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FEM represents each conditional factor as an energy landscape over learned discrete-parent embeddings and continuous observations, enabling posterior evaluation, generative sampling, and compositional inference across multiple continuous leaves by energy addition under conditional independence.\n  A central finding is the mode-bridge artifact: standard conditional energy models can create low-energy ridges between separated modes of the same class, producing overconfident posteriors at off-data interior points. 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We analyze this failure and propose valley regularization, an off-data calibration term that restores near-uniform posteriors in such regions while preserving in-data fit.\n  Across synthetic multimodal hybrid-BN benchmarks, FEM substantially reduces KL ","title":"Free Energy Manifold: Score-Based Inference for Hybrid Bayesian Networks","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/2605.09839"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:5fa5fced861e61a375e69df491684edfcc3c978bb5e3741e6f07720d5dcd095cce648d6c2123ccd6fed90ac8ac0dd4fb281cd73e64e5280d5fd3dc26a2d5e30e","signer":"crovia.substrate","subject":{"observed_at":"2026-05-12T04:43:42Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.09839"},"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":"eb105bba5c1287eb4fd54472b4ca405d1756cdfa433957e53e5635d45a5d3cda","leaf_index":128780,"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":"884914f793d727c010491c82a9e9d7c87f15d36c9e88e38a8190175fe2dec632","side":"right"},{"sibling":"9175444427acf1bed55082cc19118b10aff1e2b33cacb0397b19dc0cac662346","side":"right"},{"sibling":"28e6c5e698f593baa56c94c052d5f4f0ad8f7b9130d1f6c6f79664f027ec41df","side":"left"},{"sibling":"4918be914436b07f0dc6d28a56454103a45147061e522f7ab01ae914bf446f4b","side":"left"},{"sibling":"688efed6122cf26757c65f1eb2a37e3807f1205d2f07d5e5eacadf68002e5d31","side":"right"},{"sibling":"574d9f04b62e335d90fd1f4e0b42da3705cb647d1b2f86fa9af00550f2c4c7ff","side":"right"},{"sibling":"7d5dfe392e436336d9499115df1837fc738109d5b2eebb2bd7de357ccfc2b0a7","side":"right"},{"sibling":"17788012ee9d23c33d35ead8be5aa8d08d73dd70833c55b77c06f0f8d286c3ef","side":"right"},{"sibling":"9b7895252355a8c8a373671590682bbf4d36d41befce49b5e889eaf896415156","side":"left"},{"sibling":"1d74b0fb79eace68949b4d82b0e430b1d9eb122c125f67f5be7d50c074c228e7","side":"left"},{"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_e8da305715e78d0b17b361540e8425100e6c15c7da25dac2c17a9109022520f4"}}