{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MJ6AYCOVJF7DZTCTDRWFW6KXA3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7c3b7a968c04f66ecf7392aeb67e51b9e86fb51fa73931a8a097e551d87d8926","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-30T04:15:23Z","title_canon_sha256":"9953d836bb27330928e35ff0cef33566bb3f1d1a4cff05a74ac5a18a4d635638"},"schema_version":"1.0","source":{"id":"2606.00517","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00517","created_at":"2026-06-02T01:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00517v1","created_at":"2026-06-02T01:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00517","created_at":"2026-06-02T01:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"MJ6AYCOVJF7D","created_at":"2026-06-02T01:03:57Z"},{"alias_kind":"pith_short_16","alias_value":"MJ6AYCOVJF7DZTCT","created_at":"2026-06-02T01:03:57Z"},{"alias_kind":"pith_short_8","alias_value":"MJ6AYCOV","created_at":"2026-06-02T01:03:57Z"}],"graph_snapshots":[{"event_id":"sha256:a86832682e2bf251051f4c392999b02d16e375668d9cc9d0768e2597040dd0ee","target":"graph","created_at":"2026-06-02T01:03:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.00517/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the regularization of ill-posed inverse problems by deep neural networks (DNNs). We extend architecture-based regularization from shallow networks to deep models by developing a deterministic framework in which the admissible network class is enlarged adaptively and the resulting architecture complexity acts as the regularization mechanism. We propose two discrepancy-principle-driven expanding DNN algorithms to treat the cases where an explicit parameter-radius bound is available and unavailable, respectively. For both algorithms, we prove the finite termination of the adapt","authors_text":"Lan Wang, Qiao Zhu, Ye Zhang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-30T04:15:23Z","title":"Deep neural network yields regularization for ill-posed inverse problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00517","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:11e7ec8673636464f135283dbee8e944151a53cd10896c5159244e66a9c2615a","target":"record","created_at":"2026-06-02T01:03:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7c3b7a968c04f66ecf7392aeb67e51b9e86fb51fa73931a8a097e551d87d8926","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-30T04:15:23Z","title_canon_sha256":"9953d836bb27330928e35ff0cef33566bb3f1d1a4cff05a74ac5a18a4d635638"},"schema_version":"1.0","source":{"id":"2606.00517","kind":"arxiv","version":1}},"canonical_sha256":"627c0c09d5497e3ccc531c6c5b795706fc148d4fad98c1a6ac1a76586fa5079a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"627c0c09d5497e3ccc531c6c5b795706fc148d4fad98c1a6ac1a76586fa5079a","first_computed_at":"2026-06-02T01:03:57.053304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:57.053304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+XgHuv5oLsJzY85gL44u5Hlknj4BNSpdPNcE3QDvd0BgbmBZF4Zpnso1jPqz+zR8zUZ1uBnaNqFuFaP/aIJtAA==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:57.054685Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00517","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11e7ec8673636464f135283dbee8e944151a53cd10896c5159244e66a9c2615a","sha256:a86832682e2bf251051f4c392999b02d16e375668d9cc9d0768e2597040dd0ee"],"state_sha256":"eb34ff1f78e6165ec6a15c313107bf9e09e861ee5f1a0a16cbc918365cee0618"}