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We find that when this guidance spans the full response, all-token KL spends gradients on mostly redundant positions and amplifies privileged-information leakage, causing entropy rise, shortened reasoning, and out-of-distribution degradation in long-horizon math training. We propose Token-Routed Alignment for Critical rEasoning (TRACE), which distills only on annotator-marked critical spans: forward KL on key spans of correct rollouts, optional reverse KL on localized error spans, and GRPO on all remaining tokens, with the KL channel annealed away after a short warm-up. Our analysis explains TRACE through two effects: forward KL provides non-vanishing lift to teacher-supported tokens that the student under-allocates, while span masking and decay keep cumulative privileged-gradie","title":"TRACE: Distilling Where It Matters via Token-Routed Self On-Policy Alignment","url":"https://arxiv.org/abs/2605.10194","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.10194v1 Announce Type: new \nAbstract: On-policy self-distillation (self-OPD) densifies reinforcement learning with verifiable rewards (RLVR) by letting a policy teach itself under privileged context. We find that when this guidance spans the full response, all-token KL spends gradients on mostly redundant positions and amplifies privileged-information leakage, causing entropy rise, shortened reasoning, and out-of-distribution degradation in long-horizon math training. We propose Token-Routed Alignment for Critical rEasoning (TRACE), which distills only on annotator-marked critical spans: forward KL on key spans of correct rollouts, optional reverse KL on localized error spans, and GRPO on all remaining tokens, with the KL channel annealed away after a short warm-up. Our analysis explains TRACE through two effects: forward KL provides non-vanishing lift to teacher-supported tokens that the student under-allocates, while span masking and decay keep cumulative privileged-gradie","title":"TRACE: Distilling Where It Matters via Token-Routed Self On-Policy Alignment","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-12T04:43:42Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.10194"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:ec78766f60276123a8332f4a9af27c6b3ce3cb98f2f79b6ca6d705c94c4b522eb933db485ed133323099c8875cdc5f96fc42936fcabb660395fc1888d005300e","signer":"crovia.substrate","subject":{"observed_at":"2026-05-12T04:43:42Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.10194"},"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":"24c53788933dffe3597b6f380824abf5eb06fe0eba8541ceabaef7823c73737d","leaf_index":128387,"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":"dd8972661d3b52d0800b230bfe4b6269a43fd6d859ff3c9394a58f377958124a","side":"left"},{"sibling":"0d06264048572d0662942dddfc6df41187895fab38fd1f657b06a20a0ac75a84","side":"left"},{"sibling":"448c5d83567e6f8df8a5f418edab1604b6ae18846d9e229f1d5f6851826f45c0","side":"right"},{"sibling":"7c93d67e768da26a1c3ba5abbcfa5f631ee03668e6d01157259ccdb3e1a152f4","side":"right"},{"sibling":"74a80a946219694efa648e58f0948e11fdf098584db6277c79d21e6a2fe1e0d7","side":"right"},{"sibling":"1e76569690aeb5370536438a4bfc114293525ce17ebff00b5334781803f05b1b","side":"right"},{"sibling":"0d2e2a03cbbaaaf9b359ac04d26d1134ca661c8a9f351c4874b0b3550f597903","side":"right"},{"sibling":"0fac4565968e7e49cfc1d10e28cfc4966c72b4dd0deb14bce20d28acb7a0d65a","side":"left"},{"sibling":"aa3ddc60ad25fcdd4bf93520d8baeca26d807789d80fb0deffbb19c4f8882286","side":"left"},{"sibling":"077005bbaed7b42537914de0b512ed52d33243215eab288181aba807d37bf04e","side":"right"},{"sibling":"c6eaf7a4fcab2db96e9e9423acb6922c80f64882d0f3f50d09e53a4807d23084","side":"left"},{"sibling":"df12eaabc0a370aff5d0488478f48d2b3f90d025c903643f98ea804b017688ec","side":"right"},{"sibling":"ffc4d51379293bc3e1910c7d612f409dc610fd9acf8241793fb89f82e1bad4ef","side":"left"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","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_170c4b6e5908afa4e2e615140a97078ffb43f7ca4d7831013b6f07e81355a09d"}}