Pith Number

pith:5CYHBLTG

pith:2026:5CYHBLTGNBUTKIN4Q5JWUHMJOQ

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Online Learnability of Chain-of-Thought Verifiers: Soundness and Completeness Trade-offs

Avrim Blum, Dravyansh Sharma, Kiriaki Fragkia, Maria-Florina Balcan, Zhiyuan Li

Extensions of the Littlestone dimension tightly characterize the online mistake bounds for learning chain-of-thought verifiers under asymmetric soundness and completeness costs.

arxiv:2603.03538 v3 · 2026-03-03 · cs.LG

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\usepackage{pith}
\pithnumber{5CYHBLTGNBUTKIN4Q5JWUHMJOQ}

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Record completeness

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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

We introduce novel extensions of the Littlestone dimension which tightly characterize the mistake bounds for learning a verifier in the realizable setting. We provide optimal algorithms for finding the Pareto-frontier (the smallest total number of mistakes given a budget of soundness mistakes) as well as for minimizing a linear combination of asymmetric costs.

C2weakest assumption

With the mild assumption that one of the generators can generate the next reasoning step correctly with some minimal probability, we show how to learn a strong generator with small error and abstention rates.

C3one line summary

The paper shows that chain-of-thought verifiers are online learnable via novel extensions of the Littlestone dimension that characterize soundness and completeness mistake bounds, with algorithms for Pareto-optimal trade-offs and boosting weak generators under a mild assumption.

Receipt and verification

First computed	2026-05-20T00:02:10.378087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8b070ae6668693521bc87536a1d89743b621bc0ce393524b393dc0a76890452

Aliases

arxiv: 2603.03538 · arxiv_version: 2603.03538v3 · doi: 10.48550/arxiv.2603.03538 · pith_short_12: 5CYHBLTGNBUT · pith_short_16: 5CYHBLTGNBUTKIN4 · pith_short_8: 5CYHBLTG

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/5CYHBLTGNBUTKIN4Q5JWUHMJOQ \
  | 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: e8b070ae6668693521bc87536a1d89743b621bc0ce393524b393dc0a76890452

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9534669cf96ec8e3ec35b9effd02fa96eebd71a1e520fbf9f63a991e5469dc41",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-03T21:50:14Z",
    "title_canon_sha256": "9f081ca9c91bfcdd4ede8dfe92fe1b6f20dbf71aa4aceb8593b1f20270a0d9a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.03538",
    "kind": "arxiv",
    "version": 3
  }
}