{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V6Q4A2OFBSLCBAX6QN5NP74FGM","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":"68d899ed4463575e5bfbbc82c09053314efb3c52dc8c3dcec4bdf1e0d9611e28","cross_cats_sorted":["cs.AI","cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-08T00:11:51Z","title_canon_sha256":"59e8775d4e1f351efa46afdd1bab106c61163a450920a7191bb93d09a7fbaabe"},"schema_version":"1.0","source":{"id":"1809.02721","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02721","created_at":"2026-05-18T00:00:34Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02721v3","created_at":"2026-05-18T00:00:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02721","created_at":"2026-05-18T00:00:34Z"},{"alias_kind":"pith_short_12","alias_value":"V6Q4A2OFBSLC","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"V6Q4A2OFBSLCBAX6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"V6Q4A2OF","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:6bb9b6b3b5b29416b8d11d82b672e12b17ddd731decfc899b192adf5cc7eec9c","target":"graph","created_at":"2026-05-18T00:00:34Z","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":"Graph Neural Networks (GNN) are a promising technique for bridging differential programming and combinatorial domains. GNNs employ trainable modules which can be assembled in different configurations that reflect the relational structure of each problem instance. In this paper, we show that GNNs can learn to solve, with very little supervision, the decision variant of the Traveling Salesperson Problem (TSP), a highly relevant $\\mathcal{NP}$-Complete problem. Our model is trained to function as an effective message-passing algorithm in which edges (embedded with their weights) communicate with ","authors_text":"Henrique Lemos, Luis Lamb, Marcelo O. R. Prates, Moshe Vardi, Pedro H. C. Avelar","cross_cats":["cs.AI","cs.NE","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-08T00:11:51Z","title":"Learning to Solve NP-Complete Problems - A Graph Neural Network for Decision TSP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02721","kind":"arxiv","version":3},"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":"sha256:0185347c2e43f2d7856a7a82319243a85ba0f0de7c6ef15679c4103c39a72652","target":"record","created_at":"2026-05-18T00:00:34Z","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":"68d899ed4463575e5bfbbc82c09053314efb3c52dc8c3dcec4bdf1e0d9611e28","cross_cats_sorted":["cs.AI","cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-08T00:11:51Z","title_canon_sha256":"59e8775d4e1f351efa46afdd1bab106c61163a450920a7191bb93d09a7fbaabe"},"schema_version":"1.0","source":{"id":"1809.02721","kind":"arxiv","version":3}},"canonical_sha256":"afa1c069c50c962082fe837ad7ff853321337e8c1ff9aa0fc3794c2bfa23b261","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afa1c069c50c962082fe837ad7ff853321337e8c1ff9aa0fc3794c2bfa23b261","first_computed_at":"2026-05-18T00:00:34.805940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:34.805940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ugk3vq98l6fn4xecpOZ/QI5mFPuRSSs3GvI4Ie1PGxkX/ko1TPyEnGTcf8xkO7n/wNGfiXy8AY2PCX/qiqVKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:34.806513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02721","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0185347c2e43f2d7856a7a82319243a85ba0f0de7c6ef15679c4103c39a72652","sha256:6bb9b6b3b5b29416b8d11d82b672e12b17ddd731decfc899b192adf5cc7eec9c"],"state_sha256":"e995cba5c4b81884eaaa9404db1224c43ad960aecff1092db0d967b5a3d8b99b"}