{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MTQWQOVEY5KTB4QFULZYIJJFBP","short_pith_number":"pith:MTQWQOVE","canonical_record":{"source":{"id":"1901.08710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-25T01:47:59Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"d89d6085796bbd5688e042c2f522fc6f1a250aa7bc5662cb66a0e38f9eb2ade4","abstract_canon_sha256":"5c2b47cb444ec5d3588dcb66e288071040527784bd67b50d0b42f2d9d1c9ec03"},"schema_version":"1.0"},"canonical_sha256":"64e1683aa4c75530f205a2f38425250bd109ff4b8ff6f53bb54ba249d0b6412a","source":{"kind":"arxiv","id":"1901.08710","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.08710","created_at":"2026-05-17T23:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1901.08710v1","created_at":"2026-05-17T23:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08710","created_at":"2026-05-17T23:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"MTQWQOVEY5KT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"MTQWQOVEY5KTB4QF","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"MTQWQOVE","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MTQWQOVEY5KTB4QFULZYIJJFBP","target":"record","payload":{"canonical_record":{"source":{"id":"1901.08710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-25T01:47:59Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"d89d6085796bbd5688e042c2f522fc6f1a250aa7bc5662cb66a0e38f9eb2ade4","abstract_canon_sha256":"5c2b47cb444ec5d3588dcb66e288071040527784bd67b50d0b42f2d9d1c9ec03"},"schema_version":"1.0"},"canonical_sha256":"64e1683aa4c75530f205a2f38425250bd109ff4b8ff6f53bb54ba249d0b6412a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:33.336721Z","signature_b64":"IN2Q2A5H56dJJ2G3MvFHJQMLE8QdRNjJ6bIl2wq5mIYDsnay/m0CTQdfI72QF0JNpTuPNO0LEH9Oja8qV6s8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64e1683aa4c75530f205a2f38425250bd109ff4b8ff6f53bb54ba249d0b6412a","last_reissued_at":"2026-05-17T23:55:33.335940Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:33.335940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.08710","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":"2026-05-17T23:55:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iki9MVyXXkKt9Zbz8yN4uIIO5pqkqOcHVvxkmsVy9ddj4NWAnaTY8c6H2dD9SwbE3+WY0cBo9qZiFdzVpzpVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:11:56.434835Z"},"content_sha256":"7a322bca0ad36027f315e5d6704ddc83902cee40288388b3b9d37f6d12b7054f","schema_version":"1.0","event_id":"sha256:7a322bca0ad36027f315e5d6704ddc83902cee40288388b3b9d37f6d12b7054f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MTQWQOVEY5KTB4QFULZYIJJFBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When Can Neural Networks Learn Connected Decision Regions?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dinh Phung, Trung Le","submitted_at":"2019-01-25T01:47:59Z","abstract_excerpt":"Previous work has questioned the conditions under which the decision regions of a neural network are connected and further showed the implications of the corresponding theory to the problem of adversarial manipulation of classifiers. It has been proven that for a class of activation functions including leaky ReLU, neural networks having a pyramidal structure, that is no layer has more hidden units than the input dimension, produce necessarily connected decision regions. In this paper, we advance this important result by further developing the sufficient and necessary conditions under which the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08710","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":""},"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":"2026-05-17T23:55:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBcthnr+REeFM2CV65/E4gbkyXXSSGhhZ3n7FAamU2RNTCwzVU8K6doch3nyASCFsVGKO+EORQnjPjlR4HJCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:11:56.435560Z"},"content_sha256":"437a1aa90ab3f85a5f562a1399141c55a72d4a59b28aef50818314309acc7496","schema_version":"1.0","event_id":"sha256:437a1aa90ab3f85a5f562a1399141c55a72d4a59b28aef50818314309acc7496"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTQWQOVEY5KTB4QFULZYIJJFBP/bundle.json","state_url":"https