{"paper":{"title":"Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A four-stage workflow with sparse-reward RL on a teacher followed by on-policy distillation outperforms direct GRPO on LLM math reasoning.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Alborz Geramifard, Hejian Sang, Ran He, Yuanda Xu, Zhengze Zhou, Zhipeng Wang","submitted_at":"2026-05-12T17:57:48Z","abstract_excerpt":"We present a four-stage post-training workflow for LLM reasoning that allocates scarce labeled training data more effectively than standard recipes. The stages are: (1) sparse-reward RL on a larger teacher; (2a) forward-KL warmup on teacher rollouts; (2b) on-policy distillation under student rollouts; (3) optional sparse-reward RL on the deployment student using any held-out labeled data. On verifiable math with a Qwen3-1.7B deployment student, the workflow reaches $79.3\\%$ MATH and $25.2\\%$ AIME~2024 (avg@16), versus $75.9\\%$ and $19.8\\%$ for direct GRPO on the same student. We justify the wo"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"On verifiable math with a Qwen3-1.7B deployment student, the workflow reaches 79.3% MATH and 25.2% AIME 2024 (avg@16), versus 75.9% and 19.8% for direct GRPO on the same student.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The teacher model must itself be reward-shaped (condition C1) and lie within a small KL divergence of the student (condition C2) for the on-policy distillation stage to provide informative dense implicit rewards.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A four-stage sparse-to-dense reward workflow for LLM post-training reaches 79.3% on MATH and 25.2% on AIME 2024 with a 1.7B student, outperforming direct GRPO by enforcing dense implicit rewards from a shaped teacher.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A four-stage workflow with sparse-reward RL on a teacher followed by on-policy distillation outperforms direct GRPO on LLM math reasoning.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5c9e23903cd85fb5cdb33a44308b26fe82c54b6e8c744ee0d27760639f76a73a"},"source":{"id":"2605.12483","kind":"arxiv","version":3},"verdict":{"id":"96d23965-f712-4d00-99d7-f499e253406f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T16:37:05.873569Z","strongest_claim":"On verifiable math with a Qwen3-1.7B deployment student, the workflow reaches 79.3% MATH and 25.2% AIME 2024 (avg@16), versus 75.9% and 19.8% for direct GRPO on the same student.","one_line_summary":"A four-stage sparse-to-dense reward workflow for LLM post-training reaches 79.3% on MATH and 25.2% on AIME 2024 with a 1.7B student, outperforming direct GRPO by enforcing dense implicit rewards from a shaped teacher.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The teacher model must itself be reward-shaped (condition C1) and lie within a small KL divergence of the student (condition C2) for the on-policy distillation stage to provide informative dense implicit rewards.","pith_extraction_headline":"A four-stage workflow with sparse-reward RL on a teacher followed by on-policy distillation outperforms direct GRPO on LLM math reasoning."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.12483/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T22:21:57.804122Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T10:34:39.758162Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T08:01:17.948604Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T07:26:27.872311Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7bc778090ef335bac4b8ccec696206fbfce4ab2ef7583ecddbcb592ac287f49d"},"references":{"count":30,"sample":[{"doi":"","year":null,"title":"Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback","work_id":"a1f2574b-a899-4713-be60-c87ba332656c","ref_index":1,"cited_arxiv_id":"2204.05862","is_internal_anchor":true},{"doi":"","year":null,"title":"Rubric-based On-policy Distillation","work_id":"c10aafd2-e520-4829-b1a8-b460c24ea267","ref_index":2,"cited_arxiv_id":"2605.07396","is_internal_anchor":true},{"doi":"","year":null,"title":"The Llama 3 Herd of Models","work_id":"1549a635-88af-4ac1-acfe-51ae7bb53345","ref_index":3,"cited_arxiv_id":"2407.21783","is_internal_anchor":true},{"doi":"","year":null,"title":"Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision","work_id":"075fcc48-23c0-4231-bf6e-c629eb2a169b","ref_index":4,"cited_arxiv_id":"2604.12002","is_internal_anchor":true},{"doi":"","year":null,"title":"Distilling the Knowledge in a Neural Network","work_id":"d927ab1f-17b8-4002-9d09-c3d55764fbad","ref_index":5,"cited_arxiv_id":"1503.02531","is_internal_anchor":true}],"resolved_work":30,"snapshot_sha256":"c65db4e06548ee0df5284946a6b3aa75679bca4e3fe0d006b623aa1b466f122f","internal_anchors":21},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}