{"paper":{"title":"Design Conditions for Intra-Group Learning of Sequence-Level Rewards: Token Gradient Cancellation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Intra-group objectives for sequence rewards must preserve gradient exchangeability across tokens to enable cancellation on weak-credit high-frequency tokens and block reward-irrelevant drift.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Fei Ding, Yongkang Zhang, youwei wang, Zijian Zeng","submitted_at":"2026-04-04T02:47:28Z","abstract_excerpt":"Reinforcement learning for multi-step reasoning with large language models (LLMs) typically relies on sparse terminal rewards, which creates a poorly conditioned credit-assignment problem: the final feedback is propagated uniformly across all intermediate decisions. This leads to high gradient variance, unstable training, and many ineffective updates, ultimately limiting sustained model improvement. We propose a counterfactual-comparison framework for credit assignment. For each input, the framework samples multiple reasoning trajectories and treats their differences as implicit approximations"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"to prevent reward-irrelevant drift, intra-group objectives must maintain gradient exchangeability across token updates, enabling gradient cancellation on weak-credit/high-frequency tokens.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the observed training failures (learning tax, solution probability drift, entropy collapse) are primarily caused by disruption of token-level gradient exchangeability rather than other factors such as reward sparsity itself or optimizer dynamics.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Intra-group objectives in sparse-reward RL must maintain token gradient exchangeability to enable cancellation on weak-credit tokens and stabilize training.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Intra-group objectives for sequence rewards must preserve gradient exchangeability across tokens to enable cancellation on weak-credit high-frequency tokens and block reward-irrelevant drift.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3f85b0770105bfd8309f1126dc1cc79601f3b00ab70d3d0a17db89cea286f84c"},"source":{"id":"2604.13088","kind":"arxiv","version":2},"verdict":{"id":"b38de77e-6f47-426b-9868-4fb6a5965e2a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T18:38:00.557651Z","strongest_claim":"to prevent reward-irrelevant drift, intra-group objectives must maintain gradient exchangeability across token updates, enabling gradient cancellation on weak-credit/high-frequency tokens.","one_line_summary":"Intra-group objectives in sparse-reward RL must maintain token gradient exchangeability to enable cancellation on weak-credit tokens and stabilize training.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the observed training failures (learning tax, solution probability drift, entropy collapse) are primarily caused by disruption of token-level gradient exchangeability rather than other factors such as reward sparsity itself or optimizer dynamics.","pith_extraction_headline":"Intra-group objectives for sequence rewards must preserve gradient exchangeability across tokens to enable cancellation on weak-credit high-frequency tokens and block reward-irrelevant drift."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.13088/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":1,"snapshot_sha256":"a7ec499fa2984d6b9f2c116cd0ee6128a352566b47d42486cde3d12b97a0a9c0"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}