{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IUXUKNLIL52RRVJQRUZGAK2MKI","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":"713b6611035be1b320615cc0f76f1ec7fc173cc588652aa2cf665e1b630f196e","cross_cats_sorted":["cs.LG","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-20T05:57:38Z","title_canon_sha256":"7b3f7ca580054bc37a9aedf8c95a875f260cb23e85b858b10fd7e6fba1569ff6"},"schema_version":"1.0","source":{"id":"1810.08754","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08754","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08754v1","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08754","created_at":"2026-05-17T23:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"IUXUKNLIL52R","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IUXUKNLIL52RRVJQ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IUXUKNLI","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:12eddfccddf6ad3783cd6f46063146277dd9e7aa5bba71395210172514b06b6c","target":"graph","created_at":"2026-05-17T23:50:23Z","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"},"paper":{"abstract_excerpt":"This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in [Communications on Pure and Applied Mathematics, 44(2), 141-183]. The nonstandard form is a highly effective wavelet-based compression scheme for linear integral operators. In this work, we first represent the matrix-vector product algorithm of the nonstandard form as a linear neural network where every scale of the multiresolution computation is carried out by a locally connected linear sub-network. In order to address nonlinear problems, we propose an extensio","authors_text":"Cindy Orozco Bohorquez, Lexing Ying, Yuwei Fan","cross_cats":["cs.LG","eess.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-20T05:57:38Z","title":"BCR-Net: a neural network based on the nonstandard wavelet form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08754","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":"sha256:5c64138615693ab0de4ffc7f7a6d989eb0103d2d75e2205a8011a488d589c99d","target":"record","created_at":"2026-05-17T23:50:23Z","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":"713b6611035be1b320615cc0f76f1ec7fc173cc588652aa2cf665e1b630f196e","cross_cats_sorted":["cs.LG","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-20T05:57:38Z","title_canon_sha256":"7b3f7ca580054bc37a9aedf8c95a875f260cb23e85b858b10fd7e6fba1569ff6"},"schema_version":"1.0","source":{"id":"1810.08754","kind":"arxiv","version":1}},"canonical_sha256":"452f4535685f7518d5308d32602b4c520f8e6e2dc2698b44a213e61eaa152c4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"452f4535685f7518d5308d32602b4c520f8e6e2dc2698b44a213e61eaa152c4b","first_computed_at":"2026-05-17T23:50:23.321967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:23.321967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rH5Qa6NQ/TOhvN2bLSdbefP2Mw4L7qBVZV2z/TMAzO040t6JPZHrzIhMO9m58isr8b1dWdDv4nwQsdMxwcAPCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:23.322388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08754","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c64138615693ab0de4ffc7f7a6d989eb0103d2d75e2205a8011a488d589c99d","sha256:12eddfccddf6ad3783cd6f46063146277dd9e7aa5bba71395210172514b06b6c"],"state_sha256":"4c96f11c11d2633ced0b2dda610d5827ea987230f1e22e32f22e179e88495408"}