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Common hybrid modeling designs are specified primarily through their architectures and training losses, which offers a limited basis for a shared semantic interface to compare or verify them across domains, with comparatively little attention paid to epistemic uncertainty in the mechanistic part.\n  We bridge hybrid modeling and neuro-symbolic (NeSy) AI by reconstructing these designs as instances of NeSy interface. The resulting translation, Hybrid-to-NeSy (H2N), places mechanistic knowledge on the language side, learned modules on the belief side, and validity domains together with constraints on the logic side. For each design, H2N then yields an explicit NeSy inference functional and a logic-belief decomposition.\n  From this decomposition we derive two metrics: s","title":"From Hybrid Mechanistic--Data-Driven Modeling Toward Neuro-Symbolic AI: What, Why, and How","url":"https://arxiv.org/abs/2607.22811","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.22811v1 Announce Type: cross \nAbstract: Hybrid mechanistic/data-driven models, which combine first-principles with learned components, are increasingly used in process engineering and scientific machine learning. Common hybrid modeling designs are specified primarily through their architectures and training losses, which offers a limited basis for a shared semantic interface to compare or verify them across domains, with comparatively little attention paid to epistemic uncertainty in the mechanistic part.\n  We bridge hybrid modeling and neuro-symbolic (NeSy) AI by reconstructing these designs as instances of NeSy interface. The resulting translation, Hybrid-to-NeSy (H2N), places mechanistic knowledge on the language side, learned modules on the belief side, and validity domains together with constraints on the logic side. For each design, H2N then yields an explicit NeSy inference functional and a logic-belief decomposition.\n  From this decomposition we derive two metrics: s","title":"From Hybrid Mechanistic--Data-Driven Modeling Toward Neuro-Symbolic AI: What, Why, and How","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-28T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.22811"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c57a70165c1eb701962f11998a0212b0cc895a4c7fb78206bbc13ad06350fafa90f2ced4a0bb5345d0a911e981ea23222d2163c0df26978db15adb664eeb730e","signer":"crovia.substrate","subject":{"observed_at":"2026-07-28T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.22811"},"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":"8644f5f3310409792162bb7bfdcae9d23f48f1fd14e65e8c9aac6269066026e3","leaf_index":360541,"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":"945c705bc0c41e7d4fd1cc31ac9258d659a2621f27331f3524f8a58845f61965","side":"left"},{"sibling":"dff95c1d2112c05ccfde26b6cd436d329aae261e121cd38d399237b4ac75d1e1","side":"right"},{"sibling":"71676738fc5351ebd30bf56728a8adefa0096c08a40d1cc60a7633beb699ce15","side":"left"},{"sibling":"31754133aa46fc64636eafe02eac4919380c5e1df71680e78299a0051d8d17c2","side":"left"},{"sibling":"cab8fdfb288cba943ebebcc740eb71db412a9a6b5b30f62c6c9bd1bdbcf78d4f","side":"left"},{"sibling":"4bbf675ec568ad664ad69589b79a61b93586b04ba93f602704fb68f7672a6fef","side":"right"},{"sibling":"a75ea3fe312c1d9ab3776bfe70acd45752855705bf7bb0ab8e19b5f21d865d19","side":"left"},{"sibling":"7da15787b28ee42d6f6ffa689ccb25f3c7958b4ad112266a2a4acad4347e0386","side":"right"},{"sibling":"eb79f1d599c07786d2268140481af8b617999ecc5688c6283fe58e5e6f3a2640","side":"right"},{"sibling":"fe03c6d0b083c4097049d7fc6d7d08dfdb05d9c198b2786336689712d66eabf0","side":"right"},{"sibling":"590ea76fdfc1b9e8072055c378be3182f916709e8d06bd955232e650a7188b86","side":"right"},{"sibling":"d92781c59301ffd5bfb0bad75d9fdf6d73879f715518149d383f7362213e0daf","side":"right"},{"sibling":"f315303d4402b57497416d48eb4c4bb50405b40862d41c7caf318cb3d29c5237","side":"right"},{"sibling":"36973eb5f586cd67e0c0dc055dd87e734aa544c35d4400d2c9f932f8ef8fb27f","side":"right"},{"sibling":"e39f7900355489c4718b21cc2d3d06382e1d2f22b864d10be9ebc9d498b279a1","side":"right"},{"sibling":"1f9a970b25dd938c98cabc9e0a55c5a6f46292b9fa37cc89d90ef0cbb1e05a8c","side":"left"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"3b50864499c874394ea0928567747666eaf59b01380e46cd52164ec5acec0f71","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":361008,"merkle_root":"3065e8369ea437c06beba806dc4e4bb159979adeb21fe632242c1906a7204647","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260728T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-28T05:38:48Z","sig_algorithm":"ed25519","signature":"9141644407577a82611c1579110f667de2d46dc6b93c6322edf26f4c3056ea99f0e56502853908e30d87c38bcf95eb6e0ab5130525aa51505bd6f61938120609","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_7b6fa4467c02de2654a9e58aa1a9216667f428cb947b65ebe87736907cd3bd2f"}}