{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_f5e757438513213256fcb3a6bb033cc1cd58288fa95318b63ef1bc35878632fa","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_f5e757438513213256fcb3a6bb033cc1cd58288fa95318b63ef1bc35878632fa","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"96f88cb083bfff624be803d445f3ee37ea350de21fe0f886ab74287d5510ab62","published":"Mon, 29 Jun 2026 00:00:00 -0400","receipt_hash":"96f88cb083bfff624be803d445f3ee37ea350de21fe0f886ab74287d5510ab62","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"96f88cb083bfff624be803d445f3ee37ea350de21fe0f886ab74287d5510ab62","observed_at":"2026-06-29T04:44:03.414425Z","parent_run_hash":"36b5ab5c57ae76dc9e1a863501c4d38f172868cfae31b4ba5baf3caffaafb2c4","published":"Mon, 29 Jun 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2510.09685v2 Announce Type: replace-cross \nAbstract: Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to theoretical understanding, interpretability, and generalization. To address these issues, researchers are increasingly adopting a differential equations perspective to propose a unified theoretical framework and systematic design methodologies for neural networks. In this paper, we provide an extensive review of deep neural network architectures and dynamic modeling methods inspired by differential equations. We specifically examine deep neural network models and deterministic dynamical network constructs based on ordinary differential equations (ODEs), as well as regularization techniques and stochastic dynamical network models informed by stochastic differential equations (SDEs). We present numer","title":"Deep Neural Networks Inspired by Differential Equations","url":"https://arxiv.org/abs/2510.09685","vendor":"arxiv_cs_ai"},"summary":"arXiv:2510.09685v2 Announce Type: replace-cross \nAbstract: Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to theoretical understanding, interpretability, and generalization. To address these issues, researchers are increasingly adopting a differential equations perspective to propose a unified theoretical framework and systematic design methodologies for neural networks. In this paper, we provide an extensive review of deep neural network architectures and dynamic modeling methods inspired by differential equations. We specifically examine deep neural network models and deterministic dynamical network constructs based on ordinary differential equations (ODEs), as well as regularization techniques and stochastic dynamical network models informed by stochastic differential equations (SDEs). We present numer","title":"Deep Neural Networks Inspired by Differential Equations","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-29T04:44:03Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2510.09685"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c203a860c67ac87b1b82b94456c217810ea274546bd88ddfff9ccf40d6c1d864f97752aeec273040f583815d59f3ec5ac0189f4ae1cec1c2b70b8ab7e262420a","signer":"crovia.substrate","subject":{"observed_at":"2026-06-29T04:44:03Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2510.09685"},"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":"72a74ebb2a180f00bb22702bba726349ea03910b4f7fa3c7d9cdff5baa9089f5","leaf_index":261492,"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":"9a6f2f859f1f06d0a1d13566299a20ab9e020d5221689a1b0f2c5e6bcb0f5ef0","side":"right"},{"sibling":"04a1b91503496419fcda970d50bb0fa29bfbb673c8e872ca378eb259d469f817","side":"right"},{"sibling":"c37d0e4ab9e290ddf667c2c136409d056c80b8c8845f6a680cb235dc8c264ef2","side":"left"},{"sibling":"1bc96f3b494ad071dbe7f9a38a6cc8bbb332a1379e475c8e21e5ca19d5c332ba","side":"right"},{"sibling":"2d5bbc44556a92eee2f169949b388e3285d093ebd56021315cd030f4a66f5ad5","side":"left"},{"sibling":"d6cf72c7d9c886efcdcf4e7b5f7c8e925e8e0ea6de18ceb8d47544007b92130a","side":"left"},{"sibling":"a600c67ab28d0232fe4727e4641fc665bde749779b50edf849b1a9c8287bc809","side":"left"},{"sibling":"4b4bda5fa1fb23989b8f6f192c36dadc8266c378c69d42945af35c9d6ab81a10","side":"right"},{"sibling":"6d1df65d14253ed3a13c03e25aa9adcd9a091d8062a82e8586bcaee74013b90e","side":"left"},{"sibling":"9f9daa9d12e65b219f34c92aec45450536b79a42b8892050d66961432ae28ed1","side":"right"},{"sibling":"b5725d7b0807dc6da32d9788f20057fa8726be38d30a9ebdabc605ae92739122","side":"left"},{"sibling":"e321b2cac14cbe28f76ccb7938249a40ff60cd5d2128b5634be046ea10e984b8","side":"left"},{"sibling":"5900dc6c7d13855af9d0385baf1691ec386df33e450c422af1cabe0a36e40ad8","side":"left"},{"sibling":"ae636ddee98c71ab7a7dc55ddfab70c7f710a2b6abfdf7a8b5d16a4017d1c0d1","side":"left"},{"sibling":"f29798d8bb6aa9900eab878992d9ff0c53266debd87472f31ab26a6a3fb55880","side":"left"},{"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":261662,"merkle_root":"aa8865c239aa2eb6c8aa7c6250f56b3cd5709854a8a07f6a29eb4ddd8802cb6f","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260629T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-29T05:38:02Z","sig_algorithm":"ed25519","signature":"476329233e82fb35fba2552ddc5d1d75b2bdd8513bbd281e9c40a0b8e475df374a62dcd8b456b0c5e8815984f5b4bf0983ae95d2cf4d7412ebb13a433b933c0a","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_f5e757438513213256fcb3a6bb033cc1cd58288fa95318b63ef1bc35878632fa"}}