW

not attested not anchored not stored refs resolved

Strategic PAC Learnability via Geometric Definability

Alexander Shlimovich, Elizaveta Nesterova, Nir Rosenfeld, Shay Moran, Yuval Filmus

A geometric definability assumption ensures strategic classification remains PAC learnable with sample complexity governed by formula complexity.

arxiv:2605.13426 v2 · 2026-05-13 · cs.LG · math.AG

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2 Internet Archive

3 Author claim open · sign in to claim

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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 the geometric definability assumption, learnability is preserved, with sample complexity controlled by the complexity of the defining formulas.

C2weakest assumption

Both the hypothesis class and the cost-induced neighborhood relation can be defined by first-order formulas over R_exp.

C3one line summary

Strategic PAC learnability is preserved when hypothesis classes and cost-induced neighborhoods are first-order definable over the reals with exponentiation, controlling sample complexity by formula complexity.

References

58 extracted · 58 resolved · 0 Pith anchors

[1] Honest Compressions and Their Application to Compression Schemes , booktitle = 2013

[2] CoRR , volume = 2023 · doi:10.48550/arxiv.2312.00379

[3] Sign rank versus 2016

[4] Limitations of Learning Via Embeddings in Euclidean Half Spaces , journal = 2002

[5] Talagrand , title =

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:47.262227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19413db8faf37eb7246e58fda47a457db9ea63f1b0d25584758e925c2bd341e2

Aliases

arxiv: 2605.13426 · arxiv_version: 2605.13426v2 · doi: 10.48550/arxiv.2605.13426 · pith_short_12: DFAT3OH26N7L · pith_short_16: DFAT3OH26N7LOJDO · pith_short_8: DFAT3OH2

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DFAT3OH26N7LOJDOLD62I6SFPW \
  | 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: 19413db8faf37eb7246e58fda47a457db9ea63f1b0d25584758e925c2bd341e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dff7a321cffcf6cfa146d4ac8313ad1b62769401446e2a186df49863503cd74",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T12:21:56Z",
    "title_canon_sha256": "8177de83887bb4d23e913e3b034f5a820e082352e521b45718ce1c5995d603db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13426",
    "kind": "arxiv",
    "version": 2
  }
}