{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:3SVSZISXCJ5CZJY3URFHKANTCZ","short_pith_number":"pith:3SVSZISX","canonical_record":{"source":{"id":"2009.11848","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-24T17:48:59Z","cross_cats_sorted":["cs.AI","cs.CV","stat.ML"],"title_canon_sha256":"e12e92ccbf01d1585ad19ccf6d45523251f73807b1d1e44ee196a096b1cf0498","abstract_canon_sha256":"6bb85e43b2dc698252c37a8c4bc10f52f1ab7164795c2772f29e2422097f6f30"},"schema_version":"1.0"},"canonical_sha256":"dcab2ca257127a2ca71ba44a7501b3164d58be5debb50a1fe90694e472215407","source":{"kind":"arxiv","id":"2009.11848","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11848","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11848v5","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11848","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"pith_short_12","alias_value":"3SVSZISXCJ5C","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"pith_short_16","alias_value":"3SVSZISXCJ5CZJY3","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"pith_short_8","alias_value":"3SVSZISX","created_at":"2026-07-05T02:19:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:3SVSZISXCJ5CZJY3URFHKANTCZ","target":"record","payload":{"canonical_record":{"source":{"id":"2009.11848","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-24T17:48:59Z","cross_cats_sorted":["cs.AI","cs.CV","stat.ML"],"title_canon_sha256":"e12e92ccbf01d1585ad19ccf6d45523251f73807b1d1e44ee196a096b1cf0498","abstract_canon_sha256":"6bb85e43b2dc698252c37a8c4bc10f52f1ab7164795c2772f29e2422097f6f30"},"schema_version":"1.0"},"canonical_sha256":"dcab2ca257127a2ca71ba44a7501b3164d58be5debb50a1fe90694e472215407","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:19:56.081656Z","signature_b64":"heatRctN8QzDwDydLEGkW8jyfxlM+sp/AU6HherI+KwQyOe0rZy5RCjpbraceQweY0fxCppGgwyUSZeFuAx+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcab2ca257127a2ca71ba44a7501b3164d58be5debb50a1fe90694e472215407","last_reissued_at":"2026-07-05T02:19:56.081174Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:19:56.081174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.11848","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:19:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YpMlNGny7T0/ySuuySlzXvjB3bOo9GsKARTD5UXBg+zT+vvpPQRyzpIs3m7xVLSSSMvlGGQc4AVlPM8R40RSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T08:04:04.770459Z"},"content_sha256":"7ad867bae086bb8cf5e5ca1521287029f40e71b0ff9ec8d89a7ad8193ea53816","schema_version":"1.0","event_id":"sha256:7ad867bae086bb8cf5e5ca1521287029f40e71b0ff9ec8d89a7ad8193ea53816"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:3SVSZISXCJ5CZJY3URFHKANTCZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CV","stat.ML"],"primary_cat":"cs.LG","authors_text":"Jingling Li, Ken-ichi Kawarabayashi, Keyulu Xu, Mozhi Zhang, Simon S. Du, Stefanie Jegelka","submitted_at":"2020-09-24T17:48:59Z","abstract_excerpt":"We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neural networks, a.k.a. multilayer perceptrons (MLPs), do not extrapolate well in certain simple tasks, Graph Neural Networks (GNNs) -- structured networks with MLP modules -- have shown some success in more complex tasks. Working towards a theoretical explanation, we identify conditions under which MLPs and GNNs extrapolate well. First, we quantify t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11848","kind":"arxiv","version":5},"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/2009.11848/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":"2026-07-05T02:19:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MwhWgRH6WcwlxQKs80+fLfzno5+ggNQTULvG5tlVQAylRhXPSi+Z9QR9BlP8qjM597SQ2YlCbb4I5npN+dx/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T08:04:04.771392Z"},"content_sha256":"b5e9a09956246d8d0c302313a652590a8ebdb8c93a410d2c2ec08abc0ea16ab0","schema_version":"1.0","event_id":"sha256:b5e9a09956246d8d0c302313a652590a8ebdb8c93a410d2c2ec08abc0ea16ab0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3SVSZISXCJ5CZJY3URFHKANTCZ/bundle.json","state_url":"https://pith.science