{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:INIQUM34XBF4CBU3LBHUTV3ZRL","short_pith_number":"pith:INIQUM34","canonical_record":{"source":{"id":"2411.15111","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-11-22T18:25:13Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"6de59b2beccfefa4599595cb74c8909ab21ea5b3a5dd86adfc445c6caa08bc4a","abstract_canon_sha256":"24a011d52ddaa7c7890d59a6f68c3383e2ea5502fc17bbc25097157a364d1633"},"schema_version":"1.0"},"canonical_sha256":"43510a337cb84bc1069b584f49d7798acc7c1998414a645937d2bad388baef66","source":{"kind":"arxiv","id":"2411.15111","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15111","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15111v4","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15111","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"INIQUM34XBF4","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"pith_short_16","alias_value":"INIQUM34XBF4CBU3","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"pith_short_8","alias_value":"INIQUM34","created_at":"2026-07-05T11:20:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:INIQUM34XBF4CBU3LBHUTV3ZRL","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15111","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-11-22T18:25:13Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"6de59b2beccfefa4599595cb74c8909ab21ea5b3a5dd86adfc445c6caa08bc4a","abstract_canon_sha256":"24a011d52ddaa7c7890d59a6f68c3383e2ea5502fc17bbc25097157a364d1633"},"schema_version":"1.0"},"canonical_sha256":"43510a337cb84bc1069b584f49d7798acc7c1998414a645937d2bad388baef66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:20:48.160138Z","signature_b64":"D10a4DN4RIObw8dzntzEr7YXrgSomHj0hq2qC7vgtg/wuRe63UkM/nJHAS0UUqGCH40KYdog4uWz6lfiHva8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43510a337cb84bc1069b584f49d7798acc7c1998414a645937d2bad388baef66","last_reissued_at":"2026-07-05T11:20:48.159622Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:20:48.159622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15111","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JSzSKp0i4HqCBYrO4VPio6EHjlgJfUXOTnpC5fqCuL7iMQON4lKicn+Cy460uHXmNKoXryBgQf0DeyG5/vJyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T03:31:03.959853Z"},"content_sha256":"f14cdb0a4858c70abf8a4319b3a5c04ed01c6b0a0aeef4cb09a8fc8e471a7365","schema_version":"1.0","event_id":"sha256:f14cdb0a4858c70abf8a4319b3a5c04ed01c6b0a0aeef4cb09a8fc8e471a7365"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:INIQUM34XBF4CBU3LBHUTV3ZRL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.NE","authors_text":"Afrah Farea, Mustafa Serdar Celebi","submitted_at":"2024-11-22T18:25:13Z","abstract_excerpt":"Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs). However, they face challenges related to spectral bias (the tendency to learn low-frequency components while struggling with high-frequency features) and unstable convergence dynamics (mainly stemming from the multi-objective nature of the PINN loss function). These limitations impact their accuracy for problems involving rapid oscillations, sharp gradients, and complex boundary behaviors. We systematically investigate learnable activation functions as a solution to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15111","kind":"arxiv","version":4},"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/2411.15111/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":"2026-07-05T11:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZT9mAzaDIAe5Ihvt4F7QG7g+c9XHqRYKc/S0cV2BPRtr4e9GXCQSoN3X9mWtQP349fr7UoynSPJE8cGIprjMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T03:31:03.960365Z"},"content_sha256":"2eb8f1d017bbbad15daa6c9166513fe73c79a4b0e4084f1a7ec29d9e2a790617","schema_version":"1.0","event_id":"sha256:2eb8f1d017bbbad15daa6c9166513fe73c79a4b0e4084f1a7ec29d9e2a790617"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/INIQUM34XBF4CBU3LBHUTV3ZRL/bundle.json","state_url":"https://pith.science/pith/INIQUM34XBF4CBU3LBHUTV3ZRL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/INIQUM34XBF4CBU3LBHUTV3ZRL/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":"2026-08-12T03:31:03Z","links":{"resolver":"https://pith.science/pith/INIQUM34XBF4CBU3LBHUTV3ZRL","bundle":"https://pith.science/pith/INIQUM34XBF4CBU3LBHUTV3ZRL/bundle.json","state":"https://pith.science/pith/INIQUM34XBF4CBU3LBHUTV3ZRL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/INIQUM34XBF4CBU3LBHUTV3ZRL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:INIQUM34XBF4CBU3LBHUTV3ZRL","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":"24a011d52ddaa7c7890d59a6f68c3383e2ea5502fc17bbc25097157a364d1633","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-11-22T18:25:13Z","title_canon_sha256":"6de59b2beccfefa4599595cb74c8909ab21ea5b3a5dd86adfc445c6caa08bc4a"},"schema_version":"1.0","source":{"id":"2411.15111","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15111","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15111v4","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15111","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"INIQUM34XBF4","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"pith_short_16","alias_value":"INIQUM34XBF4CBU3","created_at":"2026-07-05T11:20:48Z"},{"alias_kind":"pith_short_8","alias_value":"INIQUM34","created_at":"2026-07-05T11:20:48Z"}],"graph_snapshots":[{"event_id":"sha256:2eb8f1d017bbbad15daa6c9166513fe73c79a4b0e4084f1a7ec29d9e2a790617","target":"graph","created_at":"2026-07-05T11:20:48Z","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/2411.15111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs). However, they face challenges related to spectral bias (the tendency to learn low-frequency components while struggling with high-frequency features) and unstable convergence dynamics (mainly stemming from the multi-objective nature of the PINN loss function). These limitations impact their accuracy for problems involving rapid oscillations, sharp gradients, and complex boundary behaviors. We systematically investigate learnable activation functions as a solution to ","authors_text":"Afrah Farea, Mustafa Serdar Celebi","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-11-22T18:25:13Z","title":"Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15111","kind":"arxiv","version":4},"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:f14cdb0a4858c70abf8a4319b3a5c04ed01c6b0a0aeef4cb09a8fc8e471a7365","target":"record","created_at":"2026-07-05T11:20:48Z","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":"24a011d52ddaa7c7890d59a6f68c3383e2ea5502fc17bbc25097157a364d1633","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-11-22T18:25:13Z","title_canon_sha256":"6de59b2beccfefa4599595cb74c8909ab21ea5b3a5dd86adfc445c6caa08bc4a"},"schema_version":"1.0","source":{"id":"2411.15111","kind":"arxiv","version":4}},"canonical_sha256":"43510a337cb84bc1069b584f49d7798acc7c1998414a645937d2bad388baef66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43510a337cb84bc1069b584f49d7798acc7c1998414a645937d2bad388baef66","first_computed_at":"2026-07-05T11:20:48.159622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:48.159622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D10a4DN4RIObw8dzntzEr7YXrgSomHj0hq2qC7vgtg/wuRe63UkM/nJHAS0UUqGCH40KYdog4uWz6lfiHva8Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:48.160138Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15111","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f14cdb0a4858c70abf8a4319b3a5c04ed01c6b0a0aeef4cb09a8fc8e471a7365","sha256:2eb8f1d017bbbad15daa6c9166513fe73c79a4b0e4084f1a7ec29d9e2a790617"],"state_sha256":"592c31b6e63dc75a4e9bad43f7bf3e24319c8769afbcb91f319cadd10ff497df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tr+W7/2OdnpU5rlY82RLt58HGC29Dtr+YrxOnzFZKtny0QCulgIirmYyICg1mjbCVa2gVPPHHsFs4vh7KRRDCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T03:31:03.967897Z","bundle_sha256":"e92ddf8c77f59812fafeead64088ecc3dee8e134114320be3873552aa21e0ee3"}}