://pith.science/pith/MTQWQOVEY5KTB4QFULZYIJJFBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTQWQOVEY5KTB4QFULZYIJJFBP/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":"2026-06-08T18:11:56Z","links":{"resolver":"https://pith.science/pith/MTQWQOVEY5KTB4QFULZYIJJFBP","bundle":"https://pith.science/pith/MTQWQOVEY5KTB4QFULZYIJJFBP/bundle.json","state":"https://pith.science/pith/MTQWQOVEY5KTB4QFULZYIJJFBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTQWQOVEY5KTB4QFULZYIJJFBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MTQWQOVEY5KTB4QFULZYIJJFBP","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":"5c2b47cb444ec5d3588dcb66e288071040527784bd67b50d0b42f2d9d1c9ec03","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-25T01:47:59Z","title_canon_sha256":"d89d6085796bbd5688e042c2f522fc6f1a250aa7bc5662cb66a0e38f9eb2ade4"},"schema_version":"1.0","source":{"id":"1901.08710","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.08710","created_at":"2026-05-17T23:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1901.08710v1","created_at":"2026-05-17T23:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08710","created_at":"2026-05-17T23:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"MTQWQOVEY5KT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"MTQWQOVEY5KTB4QF","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"MTQWQOVE","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:437a1aa90ab3f85a5f562a1399141c55a72d4a59b28aef50818314309acc7496","target":"graph","created_at":"2026-05-17T23:55:33Z","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"},"paper":{"abstract_excerpt":"Previous work has questioned the conditions under which the decision regions of a neural network are connected and further showed the implications of the corresponding theory to the problem of adversarial manipulation of classifiers. It has been proven that for a class of activation functions including leaky ReLU, neural networks having a pyramidal structure, that is no layer has more hidden units than the input dimension, produce necessarily connected decision regions. In this paper, we advance this important result by further developing the sufficient and necessary conditions under which the","authors_text":"Dinh Phung, Trung Le","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-25T01:47:59Z","title":"When Can Neural Networks Learn Connected Decision Regions?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08710","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":"sha256:7a322bca0ad36027f315e5d6704ddc83902cee40288388b3b9d37f6d12b7054f","target":"record","created_at":"2026-05-17T23:55:33Z","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":"5c2b47cb444ec5d3588dcb66e288071040527784bd67b50d0b42f2d9d1c9ec03","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-25T01:47:59Z","title_canon_sha256":"d89d6085796bbd5688e042c2f522fc6f1a250aa7bc5662cb66a0e38f9eb2ade4"},"schema_version":"1.0","source":{"id":"1901.08710","kind":"arxiv","version":1}},"canonical_sha256":"64e1683aa4c75530f205a2f38425250bd109ff4b8ff6f53bb54ba249d0b6412a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64e1683aa4c75530f205a2f38425250bd109ff4b8ff6f53bb54ba249d0b6412a","first_computed_at":"2026-05-17T23:55:33.335940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:33.335940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IN2Q2A5H56dJJ2G3MvFHJQMLE8QdRNjJ6bIl2wq5mIYDsnay/m0CTQdfI72QF0JNpTuPNO0LEH9Oja8qV6s8BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:33.336721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.08710","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a322bca0ad36027f315e5d6704ddc83902cee40288388b3b9d37f6d12b7054f","sha256:437a1aa90ab3f85a5f562a1399141c55a72d4a59b28aef50818314309acc7496"],"state_sha256":"b3b3f06a7a49de8dbfee53768bf42ca73bcbe20114d92402f0925c8128c3be1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Yn7/jpMvUd657bK8Jp0lNtMDe9W6g8dSiWyXSN4Pohet6i1GyFzYmevDFov8nCZK1zI8wisa2e3RSQJosHfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:11:56.440108Z","bundle_sha256":"086dff2597559fa2f19b3d85be69ba5e9017bcf7dc180eae848c415439a9a2c1"}}