{"paper":{"title":"Scaling Relationship on Learning Mathematical Reasoning with Large Language Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"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.","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Chang Zhou, Chengpeng Li, Chuanqi Tan, Guanting Dong, Hongyi Yuan, Jingren Zhou, Keming Lu, Zheng Yuan","submitted_at":"2023-08-03T15:34:01Z","abstract_excerpt":"Mathematical reasoning is a challenging task for large language models (LLMs), while the scaling relationship of it with respect to LLM capacity is under-explored. In this paper, we investigate how the pre-training loss, supervised data amount, and augmented data amount influence the reasoning performances of a supervised LLM. We find that pre-training loss is a better indicator of the model's performance than the model's parameter count. We apply supervised fine-tuning (SFT) with different amounts of supervised data and empirically find a log-linear relation between data amount and model perf"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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%.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"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.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b9885aca34cf9dbad23e33ae094b469737b335d61fd858b088cc95993e59f052"},"source":{"id":"2308.01825","kind":"arxiv","version":2},"verdict":{"id":"24aeb9b5-30b3-4909-ae7e-b9f017abcce0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T00:16:47.344407Z","strongest_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.","one_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%.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"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."},"references":{"count":93,"sample":[{"doi":"","year":null,"title":"Emergent Abilities of Large Language Models , author=. 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