Pith Number

pith:3WE7LPRT

pith:2023:3WE7LPRTJJF7PEZ2S25A2IAP3W

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Scaling Relationship on Learning Mathematical Reasoning with Large Language Models

Chang Zhou, Chengpeng Li, Chuanqi Tan, Guanting Dong, Hongyi Yuan, Jingren Zhou, Keming Lu, Zheng Yuan

Pre-training loss predicts LLM mathematical reasoning performance better than parameter count, and rejection sampling fine-tuning lifts LLaMA-7B to 49.3 percent accuracy on GSM8K.

arxiv:2308.01825 v2 · 2023-08-03 · cs.CL

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4 Citations open

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Claims

C1strongest claim

We find that pre-training loss is a better indicator of the model's performance than the model's parameter count. ... we combine rejection samples from multiple models which push LLaMA-7B to an accuracy of 49.3% on GSM8K which outperforms the supervised fine-tuning (SFT) accuracy of 35.9% significantly.

C2weakest assumption

That model-generated reasoning paths can be reliably verified as correct by the same or similar models without introducing systematic errors or false positives in the rejection filter.

C3one line summary

Pre-training loss predicts LLM math reasoning better than parameter count; rejection sampling fine-tuning with diverse paths raises LLaMA-7B accuracy on GSM8K from 35.9% with SFT to 49.3%.

References

93 extracted · 93 resolved · 10 Pith anchors

[2] Emergent Abilities of Large Language Models , author=. Trans. Mach. Learn. Res. , year=

[3] Finetuned Language Models Are Zero-Shot Learners , author=. ArXiv , year=

[4] Chain of Thought Prompting Elicits Reasoning in Large Language Models , author=. ArXiv , year=

[5] The Eleventh International Conference on Learning Representations , year=

[6] Scaling Data-Constrained Language Models , author=. 2023 , eprint= 2023

Formal links

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Cited by

42 papers in Pith

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A Survey of Scaling in Large Language Model Reasoning

Receipt and verification

First computed	2026-05-17T23:39:19.734436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd89f5be334a4bf7933a96ba0d200fdda07c40408dee4eb6a83fba23befb2395

Aliases

arxiv: 2308.01825 · arxiv_version: 2308.01825v2 · doi: 10.48550/arxiv.2308.01825 · pith_short_12: 3WE7LPRTJJF7 · pith_short_16: 3WE7LPRTJJF7PEZ2 · pith_short_8: 3WE7LPRT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3WE7LPRTJJF7PEZ2S25A2IAP3W \
  | 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: dd89f5be334a4bf7933a96ba0d200fdda07c40408dee4eb6a83fba23befb2395

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2023-08-03T15:34:01Z",
    "title_canon_sha256": "c762f07c2dee1db9acd2261bf247e9a3ef1c3108732525103ccfca0718b6a249"
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