{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:RTLJMTRM45IDAIUTFGFESCHOCX","short_pith_number":"pith:RTLJMTRM","schema_version":"1.0","canonical_sha256":"8cd6964e2ce750302293298a4908ee15ec77ea69f41b04b6c8fba53d7a35ef33","source":{"kind":"arxiv","id":"2305.19638","version":2},"attestation_state":"computed","paper":{"title":"A Unified Framework for U-Net Design and Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.LG","eess.IV"],"primary_cat":"stat.ML","authors_text":"Arnaud Doucet, Chris Holmes, Christopher Williams, Fabian Falck, George Deligiannidis, Saifuddin Syed","submitted_at":"2023-05-31T08:07:44Z","abstract_excerpt":"U-Nets are a go-to, state-of-the-art neural architecture across numerous tasks for continuous signals on a square such as images and Partial Differential Equations (PDE), however their design and architecture is understudied. In this paper, we provide a framework for designing and analysing general U-Net architectures. We present theoretical results which characterise the role of the encoder and decoder in a U-Net, their high-resolution scaling limits and their conjugacy to ResNets via preconditioning. We propose Multi-ResNets, U-Nets with a simplified, wavelet-based encoder without learnable "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2305.19638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-05-31T08:07:44Z","cross_cats_sorted":["cs.CV","cs.LG","eess.IV"],"title_canon_sha256":"2fc5dbc2a6d54d22939d6053e06a399c9ffa9330c2d16379c2231ed59a7b84cf","abstract_canon_sha256":"d5417f590bef2b571231c5f111f80efdb4b6e9c495ab49ed4fbd819fc84488df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:32:09.725687Z","signature_b64":"IyvnR4dGU9aI5jbGnzGpl/PolmPnt0h4a7PfSuxTfr6r1NrnN6fNV4pr6jBZxvgyEWMkSkh5q5B2wcLe8RkxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cd6964e2ce750302293298a4908ee15ec77ea69f41b04b6c8fba53d7a35ef33","last_reissued_at":"2026-07-05T07:32:09.724984Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:32:09.724984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Unified Framework for U-Net Design and Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.LG","eess.IV"],"primary_cat":"stat.ML","authors_text":"Arnaud Doucet, Chris Holmes, Christopher Williams, Fabian Falck, George Deligiannidis, Saifuddin Syed","submitted_at":"2023-05-31T08:07:44Z","abstract_excerpt":"U-Nets are a go-to, state-of-the-art neural architecture across numerous tasks for continuous signals on a square such as images and Partial Differential Equations (PDE), however their design and architecture is understudied. In this paper, we provide a framework for designing and analysing general U-Net architectures. We present theoretical results which characterise the role of the encoder and decoder in a U-Net, their high-resolution scaling limits and their conjugacy to ResNets via preconditioning. We propose Multi-ResNets, U-Nets with a simplified, wavelet-based encoder without learnable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.19638","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.19638/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2305.19638","created_at":"2026-07-05T07:32:09.725073+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.19638v2","created_at":"2026-07-05T07:32:09.725073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.19638","created_at":"2026-07-05T07:32:09.725073+00:00"},{"alias_kind":"pith_short_12","alias_value":"RTLJMTRM45ID","created_at":"2026-07-05T07:32:09.725073+00:00"},{"alias_kind":"pith_short_16","alias_value":"RTLJMTRM45IDAIUT","created_at":"2026-07-05T07:32:09.725073+00:00"},{"alias_kind":"pith_short_8","alias_value":"RTLJMTRM","created_at":"2026-07-05T07:32:09.725073+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RTLJMTRM45IDAIUTFGFESCHOCX","json":"https://pith.science/pith/RTLJMTRM45IDAIUTFGFESCHOCX.json","graph_json":"https://pith.science/api/pith-number/RTLJMTRM45IDAIUTFGFESCHOCX/graph.json","events_json":"https://pith.science/api/pith-number/RTLJMTRM45IDAIUTFGFESCHOCX/events.json","paper":"https://pith.science/paper/RTLJMTRM"},"agent_actions":{"view_html":"https://pith.science/pith/RTLJMTRM45IDAIUTFGFESCHOCX","download_json":"https://pith.science/pith/RTLJMTRM45IDAIUTFGFESCHOCX.json","view_paper":"https://pith.science/paper/RTLJMTRM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.19638&json=true","fetch_graph":"https://pith.science/api/pith-number/RTLJMTRM45IDAIUTFGFESCHOCX/graph.json","fetch_events":"https://pith.science/api/pith-number/RTLJMTRM45IDAIUTFGFESCHOCX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RTLJMTRM45IDAIUTFGFESCHOCX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RTLJMTRM45IDAIUTFGFESCHOCX/action/storage_attestation","attest_author":"https://pith.science/pith/RTLJMTRM45IDAIUTFGFESCHOCX/action/author_attestation","sign_citation":"https://pith.science/pith/RTLJMTRM45IDAIUTFGFESCHOCX/action/citation_signature","submit_replication":"https://pith.science/pith/RTLJMTRM45IDAIUTFGFESCHOCX/action/replication_record"}},"created_at":"2026-07-05T07:32:09.725073+00:00","updated_at":"2026-07-05T07:32:09.725073+00:00"}