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Critic-free alternatives derived from on-policy distillation supply per-token signals through oracle-conditioned likelihood ratios, yet apply each signal in isolation from the trajectory-level evidence accumulated up to that position. We propose Oracle-Prompted Policy Optimization (OPPO), which rests on a single observation: the oracle signal used by prior distillation-style methods for local discrimination is also the natural Bayesian update of the model's belief about eventual success. Accumulating the signal along a trajectory yields, in closed form and at the cost of one extra forward pass, a running estimate of the success probability at e","title":"OPPO: Bayesian Value Recursion for Token-Level Credit Assignment in LLM Reasoning","url":"https://arxiv.org/abs/2605.21851","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.21851v2 Announce Type: replace-cross \nAbstract: Reinforcement learning with verifiable rewards has become the standard recipe for improving LLM reasoning, but the dominant algorithm GRPO assigns a single trajectory-level advantage to every token, diluting the signal at pivotal reasoning steps and injecting noise at uninformative ones. Critic-free alternatives derived from on-policy distillation supply per-token signals through oracle-conditioned likelihood ratios, yet apply each signal in isolation from the trajectory-level evidence accumulated up to that position. We propose Oracle-Prompted Policy Optimization (OPPO), which rests on a single observation: the oracle signal used by prior distillation-style methods for local discrimination is also the natural Bayesian update of the model's belief about eventual success. Accumulating the signal along a trajectory yields, in closed form and at the cost of one extra forward pass, a running estimate of the success probability at e","title":"OPPO: Bayesian Value Recursion for Token-Level Credit Assignment in LLM Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-25T04:43:48Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.21851"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:77f6ba87692425e79ba0f753c69d77467af22b35ae49e9353bf374bbd5f3b180ab70d66c5ceac1150da50106117727bea3436e73f24f94fbfb3e544a3e508006","signer":"crovia.substrate","subject":{"observed_at":"2026-05-25T04:43:48Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.21851"},"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":"a34e97a751dbd1c438e8c92da951649f9fcf495dabbb5b6a83c18db190a1b705","leaf_index":149781,"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":"6ea4d500ef5ee1ec5a1aac2797762af800dc97cac774a6f720611aa2ec8001f4","side":"left"},{"sibling":"d7027a30a3d8df5cca1473dde074d2592299e7cee4e4ec1c756e024bf7c8c41a","side":"right"},{"sibling":"221170144aa51c4281cd66c8c88036af2c187cd71ca50b60ed1c08170fa0ae9b","side":"left"},{"sibling":"cee4ec67f607dab2090c3d488c036fbfc69eafa913a4baeb343a4e5d074d1ed5","side":"right"},{"sibling":"0b10de68779b67350d2c0e95abc5680a2105461befd535da53940b0938597cd4","side":"left"},{"sibling":"0056ee67f86a31be6331b48f491dfa370c69a2c85230b156659bff6177e119f9","side":"right"},{"sibling":"92ad4fc36e2d8bd64a4d83e76fd8e6e0c9cc03786f4e389a46451d49428799b6","side":"right"},{"sibling":"5203bb116cea5471bab102351ae528fe783239665ad8c3a791a604a7146f231b","side":"right"},{"sibling":"b4b5fac84e1432ae7c3747859a1ce8e49081cee98975ffeee0646d5da13dd35d","side":"left"},{"sibling":"6be461ecf12dedf98a31921aa7b5c32d4a32df6897e0f697b8bf1a4ba3e2d324","side":"right"},{"sibling":"c2861a8cef3eb66bf2726aa377c24a6bf6e8b7489dcd0e870b61d62a35ccadfb","side":"right"},{"sibling":"134949308b15cffd6792ee2cf678119af34d69a64764d7c89cd47573c94e1cda","side":"left"},{"sibling":"debbc1a6232ea7970009b91bdc2345041b2de5ac59551f955855d579001e512c","side":"right"},{"sibling":"216869846f40bd905626884f58cb67b9019e488b3656946a7808c436ab7339ac","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"e734b0c6d6d13acb5f4cf00367b3913e5bbf1aa717377aa4e4820c6de24b7673","side":"right"},{"sibling":"4bbb7f78e96179bb9cdd06d7207b66b3503ab68e4880438263025b04ebe8f7ec","side":"right"},{"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":149835,"merkle_root":"51484a548bc0cf3d178eec868e98935c87f0aa83369143b7c96b048585e5ba01","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260525T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-25T05:37:33Z","sig_algorithm":"ed25519","signature":"99a657e53a015ace0bade5d7fbb3f60f950b6d1e1128251a63afcc454a492422cae5efdc0c18503b4f7e62f371bd48f2889be78d9048c4681d6c1e73f754d705","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_71613fb9360de48cdcfb37cef65ce3f28282e41a57ca23f4eef245f1b4a84caa"}}