Pith Number

pith:FBNZSVAA

pith:2025:FBNZSVAADCMHIAINYGJFFYTTUH

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Reasoning with Sampling: Your Base Model is Smarter Than You Think

Aayush Karan, Yilun Du

A simple iterative sampling algorithm using only a base model's likelihoods can elicit reasoning performance that nearly matches or exceeds reinforcement learning on tasks like math and coding.

arxiv:2510.14901 v1 · 2025-10-16 · cs.LG · cs.AI · cs.CL

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\pithnumber{FBNZSVAADCMHIAINYGJFFYTTUH}

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2 Internet Archive

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

Over different base models, we show that our algorithm offers substantial boosts in reasoning that nearly match and even outperform those from RL on a wide variety of single-shot tasks, including MATH500, HumanEval, and GPQA.

C2weakest assumption

That the base model's likelihoods contain sufficient signal to be iteratively reshaped into higher-quality reasoning trajectories via a simple MCMC-style sampler without any training or external verifier.

C3one line summary

An MCMC-inspired iterative sampler applied to base LLMs elicits reasoning performance that nearly matches or exceeds RL-posttrained models on MATH500, HumanEval, and GPQA while preserving output diversity.

Formal links

2 machine-checked theorem links

Cited by

24 papers in Pith

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Beyond Mode Collapse: Distribution Matching for Diverse Reasoning

Receipt and verification

First computed	2026-05-17T23:38:15.272016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

285b995400189874010dc19252e273a1c0d274ea513fd36e9abf8f9ffc69d84e

Aliases

arxiv: 2510.14901 · arxiv_version: 2510.14901v1 · doi: 10.48550/arxiv.2510.14901 · pith_short_12: FBNZSVAADCMH · pith_short_16: FBNZSVAADCMHIAIN · pith_short_8: FBNZSVAA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FBNZSVAADCMHIAINYGJFFYTTUH \
  | 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: 285b995400189874010dc19252e273a1c0d274ea513fd36e9abf8f9ffc69d84e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ecb3b6cb04907b232cb999bb15cf3e1b01ea1ad94e7c536f7256b8d3dc1ee33",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-10-16T17:18:11Z",
    "title_canon_sha256": "cea8936658e1fb416995205bc8324e264599d38a3883317244765200d3346c24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.14901",
    "kind": "arxiv",
    "version": 1
  }
}