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We study this distinction for classical neural operators on compact Sobolev subsets through a constructive comparison between routed mixtures of neural operators (MoNOs) and a fixed single-neural-operator construction. The comparison concerns expert-active complexity relative to that baseline, with total stored size and routing search accounted separately. A MoNO routes each input function through a tree to one expert. Our main theorem shows that every scalar uniformly continuous nonlinear operator with bounded output Sobolev radius on the approximation set admits a MoNO approximation whose active expert has smaller depth, width, and rank scaling than the analyzed single-neural-operator construction; for Lipschitz targets these expert quantities are bounded by $\\m","title":"Mixtures of Neural Operators Reduce Active Complexity in Operator Learning","url":"https://arxiv.org/abs/2404.09101","vendor":"arxiv_cs_ai"},"summary":"arXiv:2404.09101v3 Announce Type: replace-cross \nAbstract: Operator-learning systems are not governed solely by total parameter count; for one query, the relevant bottleneck can be the model that must be loaded and evaluated. We study this distinction for classical neural operators on compact Sobolev subsets through a constructive comparison between routed mixtures of neural operators (MoNOs) and a fixed single-neural-operator construction. The comparison concerns expert-active complexity relative to that baseline, with total stored size and routing search accounted separately. A MoNO routes each input function through a tree to one expert. Our main theorem shows that every scalar uniformly continuous nonlinear operator with bounded output Sobolev radius on the approximation set admits a MoNO approximation whose active expert has smaller depth, width, and rank scaling than the analyzed single-neural-operator construction; for Lipschitz targets these expert quantities are bounded by $\\m","title":"Mixtures of Neural Operators Reduce Active Complexity in Operator Learning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-10T04:43:37Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2404.09101"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:b851f2a1b2cfd56526878a596563ce07ff324fe5ca56cb4f8eb4270e5c4111a5c733317b3b95290cffa3b5ddc4fb89e9af191a4bae7383ef0e7f80eff90d220d","signer":"crovia.substrate","subject":{"observed_at":"2026-06-10T04:43:37Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2404.09101"},"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":"6174890b3d1609f36d07682e9df5f863e7ff92834489d78784cc073bfc9249a1","leaf_index":226154,"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":"936fc88ae1143037d40800dd5e10b04228774a45d7c06fc8dd4b281b4a7b5760","side":"right"},{"sibling":"87e654d75a4688b1a8cb5859bebd9c989ce80a737d0d1becf84bf4cfd7310f19","side":"left"},{"sibling":"6b945339eaa5e0a4073a1f4bb6b7cf4b671f5902cc719cf6e4aa0ecc70a7fa1c","side":"right"},{"sibling":"d759e0521f9a2707e0aef1a68b3fd4c1e7992cd85d10fe2de300e9860674e997","side":"left"},{"sibling":"2d558ff51a09d763b13bd697b73e878e1dd5a7c359e0667dcae599210adbfab5","side":"right"},{"sibling":"34b38c531e97e4bcb4b09e12b6e818e193a7166cbebfcd179d08650d5b263c69","side":"left"},{"sibling":"c20ffe9501388a4e560b300f20c62c7cd1bd74b8c3502a50047853354b09279c","side":"left"},{"sibling":"670eed753a274b9b7494adeace1b88e7adfaecd7eeaa78b82e0fc83a75d20865","side":"right"},{"sibling":"b180cfc3f8638c912e90139ec42e2e3fd9b67b3fe342b36e8954314633ae5f61","side":"left"},{"sibling":"a4d17aefe58175050dc159af6246658fcf1c9f3ed57aacf1b350fc3261de4e69","side":"left"},{"sibling":"280b980aa0c7756b0b0cb22658f26466d36f0e70fbc3312cd2311d9898e30b8f","side":"right"},{"sibling":"c98954d4b658b1dda60fe52576fcf9bf21a2d49c67fb63f8c30f16ab5f721938","side":"right"},{"sibling":"cdb58f86163046d3b15f857b03372ec75e1ad9ea4548e086793d528b9eed364d","side":"left"},{"sibling":"533d82482604463aa4a281b9d8b85917b383b7c5f924b2b494039524c55e8797","side":"left"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"6cea4964f32722eb370847c2f7c9d6a9f0622c239538b07e6815a59d6fd8d49c","side":"right"},{"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":228173,"merkle_root":"7e416202c0bfd759bd2eea4236713b403993d99793fe8badb5065040080bece3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260611T143708Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-11T21:59:35Z","sig_algorithm":"ed25519","signature":"231c80024bc3982dd493c45b31af95097e97aabc6d712a4e5bad7d0cbdd3c08e01ff395b0f8e72754bac97016e0cd0eed88b8a13cb71edbbcb9b6d72c10a7b03","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_ccf1ffe242c0527fab43c4f5635b25c69f59bfc57bd308b4b27a0794deee4ed4"}}