/pith/3SVSZISXCJ5CZJY3URFHKANTCZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3SVSZISXCJ5CZJY3URFHKANTCZ/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":"2026-08-10T08:04:04Z","links":{"resolver":"https://pith.science/pith/3SVSZISXCJ5CZJY3URFHKANTCZ","bundle":"https://pith.science/pith/3SVSZISXCJ5CZJY3URFHKANTCZ/bundle.json","state":"https://pith.science/pith/3SVSZISXCJ5CZJY3URFHKANTCZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3SVSZISXCJ5CZJY3URFHKANTCZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3SVSZISXCJ5CZJY3URFHKANTCZ","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":"6bb85e43b2dc698252c37a8c4bc10f52f1ab7164795c2772f29e2422097f6f30","cross_cats_sorted":["cs.AI","cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-24T17:48:59Z","title_canon_sha256":"e12e92ccbf01d1585ad19ccf6d45523251f73807b1d1e44ee196a096b1cf0498"},"schema_version":"1.0","source":{"id":"2009.11848","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11848","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11848v5","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11848","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"pith_short_12","alias_value":"3SVSZISXCJ5C","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"pith_short_16","alias_value":"3SVSZISXCJ5CZJY3","created_at":"2026-07-05T02:19:56Z"},{"alias_kind":"pith_short_8","alias_value":"3SVSZISX","created_at":"2026-07-05T02:19:56Z"}],"graph_snapshots":[{"event_id":"sha256:b5e9a09956246d8d0c302313a652590a8ebdb8c93a410d2c2ec08abc0ea16ab0","target":"graph","created_at":"2026-07-05T02:19:56Z","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/2009.11848/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neural networks, a.k.a. multilayer perceptrons (MLPs), do not extrapolate well in certain simple tasks, Graph Neural Networks (GNNs) -- structured networks with MLP modules -- have shown some success in more complex tasks. Working towards a theoretical explanation, we identify conditions under which MLPs and GNNs extrapolate well. First, we quantify t","authors_text":"Jingling Li, Ken-ichi Kawarabayashi, Keyulu Xu, Mozhi Zhang, Simon S. Du, Stefanie Jegelka","cross_cats":["cs.AI","cs.CV","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-24T17:48:59Z","title":"How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11848","kind":"arxiv","version":5},"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":"sha256:7ad867bae086bb8cf5e5ca1521287029f40e71b0ff9ec8d89a7ad8193ea53816","target":"record","created_at":"2026-07-05T02:19:56Z","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":"6bb85e43b2dc698252c37a8c4bc10f52f1ab7164795c2772f29e2422097f6f30","cross_cats_sorted":["cs.AI","cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-09-24T17:48:59Z","title_canon_sha256":"e12e92ccbf01d1585ad19ccf6d45523251f73807b1d1e44ee196a096b1cf0498"},"schema_version":"1.0","source":{"id":"2009.11848","kind":"arxiv","version":5}},"canonical_sha256":"dcab2ca257127a2ca71ba44a7501b3164d58be5debb50a1fe90694e472215407","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcab2ca257127a2ca71ba44a7501b3164d58be5debb50a1fe90694e472215407","first_computed_at":"2026-07-05T02:19:56.081174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:19:56.081174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"heatRctN8QzDwDydLEGkW8jyfxlM+sp/AU6HherI+KwQyOe0rZy5RCjpbraceQweY0fxCppGgwyUSZeFuAx+Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:19:56.081656Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.11848","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ad867bae086bb8cf5e5ca1521287029f40e71b0ff9ec8d89a7ad8193ea53816","sha256:b5e9a09956246d8d0c302313a652590a8ebdb8c93a410d2c2ec08abc0ea16ab0"],"state_sha256":"d9fa94a48e88be146765f6aa7f15bd130ac0771dab52ef1b9a9c21aaedc1ba93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/Q4VEJCJGrP5ia4QPW9Vj82Lm44IZRJXqbdw0OgtfcNtdoGRCoWtHS++pDjDXJWXXDDNKTxegJsjooX6LQ2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T08:04:04.778275Z","bundle_sha256":"449f6440cb3f8ecb13f3113af093155534365ddb5fbed63d2b888c2ae4dc8785"}}