{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YEARNEYO5GB67UV6GCCJHHABEA","short_pith_number":"pith:YEARNEYO","schema_version":"1.0","canonical_sha256":"c10116930ee983efd2be3084939c01202fd5e7de134b1b7a1179abfdc94121ff","source":{"kind":"arxiv","id":"2606.29238","version":1},"attestation_state":"computed","paper":{"title":"On the Policy Gradient Foundations of Group Relative Policy Optimization: Credit Assignment, Gradient Sparsity, and Rank Collapse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Amritansh Mishra, Berkcan Kapusuzoglu, Supriyo Chakraborty","submitted_at":"2026-06-28T06:51:45Z","abstract_excerpt":"Group Relative Policy Optimization (GRPO) eliminates the learned critic in PPO by using the mean reward of grouped rollouts as a baseline. We provide a rigorous derivation of GRPO from first principles of the policy gradient theorem, revealing a fundamental credit assignment failure: under output-only reward, every token in a rollout receives identical advantage, collapsing token-level credit to a single scalar. We prove this induces gradient sparsity that intensifies over training, and demonstrate empirically via SVD analysis of GRPO gradients on Nemotron-4B/GSM8K that the gradient matrix has"},"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":false},"canonical_record":{"source":{"id":"2606.29238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-28T06:51:45Z","cross_cats_sorted":[],"title_canon_sha256":"3140bf8c7d3db3ea825b157a62aaa5d31638303a99b7193f4498e9f8603775df","abstract_canon_sha256":"59e93e92fa3b2002c6220795978e1fc2afe0cb455d1b493cfec60b0cfa932f3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:58.526637Z","signature_b64":"8NyNCqIYjh+3zd00ikLfXZkndFVJmMso7Fj8mgwkyxJlw8zS5NNSbOVpRAUit6wMmeowahZk/deoP0JmR7oPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c10116930ee983efd2be3084939c01202fd5e7de134b1b7a1179abfdc94121ff","last_reissued_at":"2026-06-30T01:17:58.525942Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:58.525942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Policy Gradient Foundations of Group Relative Policy Optimization: Credit Assignment, Gradient Sparsity, and Rank Collapse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Amritansh Mishra, Berkcan Kapusuzoglu, Supriyo Chakraborty","submitted_at":"2026-06-28T06:51:45Z","abstract_excerpt":"Group Relative Policy Optimization (GRPO) eliminates the learned critic in PPO by using the mean reward of grouped rollouts as a baseline. We provide a rigorous derivation of GRPO from first principles of the policy gradient theorem, revealing a fundamental credit assignment failure: under output-only reward, every token in a rollout receives identical advantage, collapsing token-level credit to a single scalar. We prove this induces gradient sparsity that intensifies over training, and demonstrate empirically via SVD analysis of GRPO gradients on Nemotron-4B/GSM8K that the gradient matrix has"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29238","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29238/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.29238","created_at":"2026-06-30T01:17:58.526054+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.29238v1","created_at":"2026-06-30T01:17:58.526054+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29238","created_at":"2026-06-30T01:17:58.526054+00:00"},{"alias_kind":"pith_short_12","alias_value":"YEARNEYO5GB6","created_at":"2026-06-30T01:17:58.526054+00:00"},{"alias_kind":"pith_short_16","alias_value":"YEARNEYO5GB67UV6","created_at":"2026-06-30T01:17:58.526054+00:00"},{"alias_kind":"pith_short_8","alias_value":"YEARNEYO","created_at":"2026-06-30T01:17:58.526054+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YEARNEYO5GB67UV6GCCJHHABEA","json":"https://pith.science/pith/YEARNEYO5GB67UV6GCCJHHABEA.json","graph_json":"https://pith.science/api/pith-number/YEARNEYO5GB67UV6GCCJHHABEA/graph.json","events_json":"https://pith.science/api/pith-number/YEARNEYO5GB67UV6GCCJHHABEA/events.json","paper":"https://pith.science/paper/YEARNEYO"},"agent_actions":{"view_html":"https://pith.science/pith/YEARNEYO5GB67UV6GCCJHHABEA","download_json":"https://pith.science/pith/YEARNEYO5GB67UV6GCCJHHABEA.json","view_paper":"https://pith.science/paper/YEARNEYO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.29238&json=true","fetch_graph":"https://pith.science/api/pith-number/YEARNEYO5GB67UV6GCCJHHABEA/graph.json","fetch_events":"https://pith.science/api/pith-number/YEARNEYO5GB67UV6GCCJHHABEA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YEARNEYO5GB67UV6GCCJHHABEA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YEARNEYO5GB67UV6GCCJHHABEA/action/storage_attestation","attest_author":"https://pith.science/pith/YEARNEYO5GB67UV6GCCJHHABEA/action/author_attestation","sign_citation":"https://pith.science/pith/YEARNEYO5GB67UV6GCCJHHABEA/action/citation_signature","submit_replication":"https://pith.science/pith/YEARNEYO5GB67UV6GCCJHHABEA/action/replication_record"}},"created_at":"2026-06-30T01:17:58.526054+00:00","updated_at":"2026-06-30T01:17:58.526054+00:00"}