{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ZLDIFVCE5L7K3T5DLSWSPHGKPY","short_pith_number":"pith:ZLDIFVCE","schema_version":"1.0","canonical_sha256":"cac682d444eafeadcfa35cad279cca7e0fd9d97d688f4665766cae59e4018d90","source":{"kind":"arxiv","id":"2501.04519","version":1},"attestation_state":"computed","paper":{"title":"rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Small language models reach expert math reasoning by evolving their own search and evaluation processes over repeated rounds.","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Fan Yang, Li Lyna Zhang, Mao Yang, Ning Shang, Xinyu Guan, Yifei Liu, Yi Zhu, Youran Sun","submitted_at":"2025-01-08T14:12:57Z","abstract_excerpt":"We present rStar-Math to demonstrate that small language models (SLMs) can rival or even surpass the math reasoning capability of OpenAI o1, without distillation from superior models. rStar-Math achieves this by exercising \"deep thinking\" through Monte Carlo Tree Search (MCTS), where a math policy SLM performs test-time search guided by an SLM-based process reward model. rStar-Math introduces three innovations to tackle the challenges in training the two SLMs: (1) a novel code-augmented CoT data sythesis method, which performs extensive MCTS rollouts to generate step-by-step verified reasoning"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":true},"canonical_record":{"source":{"id":"2501.04519","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2025-01-08T14:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"2fbcdee4b0e850ff9f844008d3b960df9e2f2ad5a5c20fa8623f24b32d173b53","abstract_canon_sha256":"82ab060f96a357f36dba7338071dab1efb58065f8b576e613279dabaa82e228f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:38:15.095688Z","signature_b64":"OVZ1c/0i22uabrtoWZqAjY795S0Nthqvka5U16yygAm0cNGcfO9aEebY0OXVfNsfpaER8bQRR5SgH7VxUxYCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cac682d444eafeadcfa35cad279cca7e0fd9d97d688f4665766cae59e4018d90","last_reissued_at":"2026-05-17T23:38:15.094996Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:38:15.094996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Small language models reach expert math reasoning by evolving their own search and evaluation processes over repeated rounds.","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Fan Yang, Li Lyna Zhang, Mao Yang, Ning Shang, Xinyu Guan, Yifei Liu, Yi Zhu, Youran Sun","submitted_at":"2025-01-08T14:12:57Z","abstract_excerpt":"We present rStar-Math to demonstrate that small language models (SLMs) can rival or even surpass the math reasoning capability of OpenAI o1, without distillation from superior models. rStar-Math achieves this by exercising \"deep thinking\" through Monte Carlo Tree Search (MCTS), where a math policy SLM performs test-time search guided by an SLM-based process reward model. rStar-Math introduces three innovations to tackle the challenges in training the two SLMs: (1) a novel code-augmented CoT data sythesis method, which performs extensive MCTS rollouts to generate step-by-step verified reasoning"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Through 4 rounds of self-evolution with millions of synthesized solutions for 747k math problems, rStar-Math boosts SLMs' math reasoning to state-of-the-art levels. On the MATH benchmark, it improves Qwen2.5-Math-7B from 58.8% to 90.0% and Phi3-mini-3.8B from 41.4% to 86.4%, surpassing o1-preview by +4.5% and +0.9%.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The process preference model trained on self-generated trajectories provides unbiased, accurate step-level guidance during MCTS search and does not overfit to patterns in the synthesized data or the specific benchmarks used for evaluation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Small LLMs reach 90% on the MATH benchmark and solve 53% of AIME problems by self-evolving through MCTS with a process preference model, surpassing o1-preview without distillation from larger models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Small language models reach expert math reasoning by evolving their own search and evaluation processes over repeated rounds.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"363770b40a8df31b40ecc59add77611f89c0582ce5628d6b8f95df8052aa63f1"},"source":{"id":"2501.04519","kind":"arxiv","version":1},"verdict":{"id":"c06e96ef-f23b-47cd-b08f-5ee9e54e914b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T04:38:20.584079Z","strongest_claim":"Through 4 rounds of self-evolution with millions of synthesized solutions for 747k math problems, rStar-Math boosts SLMs' math reasoning to state-of-the-art levels. On the MATH benchmark, it improves Qwen2.5-Math-7B from 58.8% to 90.0% and Phi3-mini-3.8B from 41.4% to 86.4%, surpassing o1-preview by +4.5% and +0.9%.","one_line_summary":"Small LLMs reach 90% on the MATH benchmark and solve 53% of AIME problems by self-evolving through MCTS with a process preference model, surpassing o1-preview without distillation from larger models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The process preference model trained on self-generated trajectories provides unbiased, accurate step-level guidance during MCTS search and does not overfit to patterns in the synthesized data or the specific benchmarks used for evaluation.","pith_extraction_headline":"Small language models reach expert math reasoning by evolving their own search and evaluation processes over repeated rounds."