{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:MI3XJ7CWGIUOD6K75J6FMP77JL","short_pith_number":"pith:MI3XJ7CW","schema_version":"1.0","canonical_sha256":"623774fc563228e1f95fea7c563fff4adbd1185842a49407bb0ec4023c9c9b26","source":{"kind":"arxiv","id":"2110.07875","version":2},"attestation_state":"computed","paper":{"title":"Graph Neural Networks with Learnable Structural and Positional Representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Anh Tuan Luu, Thomas Laurent, Vijay Prakash Dwivedi, Xavier Bresson, Yoshua Bengio","submitted_at":"2021-10-15T05:59:15Z","abstract_excerpt":"Graph neural networks (GNNs) have become the standard learning architectures for graphs. GNNs have been applied to numerous domains ranging from quantum chemistry, recommender systems to knowledge graphs and natural language processing. A major issue with arbitrary graphs is the absence of canonical positional information of nodes, which decreases the representation power of GNNs to distinguish e.g. isomorphic nodes and other graph symmetries. An approach to tackle this issue is to introduce Positional Encoding (PE) of nodes, and inject it into the input layer, like in Transformers. Possible g"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2110.07875","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-10-15T05:59:15Z","cross_cats_sorted":[],"title_canon_sha256":"a4a0ff07795e1f05be6861a3118b5c4f8f40d1b443f5cf9363952339f8fc28bf","abstract_canon_sha256":"17ba3cccabaf64ceec04917e9845f51f15c5b3bce52fc4e9b43fb590e53a60c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:55:50.164082Z","signature_b64":"jwPNxeLNN5GmG2aU8j41Cmfm4xo8QvQL9ubcfz0aSrAdRZJjnY7cGJ0axJ6uJdYmsjvK/5vodHIz5269ORTLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"623774fc563228e1f95fea7c563fff4adbd1185842a49407bb0ec4023c9c9b26","last_reissued_at":"2026-07-05T03:55:50.163614Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:55:50.163614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graph Neural Networks with Learnable Structural and Positional Representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Anh Tuan Luu, Thomas Laurent, Vijay Prakash Dwivedi, Xavier Bresson, Yoshua Bengio","submitted_at":"2021-10-15T05:59:15Z","abstract_excerpt":"Graph neural networks (GNNs) have become the standard learning architectures for graphs. GNNs have been applied to numerous domains ranging from quantum chemistry, recommender systems to knowledge graphs and natural language processing. A major issue with arbitrary graphs is the absence of canonical positional information of nodes, which decreases the representation power of GNNs to distinguish e.g. isomorphic nodes and other graph symmetries. An approach to tackle this issue is to introduce Positional Encoding (PE) of nodes, and inject it into the input layer, like in Transformers. Possible g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.07875","kind":"arxiv","version":2},"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/2110.07875/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2110.07875","created_at":"2026-07-05T03:55:50.163670+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.07875v2","created_at":"2026-07-05T03:55:50.163670+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.07875","created_at":"2026-07-05T03:55:50.163670+00:00"},{"alias_kind":"pith_short_12","alias_value":"MI3XJ7CWGIUO","created_at":"2026-07-05T03:55:50.163670+00:00"},{"alias_kind":"pith_short_16","alias_value":"MI3XJ7CWGIUOD6K7","created_at":"2026-07-05T03:55:50.163670+00:00"},{"alias_kind":"pith_short_8","alias_value":"MI3XJ7CW","created_at":"2026-07-05T03:55:50.163670+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":16,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2607.08735","citing_title":"Learning Adaptive Solvers for Distributed Factor Graph Optimization on Matrix Lie