{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RMVK64RTQAOP3QQDSYDTYZXKJK","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":"b281998c0daf2b47b21ab177d115fe9a8dc5b42dd813a86879e0d1657a8109dd","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-08-30T08:58:23Z","title_canon_sha256":"e50eb5c1c668a104b1577c0e4907325b6e6d536b4ef20af841269a4d6e010a35"},"schema_version":"1.0","source":{"id":"2308.15873","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.15873","created_at":"2026-07-05T07:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"2308.15873v2","created_at":"2026-07-05T07:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.15873","created_at":"2026-07-05T07:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"RMVK64RTQAOP","created_at":"2026-07-05T07:09:52Z"},{"alias_kind":"pith_short_16","alias_value":"RMVK64RTQAOP3QQD","created_at":"2026-07-05T07:09:52Z"},{"alias_kind":"pith_short_8","alias_value":"RMVK64RT","created_at":"2026-07-05T07:09:52Z"}],"graph_snapshots":[{"event_id":"sha256:91f980c32a91c83b5cf9b5e1807dec5b57bcb2f735a7ece6d54445b0d4bc8073","target":"graph","created_at":"2026-07-05T07:09:52Z","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/2308.15873/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, there has been a growing focus on determining the minimum width requirements for achieving the universal approximation property in deep, narrow Multi-Layer Perceptrons (MLPs). Among these challenges, one particularly challenging task is approximating a continuous function under the uniform norm, as indicated by the significant disparity between its lower and upper bounds. To address this problem, we propose a framework that simplifies finding the minimum width for deep, narrow MLPs into determining a purely geometrical function denoted as $w(d_x, d_y)$. This function relies solely on","authors_text":"Geonho Hwang","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-08-30T08:58:23Z","title":"Minimum Width for Deep, Narrow MLP: A Diffeomorphism Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.15873","kind":"arxiv","version":2},"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":"sha256:2da3d8120e2675a0ffe1c6888a0b47f56881e66f8f185223e2e7b69947d353d6","target":"record","created_at":"2026-07-05T07:09:52Z","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":"b281998c0daf2b47b21ab177d115fe9a8dc5b42dd813a86879e0d1657a8109dd","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-08-30T08:58:23Z","title_canon_sha256":"e50eb5c1c668a104b1577c0e4907325b6e6d536b4ef20af841269a4d6e010a35"},"schema_version":"1.0","source":{"id":"2308.15873","kind":"arxiv","version":2}},"canonical_sha256":"8b2aaf7233801cfdc20396073c66ea4abc0c5288a0a0b80f139b50e189e551e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b2aaf7233801cfdc20396073c66ea4abc0c5288a0a0b80f139b50e189e551e3","first_computed_at":"2026-07-05T07:09:52.145416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:09:52.145416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l+nmj3A0fJDB4zx6WWPyJLrWwEjOMGx9wI2fgNHqTcp7OhAfGCths+GIOCkOCcEMQA0wiGm2D9BYD+RwO9hhAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:09:52.145907Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.15873","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2da3d8120e2675a0ffe1c6888a0b47f56881e66f8f185223e2e7b69947d353d6","sha256:91f980c32a91c83b5cf9b5e1807dec5b57bcb2f735a7ece6d54445b0d4bc8073"],"state_sha256":"0b96a0e0996fde231844a2007de4b5dd0d89531a1cd6dae0137a35d0276a4585"}