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However, existing methods based on Group Relative Policy Optimization (GRPO) rely on a binary outcome reward, which induces two structural failure modes: Zero-Advantage Collapse, in which all rollouts in a group share the same outcome and the gradient vanishes, and Hallucinated Certainty, in which the model becomes increasingly confident on incorrect rollouts late in training. We address both modes by densifying the reward with intrinsic signals computed entirely from the policy's own conditional probabilities, and propose ISPO (Intrinsic Signal Policy Optimization, which combines a sequence-level signal measuring how informative the thinking trajectory is for the final answer, with a token-level directional reward whose hallucinated-certainty hinge penalizes confidently-wrong predictions a","title":"Momentum for Reasoning: Dense Intrinsic Signals in Policy Optimization","url":"https://arxiv.org/abs/2606.08815","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.08815v1 Announce Type: new \nAbstract: Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for eliciting long-chain reasoning in large language models. However, existing methods based on Group Relative Policy Optimization (GRPO) rely on a binary outcome reward, which induces two structural failure modes: Zero-Advantage Collapse, in which all rollouts in a group share the same outcome and the gradient vanishes, and Hallucinated Certainty, in which the model becomes increasingly confident on incorrect rollouts late in training. We address both modes by densifying the reward with intrinsic signals computed entirely from the policy's own conditional probabilities, and propose ISPO (Intrinsic Signal Policy Optimization, which combines a sequence-level signal measuring how informative the thinking trajectory is for the final answer, with a token-level directional reward whose hallucinated-certainty hinge penalizes confidently-wrong predictions a","title":"Momentum for Reasoning: Dense Intrinsic Signals in Policy Optimization","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-09T04:43:45Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.08815"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:861c4384a35f39097978780947a3c7a42ece80c2af2d2d9d04ec94e8735cd4c0a597f8417abc16fcf6228532baef92b5ac4ea1a7f08b54be2cabb06ce1781b00","signer":"crovia.substrate","subject":{"observed_at":"2026-06-09T04:43:45Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.08815"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"3f0decc39ff72a17ca62886e703e8404fb7b973287d356c8693bbaeea45c5fb6","leaf_index":224011,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"2611476db524f75631a1d0c1a41f54103ed057ee36a59367964f62c9b6d4f199","side":"left"},{"sibling":"c276404b8c99f9d43c3026cc6371bcf8e1529154dfe7aa1204a96462debeef57","side":"left"},{"sibling":"3e80f7e268cf0759596ba5c5220db12c1b98582f05308b6beffe9efab189f7fe","side":"right"},{"sibling":"6ebcc6c130355ce33880787482e079e0c75370e2d9783be131f7a9d8d05d90bf","side":"left"},{"sibling":"9ed56cc86b90a849b68f64b862b9c79218ce6e4189ae2d71f48eba981d511a7c","side":"right"},{"sibling":"7639b7b8450a9c35a0488bbe3a9d302d9d58b4404f478bd3f1362ff40c9706c1","side":"right"},{"sibling":"7d319425db25fb3c3f1998c36dfe19db51428e3c4629360b23d76d78a49611fd","side":"right"},{"sibling":"e9dc257685cfad8bb0dae07b2db5d353319e50598398bbbe195a915649748f95","side":"right"},{"sibling":"dd5d61819b080d26c4380e26887a8eb889d51e2c022f796a39855defe6f68d95","side":"left"},{"sibling":"e8dcea313a54920d83e4f72d5a4223f986c719f264241d171c4712efaaf1fc54","side":"left"},{"sibling":"5480e1ea31f4744f9bd7c4261771fe51f2cdb01e705cc17320bfc202d935ca12","side":"right"},{"sibling":"24fdc29d461691aedb6fa920758206b5bb43851f477ef7a04c34aaed84b8971b","side":"left"},{"sibling":"036922da4e1e2c46d948f070454bfad299b7406fb00735ea9d8bd1e687f5f445","side":"right"},{"sibling":"533d82482604463aa4a281b9d8b85917b383b7c5f924b2b494039524c55e8797","side":"left"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"87c6b850dfec08ac35a693d9db3a3315250a68adb1cfab9b1015f212b63b15bd","side":"right"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":224761,"merkle_root":"e9f7b49b652e869ab97ffba9c5a31356b2d0e3dc5d00bb28944adf737c46b1e7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260609T103805Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-09T14:15:34Z","sig_algorithm":"ed25519","signature":"8ad8076fb12c8e486ae1d1559a9a7ba8e2ee996a9ad3d8ba7bcdbdbd88ab3a15bcb429707aca6d3e9d8b97e2ba755b3dcc77b1abb6601ccb829842719a6fb30d","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_6495308241bea332af6262f643c1e78bdbed3ad9ade2f2636b9dbc6e73433507"}}