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Acting rationally then requires inferring the unobserved quantities that govern it and updating beliefs about them as evidence accumulates. Yet most evaluations only score the model's final-turn answer in a single-turn format, leaving this process unexamined. We ask how closely LLMs' belief updates match those of a rational Bayesian reasoner in multi-turn settings, and introduce BayesBench, a suite of simulation environments that probe this across three progressively complex tasks: (i) Bayesian estimation, where the model infers an unknown parameter from sequential evidence; (ii) Bayesian prediction, where the model turns inferred beliefs about a latent variable into outcome forecasts; and (iii) latent-framed Bayesian prediction, where observations are fil","title":"BayesBench: Evaluating LLM Belief Trajectories Under Multi-Turn Evidence Accumulation","url":"https://arxiv.org/abs/2606.30850","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.30850v1 Announce Type: new \nAbstract: Large language models (LLMs) are typically deployed in multi-turn conversations, where each turn provides new evidence that should reduce epistemic uncertainty about their environment. Acting rationally then requires inferring the unobserved quantities that govern it and updating beliefs about them as evidence accumulates. Yet most evaluations only score the model's final-turn answer in a single-turn format, leaving this process unexamined. We ask how closely LLMs' belief updates match those of a rational Bayesian reasoner in multi-turn settings, and introduce BayesBench, a suite of simulation environments that probe this across three progressively complex tasks: (i) Bayesian estimation, where the model infers an unknown parameter from sequential evidence; (ii) Bayesian prediction, where the model turns inferred beliefs about a latent variable into outcome forecasts; and (iii) latent-framed Bayesian prediction, where observations are fil","title":"BayesBench: Evaluating LLM Belief Trajectories Under Multi-Turn Evidence Accumulation","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-01T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.30850"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:a299ebb7a2b8792c669185ffe8fec05ce59aba5f9384c7fe553facc6da75a6e6a31196beb40729e67e3f0c305e79c81200f166447c78ead2cfd908642da9450c","signer":"crovia.substrate","subject":{"observed_at":"2026-07-01T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.30850"},"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":"a67df95cfc779d9452f81d8034f8177fd403ed2a685ddf4e6b09f713310128c4","leaf_index":268397,"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":"4a39707c5b67fc59ac7ea0bf1b4d042d56487327ae8a6222f95f15deadb7906f","side":"left"},{"sibling":"1743e24ca194a377008f8f93154774a9e76b3fa92b79c5d86ae09961020b5ed3","side":"right"},{"sibling":"cdcb4a2930715496cc02e2db23837b0b4dda06553f51bf55ba3ee39d3cff0a57","side":"left"},{"sibling":"f88b3dde06199c807f04aa9b2a5999b8b383451e2d9d1f065208db431dcac04e","side":"left"},{"sibling":"e728e3f2327b06bc6a6748901131355b80998d70bdf14ed3f54f49ac802d54cc","side":"right"},{"sibling":"0a6ba22850d8e2e1027c8f432f8ff51c1696443f82fed1507e6baeb63b9fdb4d","side":"left"},{"sibling":"b488a9375f462266d89ab089714ccff63e65dd03b70e16996ec574fead62f3ff","side":"left"},{"sibling":"18a901b4e67e9d0166a39d7b669e3ae2a0b437d3c7ca6e5cb3d0ff57e4ed30d2","side":"right"},{"sibling":"25b5e7b84bfdaf7764d4179af698e218f4b2858d756d4fd6c30f7dc8f562c1b9","side":"right"},{"sibling":"bbd9a20451913e8c7b910f616d5661d9b281a94af70d201ba50b3112d429521b","side":"right"},{"sibling":"85af80e45748c1e0da1e2f42d9d66da8996016888a034f20eb17ff0a73b69eab","side":"right"},{"sibling":"4575fde969d1d9a2984cc01a37ac8441238f74527d42874272dc5582dadebb4f","side":"left"},{"sibling":"f536de281672cbf0b583a3dc46faef1de2823b72bd9265c7b60e889131cc268d","side":"left"},{"sibling":"95b8b0f67237052a17c41fa8cbdce2b79bcb5aeeba3fdb239d4c4497e598115d","side":"right"},{"sibling":"c2f351f771cee329448890504d9436792ba482e50250ca9a19289311131f96c8","side":"right"},{"sibling":"c39bfb2e911ca37ae997690bfc04128ae32e6806ee1cb3908781a7e6685022a0","side":"right"},{"sibling":"a101b4c60ef6854ac3d750eef02d8e2e06c153284b5ecb7111302f97eb129797","side":"right"},{"sibling":"eae2a3de5cb35455ad60125e196cfadaba8a590c53146e95028469f53f70349c","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":268860,"merkle_root":"d098f25810d0569730b6c0e170d57f329a70359d483b47874b5f2fc51d23de65","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260701T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-01T05:38:05Z","sig_algorithm":"ed25519","signature":"64f37f0e3df0556baa55b924a736cab8005643fa0ab65b503f22407de30eab293e6e0bd62904270fda38d05084bb350c8c0d0aadb2c5a6bae5f1c54598e6d30c","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_eff97360b9730fa7ffe87948c22fcb8d4323a5ce108c839c4d0f8fa75ea8311e"}}