{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:DU4FIVOJPULYZNV7LJMYVFP2DB","short_pith_number":"pith:DU4FIVOJ","canonical_record":{"source":{"id":"2305.00322","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-29T18:33:39Z","cross_cats_sorted":[],"title_canon_sha256":"f5ea0dfc507234d42f917e818aee4d3ee01bb258746d8862ecba5d9592290e59","abstract_canon_sha256":"fd7028e87e0a6c59e209c85e481a8ed2a01077fa4cfc6adc998a75aef53330b8"},"schema_version":"1.0"},"canonical_sha256":"1d385455c97d178cb6bf5a598a95fa1878433e8828b984ac43bf15a56f5a84e0","source":{"kind":"arxiv","id":"2305.00322","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.00322","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"arxiv_version","alias_value":"2305.00322v1","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.00322","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"pith_short_12","alias_value":"DU4FIVOJPULY","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"pith_short_16","alias_value":"DU4FIVOJPULYZNV7","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"pith_short_8","alias_value":"DU4FIVOJ","created_at":"2026-07-05T06:05:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:DU4FIVOJPULYZNV7LJMYVFP2DB","target":"record","payload":{"canonical_record":{"source":{"id":"2305.00322","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-29T18:33:39Z","cross_cats_sorted":[],"title_canon_sha256":"f5ea0dfc507234d42f917e818aee4d3ee01bb258746d8862ecba5d9592290e59","abstract_canon_sha256":"fd7028e87e0a6c59e209c85e481a8ed2a01077fa4cfc6adc998a75aef53330b8"},"schema_version":"1.0"},"canonical_sha256":"1d385455c97d178cb6bf5a598a95fa1878433e8828b984ac43bf15a56f5a84e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:05:40.027917Z","signature_b64":"fYLWkJJlmR+43lOU9xCLTIJG8fxDobvqnT0LSa+58ZwbrEDmRJ9oWld12TAhl9uxW1VXYFRPjjJIpIAzrDkOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d385455c97d178cb6bf5a598a95fa1878433e8828b984ac43bf15a56f5a84e0","last_reissued_at":"2026-07-05T06:05:40.027581Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:05:40.027581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.00322","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:05:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nyLq3V/El9Fuzh2zhWJkosK6Gy5JKxm3XQw3/7C1gcDygaeac6JrVcSEwZTAOAMtgf+yFmNHJ7a5gk215V4OAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T07:15:06.967731Z"},"content_sha256":"76f91bde8ee20d199800205be032eba19ae6cf34189ffcca5d281a0d856e87d4","schema_version":"1.0","event_id":"sha256:76f91bde8ee20d199800205be032eba19ae6cf34189ffcca5d281a0d856e87d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:DU4FIVOJPULYZNV7LJMYVFP2DB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toward $L_\\infty$-recovery of Nonlinear Functions: A Polynomial Sample Complexity Bound for Gaussian Random Fields","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Kefan Dong, Tengyu Ma","submitted_at":"2023-04-29T18:33:39Z","abstract_excerpt":"Many machine learning applications require learning a function with a small worst-case error over the entire input domain, that is, the $L_\\infty$-error, whereas most existing theoretical works only guarantee recovery in average errors such as the $L_2$-error. $L_\\infty$-recovery from polynomial samples is even impossible for seemingly simple function classes such as constant-norm infinite-width two-layer neural nets. This paper makes some initial steps beyond the impossibility results by leveraging the randomness in the ground-truth functions. We prove a polynomial sample complexity bound for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.00322","kind":"arxiv","version":1},"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/2305.00322/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:05:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XFbY8pSssCEQOnV+T2+JIL+GPJbCGLmFvpUfiXUdig0vNEozwGnv91yoSsVOp3h6uUPLP+yKmiwOdNr9xTkkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T07:15:06.968542Z"},"content_sha256":"4e9f83168430298702bf8deeee35bfcb7ab839ac857dd81dc0ed669503f4dcfa","schema_version":"1.0","event_id":"sha256:4e9f83168430298702bf8deeee35bfcb7ab839ac857dd81dc0ed669503f4dcfa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DU4FIVOJPULYZNV7LJMYVFP2DB/bundle.json","state_url":"https