{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3WE7LPRTJJF7PEZ2S25A2IAP3W","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1b9def5d64481b95ede3a3744d495f79937b5bf1849f35e0103828ced38257f7","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"},"schema_version":"1.0","source":{"id":"2308.01825","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.01825","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"2308.01825v2","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.01825","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"3WE7LPRTJJF7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"3WE7LPRTJJF7PEZ2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"3WE7LPRT","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:05c8d0074d57a1962dd0bd40aacd3e7e2078d9b3d1bb0b3184e43d48a5e1cda5","target":"graph","created_at":"2026-05-17T23:39:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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%."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","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."}],"snapshot_sha256":"b9885aca34cf9dbad23e33ae094b469737b335d61fd858b088cc95993e59f052"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"3953eebc194b1a96dee1e12ae9ba23642cdcb93447eb1a14fa22dd78f9d447e4"},"paper":{"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","authors_text":"Chang Zhou, Chengpeng Li, Chuanqi Tan, Guanting Dong, Hongyi Yuan, Jingren Zhou, Keming Lu, Zheng Yuan","cross_cats":[],"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.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2023-08-03T15:34:01Z","title":"Scaling Relationship on Learning Mathematical Reasoning with Large Language Models"},"references":{"count":93,"internal_anchors":10,"resolved_work":93,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Emergent Abilities of Large Language Models , author=. Trans. Mach. Learn. Res. , year=","work_id":"e7481617-8603-477e-bfea-e36897ba0381","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Finetuned Language Models Are Zero-Shot Learners , author=. ArXiv , year=","work_id":"ca4b85c3-127f-42a0-83c7-263974e3a2fd","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Chain of Thought Prompting Elicits Reasoning in Large Language Models , author=. ArXiv , year=","work_id":"75eacb63-2829-4757-8923-44fbe8ccdd56","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"The Eleventh International Conference on Learning Representations , year=","work_id":"c6ff7dc0-3e26-4410-9185-4ed25c298501","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":6,"title":"Scaling Data-Constrained Language Models , author=. 2023 , eprint=","work_id":"3d681b07-4c9c-441c-b5f3-8efb06f3656a","year":2023}],"snapshot_sha256":"3d1e11b8e1561056585bf6cb1192ba3b63516f553cc7ba8c0cdda9e5ba2e0afc"},"source":{"id":"2308.01825","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-15T00:16:47.344407Z","id":"24aeb9b5-30b3-4909-ae7e-b9f017abcce0","model_set":{"reader":"grok-4.3"},"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","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.","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.","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."}},"verdict_id":"24aeb9b5-30b3-4909-ae7e-b9f017abcce0"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b3f9c3f138bd6733df785ca60baf1b5f9dcd317a085b6b5b3634063a1ff52f00","target":"record","created_at":"2026-05-17T23:39:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1b9def5d64481b95ede3a3744d495f79937b5bf1849f35e0103828ced38257f7","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"},"schema_version":"1.0","source":{"id":"2308.01825","kind":"arxiv","version":2}},"canonical_sha256":"dd89f5be334a4bf7933a96ba0d200fdda07c40408dee4eb6a83fba23befb2395","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd89f5be334a4bf7933a96ba0d200fdda07c40408dee4eb6a83fba23befb2395","first_computed_at":"2026-05-17T23:39:19.734436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:19.734436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZryLUoUruXgyHhU8xmXanqFoQB635o5hASz0xcMjzhyPoS1++C0XV/cDs3iPWQB7YXzt6Zk20d1wLggSR5tRAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:19.735122Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.01825","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3f9c3f138bd6733df785ca60baf1b5f9dcd317a085b6b5b3634063a1ff52f00","sha256:05c8d0074d57a1962dd0bd40aacd3e7e2078d9b3d1bb0b3184e43d48a5e1cda5"],"state_sha256":"01fab06f84c14c571e32a0f1665bb3348f7f9212a1d72f4432fd7adf140056bd"}