{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:7E24PH7HSLKUO32QYKXNSCQAUT","short_pith_number":"pith:7E24PH7H","canonical_record":{"source":{"id":"2012.10047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-18T04:19:30Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"d1802c5e8f49330141a687fe4d1c8102026172074be4f9f2d9ccef748a199ce1","abstract_canon_sha256":"78a1441b76e55cbc2462b63c2939e0613048d5659398258b84dcfa0350deda98"},"schema_version":"1.0"},"canonical_sha256":"f935c79fe792d5476f50c2aed90a00a4c18c42cfcd79c90444efbf58027e0bc5","source":{"kind":"arxiv","id":"2012.10047","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.10047","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"2012.10047v1","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.10047","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"7E24PH7HSLKU","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"pith_short_16","alias_value":"7E24PH7HSLKUO32Q","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"pith_short_8","alias_value":"7E24PH7H","created_at":"2026-07-05T02:49:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:7E24PH7HSLKUO32QYKXNSCQAUT","target":"record","payload":{"canonical_record":{"source":{"id":"2012.10047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-18T04:19:30Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"d1802c5e8f49330141a687fe4d1c8102026172074be4f9f2d9ccef748a199ce1","abstract_canon_sha256":"78a1441b76e55cbc2462b63c2939e0613048d5659398258b84dcfa0350deda98"},"schema_version":"1.0"},"canonical_sha256":"f935c79fe792d5476f50c2aed90a00a4c18c42cfcd79c90444efbf58027e0bc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:49:22.228203Z","signature_b64":"XXvcOaLs0z7jqPY9YEM/MABx9ZO/R0RrIWYvi4jGrd5bXTS+dsb/CUV60lJze1QkggeJLp43M+qKMgND5AE4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f935c79fe792d5476f50c2aed90a00a4c18c42cfcd79c90444efbf58027e0bc5","last_reissued_at":"2026-07-05T02:49:22.227733Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:49:22.227733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.10047","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":"2026-07-05T02:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4yN0AQmuqA2UmZdfSfB7BYuDZebrMBzkRveD+pHYLJWD84qrSpkfh44Tfa2TtKMDpaZOXfbWwBNidhN6cld/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T04:51:35.281190Z"},"content_sha256":"8065398e6b80c26ce38ee0cee4ad6a56472aede417e8640cd326a7220e0e455d","schema_version":"1.0","event_id":"sha256:8065398e6b80c26ce38ee0cee4ad6a56472aede417e8640cd326a7220e0e455d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:7E24PH7HSLKUO32QYKXNSCQAUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Hanwen Wang, Paris Perdikaris, Sifan Wang","submitted_at":"2020-12-18T04:19:30Z","abstract_excerpt":"Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features. In this work we investigate this limitation through the lens of Neural Tangent Kernel (NTK) theory and elucidate how PINNs are biased towards learning functions along the dominant eigen-directions of their limiting NTK. Using this observation, we construct novel architectures that employ spatio-temporal and multi-scale ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10047","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/2012.10047/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":"2026-07-05T02:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rs4cs1JZyjzbVcVkwJjBOn6ySDkJ8r+I2PCPlF1UmGTWv3qOcadBUew1skjBcoRNlN8jb6g43IalrS9qpoZuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T04:51:35.281782Z"},"content_sha256":"34bd6dd81f2e969e71b6ee8ced0d0fc2d0c80285f3facf85b5e3046cfb085493","schema_version":"1.0","event_id":"sha256:34bd6dd81f2e969e71b6ee8ced0d0fc2d0c80285f3facf85b5e3046cfb085493"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7E24PH7HSLKUO32QYKXNSCQAUT/bundle.json","state_url":"https://pith.science/pith/7E24PH7HSLKUO32QYKXNSCQAUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7E24PH7HSLKUO32QYKXNSCQAUT/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":"2026-08-11T04:51:35Z","links":{"resolver":"https://pith.science/pith/7E24PH7HSLKUO32QYKXNSCQAUT","bundle":"https://pith.science/pith/7E24PH7HSLKUO32QYKXNSCQAUT/bundle.json","state":"https://pith.science/pith/7E24PH7HSLKUO32QYKXNSCQAUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7E24PH7HSLKUO32QYKXNSCQAUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:7E24PH7HSLKUO32QYKXNSCQAUT","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":"78a1441b76e55cbc2462b63c2939e0613048d5659398258b84dcfa0350deda98","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-18T04:19:30Z","title_canon_sha256":"d1802c5e8f49330141a687fe4d1c8102026172074be4f9f2d9ccef748a199ce1"},"schema_version":"1.0","source":{"id":"2012.10047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.10047","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"2012.10047v1","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.10047","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"7E24PH7HSLKU","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"pith_short_16","alias_value":"7E24PH7HSLKUO32Q","created_at":"2026-07-05T02:49:22Z"},{"alias_kind":"pith_short_8","alias_value":"7E24PH7H","created_at":"2026-07-05T02:49:22Z"}],"graph_snapshots":[{"event_id":"sha256:34bd6dd81f2e969e71b6ee8ced0d0fc2d0c80285f3facf85b5e3046cfb085493","target":"graph","created_at":"2026-07-05T02:49:22Z","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/2012.10047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features. In this work we investigate this limitation through the lens of Neural Tangent Kernel (NTK) theory and elucidate how PINNs are biased towards learning functions along the dominant eigen-directions of their limiting NTK. Using this observation, we construct novel architectures that employ spatio-temporal and multi-scale ra","authors_text":"Hanwen Wang, Paris Perdikaris, Sifan Wang","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-18T04:19:30Z","title":"On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10047","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":"sha256:8065398e6b80c26ce38ee0cee4ad6a56472aede417e8640cd326a7220e0e455d","target":"record","created_at":"2026-07-05T02:49:22Z","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":"78a1441b76e55cbc2462b63c2939e0613048d5659398258b84dcfa0350deda98","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-18T04:19:30Z","title_canon_sha256":"d1802c5e8f49330141a687fe4d1c8102026172074be4f9f2d9ccef748a199ce1"},"schema_version":"1.0","source":{"id":"2012.10047","kind":"arxiv","version":1}},"canonical_sha256":"f935c79fe792d5476f50c2aed90a00a4c18c42cfcd79c90444efbf58027e0bc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f935c79fe792d5476f50c2aed90a00a4c18c42cfcd79c90444efbf58027e0bc5","first_computed_at":"2026-07-05T02:49:22.227733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:49:22.227733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XXvcOaLs0z7jqPY9YEM/MABx9ZO/R0RrIWYvi4jGrd5bXTS+dsb/CUV60lJze1QkggeJLp43M+qKMgND5AE4Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:49:22.228203Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.10047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8065398e6b80c26ce38ee0cee4ad6a56472aede417e8640cd326a7220e0e455d","sha256:34bd6dd81f2e969e71b6ee8ced0d0fc2d0c80285f3facf85b5e3046cfb085493"],"state_sha256":"90f76010ccf9053f6dd5b4c0f1363685958bfccae1c509c686ce91fb1b96cc67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j4lcjrCfngExC5ZijB0RfQg1J57to1QDlDhwCB3Xd55rNjYsgYWdAOBLeCjf8LiKkZyDtC0bp7NUVxAAXlCEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T04:51:35.287437Z","bundle_sha256":"fc9524002570516c592a3ce93924b6e68bd30aa80a0888f0d54d8a35ff4f51e9"}}