Groups","ref_index":159,"is_internal_anchor":true},{"citing_arxiv_id":"2607.06224","citing_title":"Canopy: A Heterograph Foundation Model for Metabolic Engineering","ref_index":20,"is_internal_anchor":true},{"citing_arxiv_id":"2606.21333","citing_title":"Ramanujan Graph Rewiring with Non Negative Resistance Curvature","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2606.04154","citing_title":"EpiFormer: Learning Antigen-Antibody Interactions for Epitope Prediction via Geometric Deep Learning","ref_index":205,"is_internal_anchor":false},{"citing_arxiv_id":"2606.22429","citing_title":"Enhancing LLMs for Graph Tasks via Graph-aware LoRA Generation","ref_index":118,"is_internal_anchor":false},{"citing_arxiv_id":"2605.23708","citing_title":"Learning Dynamic Stability Landscapes in Synchronization Networks","ref_index":177,"is_internal_anchor":false},{"citing_arxiv_id":"2605.21600","citing_title":"ConTact: Contact-First Antibody CDR Design via Explicit Interface Reasoning","ref_index":227,"is_internal_anchor":false},{"citing_arxiv_id":"2605.21610","citing_title":"AgForce Enables Antigen-conditioned Generative Antibody Design","ref_index":227,"is_internal_anchor":false},{"citing_arxiv_id":"2605.21485","citing_title":"EvoStruct: Bridging Evolutionary and Structural Priors for Antibody CDR Design via Protein Language Model Adaptation","ref_index":227,"is_internal_anchor":false},{"citing_arxiv_id":"2509.21000","citing_title":"Feature Augmentation of GNNs for ILPs: Local Uniqueness Suffices","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2605.11910","citing_title":"Rethinking Positional Encoding for Neural Vehicle Routing","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2605.10247","citing_title":"Teaching LLMs to See Graphs: Unifying Text and Structural Reasoning","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04174","citing_title":"A Transferable Machine Learning Approach to Predict Optimized Orbitals for Electronic Structure Problems","ref_index":37,"is_internal_anchor":false},{"citing_arxiv_id":"2605.00354","citing_title":"VQ-SAD: Vector Quantized Structure Aware Diffusion For Molecule Generation","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15273","citing_title":"How Embeddings Shape Graph Neural Networks: Classical vs Quantum-Oriented Node Representations","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15699","citing_title":"Frequency-Corrupt Based Graph Self-Supervised Learning","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MI3XJ7CWGIUOD6K75J6FMP77JL","json":"https://pith.science/pith/MI3XJ7CWGIUOD6K75J6FMP77JL.json","graph_json":"https://pith.science/api/pith-number/MI3XJ7CWGIUOD6K75J6FMP77JL/graph.json","events_json":"https://pith.science/api/pith-number/MI3XJ7CWGIUOD6K75J6FMP77JL/events.json","paper":"https://pith.science/paper/MI3XJ7CW"},"agent_actions":{"view_html":"https://pith.science/pith/MI3XJ7CWGIUOD6K75J6FMP77JL","download_json":"https://pith.science/pith/MI3XJ7CWGIUOD6K75J6FMP77JL.json","view_paper":"https://pith.science/paper/MI3XJ7CW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.07875&json=true","fetch_graph":"https://pith.science/api/pith-number/MI3XJ7CWGIUOD6K75J6FMP77JL/graph.json","fetch_events":"https://pith.science/api/pith-number/MI3XJ7CWGIUOD6K75J6FMP77JL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MI3XJ7CWGIUOD6K75J6FMP77JL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MI3XJ7CWGIUOD6K75J6FMP77JL/action/storage_attestation","attest_author":"https://pith.science/pith/MI3XJ7CWGIUOD6K75J6FMP77JL/action/author_attestation","sign_citation":"https://pith.science/pith/MI3XJ7CWGIUOD6K75J6FMP77JL/action/citation_signature","submit_replication":"https://pith.science/pith/MI3XJ7CWGIUOD6K75J6FMP77JL/action/replication_record"}},"created_at":"2026-07-05T03:55:50.163670+00:00","updated_at":"2026-07-05T03:55:50.163670+00:00"}