://pith.science/pith/DU4FIVOJPULYZNV7LJMYVFP2DB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DU4FIVOJPULYZNV7LJMYVFP2DB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-08T07:15:06Z","links":{"resolver":"https://pith.science/pith/DU4FIVOJPULYZNV7LJMYVFP2DB","bundle":"https://pith.science/pith/DU4FIVOJPULYZNV7LJMYVFP2DB/bundle.json","state":"https://pith.science/pith/DU4FIVOJPULYZNV7LJMYVFP2DB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DU4FIVOJPULYZNV7LJMYVFP2DB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:DU4FIVOJPULYZNV7LJMYVFP2DB","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":"fd7028e87e0a6c59e209c85e481a8ed2a01077fa4cfc6adc998a75aef53330b8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-29T18:33:39Z","title_canon_sha256":"f5ea0dfc507234d42f917e818aee4d3ee01bb258746d8862ecba5d9592290e59"},"schema_version":"1.0","source":{"id":"2305.00322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.00322","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"arxiv_version","alias_value":"2305.00322v1","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.00322","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"pith_short_12","alias_value":"DU4FIVOJPULY","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"pith_short_16","alias_value":"DU4FIVOJPULYZNV7","created_at":"2026-07-05T06:05:40Z"},{"alias_kind":"pith_short_8","alias_value":"DU4FIVOJ","created_at":"2026-07-05T06:05:40Z"}],"graph_snapshots":[{"event_id":"sha256:4e9f83168430298702bf8deeee35bfcb7ab839ac857dd81dc0ed669503f4dcfa","target":"graph","created_at":"2026-07-05T06:05:40Z","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/2305.00322/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many machine learning applications require learning a function with a small worst-case error over the entire input domain, that is, the $L_\\infty$-error, whereas most existing theoretical works only guarantee recovery in average errors such as the $L_2$-error. $L_\\infty$-recovery from polynomial samples is even impossible for seemingly simple function classes such as constant-norm infinite-width two-layer neural nets. This paper makes some initial steps beyond the impossibility results by leveraging the randomness in the ground-truth functions. We prove a polynomial sample complexity bound for","authors_text":"Kefan Dong, Tengyu Ma","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-29T18:33:39Z","title":"Toward $L_\\infty$-recovery of Nonlinear Functions: A Polynomial Sample Complexity Bound for Gaussian Random Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.00322","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":"sha256:76f91bde8ee20d199800205be032eba19ae6cf34189ffcca5d281a0d856e87d4","target":"record","created_at":"2026-07-05T06:05:40Z","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":"fd7028e87e0a6c59e209c85e481a8ed2a01077fa4cfc6adc998a75aef53330b8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2023-04-29T18:33:39Z","title_canon_sha256":"f5ea0dfc507234d42f917e818aee4d3ee01bb258746d8862ecba5d9592290e59"},"schema_version":"1.0","source":{"id":"2305.00322","kind":"arxiv","version":1}},"canonical_sha256":"1d385455c97d178cb6bf5a598a95fa1878433e8828b984ac43bf15a56f5a84e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d385455c97d178cb6bf5a598a95fa1878433e8828b984ac43bf15a56f5a84e0","first_computed_at":"2026-07-05T06:05:40.027581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:05:40.027581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fYLWkJJlmR+43lOU9xCLTIJG8fxDobvqnT0LSa+58ZwbrEDmRJ9oWld12TAhl9uxW1VXYFRPjjJIpIAzrDkOAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:05:40.027917Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.00322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76f91bde8ee20d199800205be032eba19ae6cf34189ffcca5d281a0d856e87d4","sha256:4e9f83168430298702bf8deeee35bfcb7ab839ac857dd81dc0ed669503f4dcfa"],"state_sha256":"bf6bbad4bc2466b8ee17c4194f5c91144cb198003008322554456ad323f7a236"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I027NOfp5i96lK5rYOMgM5Qn7aeFsu2HhtL5nPwI420i2TltxaadvPdDuH/GLSFbH44HBtgiVF2DwwAJYlgVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T07:15:06.972090Z","bundle_sha256":"003c20df51ca93369537b68573cb35c488febaaf804244040bff563021223b65"}}