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e63b6c453d16ae8b6f6b36b6eb270c5c9a58f4ea36427a2214c3e1996dcc3af6"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.04519","created_at":"2026-05-17T23:38:15.095107+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.04519v1","created_at":"2026-05-17T23:38:15.095107+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04519","created_at":"2026-05-17T23:38:15.095107+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZLDIFVCE5L7K","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZLDIFVCE5L7K3T5D","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZLDIFVCE","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":22,"internal_anchor_count":22,"sample":[{"citing_arxiv_id":"2508.06412","citing_title":"Sample-efficient LLM Optimization with Reset Replay","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2509.02547","citing_title":"The Landscape of Agentic Reinforcement Learning for LLMs: A Survey","ref_index":202,"is_internal_anchor":true},{"citing_arxiv_id":"2509.25454","citing_title":"DeepSearch: Overcome the Bottleneck of Reinforcement Learning with Verifiable Rewards via Monte Carlo Tree Search","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2510.18245","citing_title":"Scaling Laws Meet Model Architecture: Toward Inference-Efficient LLMs","ref_index":19,"is_internal_anchor":true},{"citing_arxiv_id":"2511.00066","citing_title":"Sharpness-Guided Group Relative Policy Optimization via Probability Shaping","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2511.22277","citing_title":"TreeCoder: Systematic Exploration and Optimisation of Decoding and Constraints for LLM Code Generation","ref_index":21,"is_internal_anchor":true},{"citing_arxiv_id":"2504.21318","citing_title":"Phi-4-reasoning Technical Report","ref_index":20,"is_internal_anchor":true},{"citing_arxiv_id":"2512.14735","citing_title":"PyFi: Toward Pyramid-like Financial Image Understanding for VLMs via Adversarial Agents","ref_index":1,"is_internal_anchor":true},{"citing_arxiv_id":"2601.21619","citing_title":"On the Overscaling Curse of Parallel Thinking: System Efficacy Contradicts Sample Efficiency","ref_index":10,"is_internal_anchor":true},{"citing_arxiv_id":"2507.21046","citing_title":"A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence","ref_index":234,"is_internal_anchor":true},{"citing_arxiv_id":"2605.13511","citing_title":"Many-Shot CoT-ICL: Making In-Context Learning Truly Learn","ref_index":28,"is_internal_anchor":true},{"citing_arxiv_id":"2604.24037","citing_title":"A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws","ref_index":75,"is_internal_anchor":true},{"citing_arxiv_id":"2605.12289","citing_title":"PriorZero: Bridging Language Priors and World Models for Decision Making","ref_index":17,"is_internal_anchor":true},{"citing_arxiv_id":"2502.17419","citing_title":"From System 1 to System 2: A Survey of Reasoning Large Language Models","ref_index":143,"is_internal_anchor":true},{"citing_arxiv_id":"2506.01939","citing_title":"Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2503.09567","citing_title":"Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models","ref_index":226,"is_internal_anchor":true},{"citing_arxiv_id":"2604.24114","citing_title":"IRIS: Interleaved Reinforcement with Incremental Staged Curriculum for Cross-Lingual Mathematical Reasoning","ref_index":1,"is_internal_anchor":true},{"citing_arxiv_id":"2604.10228","citing_title":"SVSR: A Self-Verification and Self-Rectification Paradigm for Multimodal Reasoning","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"2605.07600","citing_title":"Mathematical Reasoning via Intervention-Based Time-Series Causal Discovery Using LLMs as Concept Mastery Simulators","ref_index":1,"is_internal_anchor":true},{"citing_arxiv_id":"2605.07353","citing_title":"Confidence-Aware Alignment Makes Reasoning LLMs More Reliable","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2604.14768","citing_title":"CoTEvol: Self-Evolving Chain-of-Thoughts for Data Synthesis in Mathematical Reasoning","ref_index":1,"is_internal_anchor":true},{"citing_arxiv_id":"2604.18936","citing_title":"Fine-Tuning Small Reasoning Models for Quantum Field Theory","ref_index":49,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZLDIFVCE5L7K3T5DLSWSPHGKPY","json":"https://pith.science/pith/ZLDIFVCE5L7K3T5DLSWSPHGKPY.json","graph_json":"https://pith.science/api/pith-number/ZLDIFVCE5L7K3T5DLSWSPHGKPY/graph.json","events_json":"https://pith.science/api/pith-number/ZLDIFVCE5L7K3T5DLSWSPHGKPY/events.json","paper":"https://pith.science/paper/ZLDIFVCE"},"agent_actions":{"view_html":"https://pith.science/pith/ZLDIFVCE5L7K3T5DLSWSPHGKPY","download_json":"https://pith.science/pith/ZLDIFVCE5L7K3T5DLSWSPHGKPY.json","view_paper":"https://pith.science/paper/ZLDIFVCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.04519&json=true","fetch_graph":"https://pith.science/api/pith-number/ZLDIFVCE5L7K3T5DLSWSPHGKPY/graph.json","fetch_events":"https://pith.science/api/pith-number/ZLDIFVCE5L7K3T5DLSWSPHGKPY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZLDIFVCE5L7K3T5DLSWSPHGKPY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZLDIFVCE5L7K3T5DLSWSPHGKPY/action/storage_attestation","attest_author":"https://pith.science/pith/ZLDIFVCE5L7K3T5DLSWSPHGKPY/action/author_attestation","sign_citation":"https://pith.science/pith/ZLDIFVCE5L7K3T5DLSWSPHGKPY/action/citation_signature","submit_replication":"https://pith.science/pith/ZLDIFVCE5L7K3T5DLSWSPHGKPY/action/replication_record"}},"created_at":"2026-05-17T23:38:15.095107+00:00","updated_at":"2026-05-17T23:38:15.095107+00:00"}