{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/modeling-heterogeneous-hierarchies-with","title":"Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones","arxiv_id":"2110.14923","date":"2021-10-28","proceeding":"NeurIPS 2021 12","authors":["Yushi Bai","Rex Ying","Hongyu Ren","Jure Leskovec"],"abstract":"Hierarchical relations are prevalent and indispensable for organizing human knowledge captured by a knowledge graph (KG). The key property of hierarchical relations is that they induce a partial ordering over the entities, which needs to be modeled in order to allow for hierarchical reasoning. However, current KG embeddings can model only a single global hierarchy (single global partial ordering) and fail to model multiple heterogeneous hierarchies that exist in a single KG. Here we present ConE (Cone Embedding), a KG embedding model that is able to simultaneously model multiple hierarchical as well as non-hierarchical relations in a knowledge graph. ConE embeds entities into hyperbolic cones and models relations as transformations between the cones. In particular, ConE uses cone containment constraints in different subspaces of the hyperbolic embedding space to capture multiple heterogeneous hierarchies. Experiments on standard knowledge graph benchmarks show that ConE obtains state-of-the-art performance on hierarchical reasoning tasks as well as knowledge graph completion task on hierarchical graphs. In particular, our approach yields new state-of-the-art Hits@1 of 45.3% on WN18RR and 16.1% on DDB14 (0.231 MRR). As for hierarchical reasoning task, our approach outperforms previous best results by an average of 20% across the three datasets.","url_abs":"https://arxiv.org/abs/2110.14923v2","url_pdf":"https://arxiv.org/pdf/2110.14923v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"modeling-heterogeneous-hierarchies-with","repo_url":"https://github.com/snap-stanford/ConE","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"ancestor-descendant-prediction","task_name":"Ancestor-descendant prediction"},{"task_slug":"knowledge-graph-completion","task_name":"Knowledge Graph Completion"},{"task_slug":"link-prediction","task_name":"Link Prediction"},{"task_slug":null,"task_name":"Relation"}],"methods":[],"datasets_introduced":[{"slug":"go21","name":"GO21","full_name":""}],"methods_introduced":[],"results":[{"leaderboard":"/sota/ancestor-descendant-prediction-on-wn18rr","task":"Ancestor-descendant prediction","dataset":"WN18RR","model":"ConE","rank_in_archive_order":1,"of":1,"metrics":{"mAP-0%":"0.895","mAP-100%":"0.679","mAP-50%":"0.801"},"uses_additional_data":false},{"leaderboard":"/sota/link-prediction-on-ddb14","task":"Link Prediction","dataset":"DDB14","model":"ConE","rank_in_archive_order":1,"of":1,"metrics":{"Hits@1":"0.161","Hits@10":"0.364","Hits@3":"0.252","MRR":"0.231"},"uses_additional_data":false},{"leaderboard":"/sota/link-prediction-on-fb15k-237","task":"Link Prediction","dataset":"FB15k-237","model":"ConE","rank_in_archive_order":40,"of":75,"metrics":{"Hits@1":"0.247","Hits@10":"0.54","Hits@3":"0.381","MRR":"0.345"},"uses_additional_data":false},{"leaderboard":"/sota/link-prediction-on-go21","task":"Link Prediction","dataset":"GO21","model":"ConE","rank_in_archive_order":1,"of":1,"metrics":{"Hit@1":"0.14","Hits@10":"0.347","Hits@3":"0.237","MRR":"0.211"},"uses_additional_data":false},{"leaderboard":"/sota/link-prediction-on-wn18rr","task":"Link Prediction","dataset":"WN18RR","model":"ConE","rank_in_archive_order":26,"of":75,"metrics":{"Hits@1":"0.453","Hits@10":"0.579","Hits@3":"0.515","MRR":"0.496"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2110.14923","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2110.14923"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/snap-stanford/ConE","reach":null}],"summary":{"ran":2},"by_repo_kind":{"official":{"samples":2,"ran":2,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"cf120f6a24cc78a6","entry":"EnergyFunction","repo":"snap-stanford/ConE","repo_kind":"official","path":"codes/utils/energy_function.py","file_url":"https://github.com/snap-stanford/ConE/blob/HEAD/codes/utils/energy_function.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"cf120f6a24cc78a6"}},{"code_sha256_prefix":"d6bdad4b6beebc35","entry":"EntailmentConeEnergyFunction","repo":"snap-stanford/ConE","repo_kind":"official","path":"codes/utils/energy_function.py","file_url":"https://github.com/snap-stanford/ConE/blob/HEAD/codes/utils/energy_function.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d6bdad4b6beebc35"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}