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While recent work highlights the role of exploration in improving pass@K, empirical evidence points to a paradox: RLVR and ORM/PRM typically reinforce existing paths rather than expanding the reasoning scope, raising the question of why exploration helps if no new patterns emerge.\n  To reconcile this paradox, we adopt the perspective of Kim et al. (2025), viewing easy (e.g., simplifying a fraction) versus hard (e.g., discovering the some symmetry) reasoning steps as low versus high probability Markov transitions. In this tractable model, pretraining corresponds to tree-graph discovering, while post-training corresponds to CoT reweighting. We provably show that, both RLVR and ORM/PRM would favor heavily to several high-probability paths, and ther","title":"Distributional Biases in Post-Training: A Markovian Analysis of Reasoning Trajectories","url":"https://arxiv.org/abs/2511.07368","vendor":"arxiv_cs_ai"},"summary":"arXiv:2511.07368v3 Announce Type: replace-cross \nAbstract: Foundation models exhibit broad knowledge but limited task-specific reasoning, motivating post-training strategies such as RL with verifiable rewards (RLVR) and test-time scaling (TTS). While recent work highlights the role of exploration in improving pass@K, empirical evidence points to a paradox: RLVR and ORM/PRM typically reinforce existing paths rather than expanding the reasoning scope, raising the question of why exploration helps if no new patterns emerge.\n  To reconcile this paradox, we adopt the perspective of Kim et al. 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We provably show that, both RLVR and ORM/PRM would favor heavily to several high-probability paths, and ther","title":"Distributional Biases in Post-Training: A Markovian Analysis of Reasoning Trajectories","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-15T04:43:09Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2511.07368"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:d71e1bddb2d3a07f6522b5d0a86a70b534ffd51fd9d97550d57e25976e6bfd3e646058caca50c3d2b1d24fb323e30559619bc67a3d8a47682cbffea585fe3c08","signer":"crovia.substrate","subject":{"observed_at":"2026-06-15T04:43:09Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2511.07368"},"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":"42ec89d9fb95476203ddf1c4e0ba8a7f60b910a4a3fabdcd194a396e162c045e","leaf_index":230120,"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":"c883079f7147091959f9f149271c489f40714a1f7a8848283f0075fccd444f45","side":"right"},{"sibling":"7ed5b1cd264eb0eda097062f528dd6413d3ae09dac81aae0cb7bc94ed7320964","side":"right"},{"sibling":"bfdeaad0d87800545834e45e31302bf5fd948c9be6fc58adff959025b0d84267","side":"right"},{"sibling":"cae0dd1af88cfcd57edc62cc5e935c5cb5fba506c7471b57e3e51bd8ee93ff50","side":"left"},{"sibling":"65767d1dd7d5bef7c00e05f9de59f842e8a8678b799dcd10706174ef8aae3fd2","side":"right"},{"sibling":"eef6ef787004702e69474576ff5127f1879ce40059a7232f768f384445723ff1","side":"left"},{"sibling":"777fc65e1d77be32b2c8951245c948dfc18781d8f5bfe13e83f1975313bc571c","side":"left"},{"sibling":"4facde6857295772880043256429f729859e11968ea6221d9fa688e71b3a2184","side":"left"},{"sibling":"14c50c43949e1ad41f149ffea691627d3f715c5861766c693b9fbac9d03b0d90","side":"right"},{"sibling":"74897e850164dddc689c3c65b33f9bae0268ab0bf429867a4e193d9b9b685040","side":"left"},{"sibling":"bde25d7e94e64717e426a97f6fcb4907e92b5c61fc89d92d7e0947a2249c3f6b","side":"right"},{"sibling":"d10d772a4984cae00e65ab24af21d1d260e475bbaae3f17871859eb705bd3999","side":"right"},{"sibling":"e79159853f2f35ddae8e3247d515e433c534277b287d65bbd77ae989aa4992fa","side":"right"},{"sibling":"3054319f1840cce0eaaf0bc4b1ae38e5bf8b6210927d924a750775cc7d77cca6","side":"right"},{"sibling":"0fd8b5059f279c4a4a6688de2472fdbc25543fee183df19b21dacca880354cff","side":"right"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"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":232015,"merkle_root":"62bfb7809bb55667ad7eeebdb48267b9b2c1ee89bb808ea1e6d3a814a15aa402","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260617T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-17T13:39:59Z","sig_algorithm":"ed25519","signature":"930a3563c643cc7518d048b12a1f5392a96a5edce49533ba0a56f11b6cc69319bb1c800aacc46b52a6941c4d05dae255a45cac757d6093c971b96852c24f140e","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_fb0a372bedc345d87750b833486ac592f97de3dc7ef03746bc71186fa0941aab"}}