{"id":"https://openalex.org/W7160027026","doi":"https://doi.org/10.48550/arxiv.2605.00265","title":"Polaris: Coupled Orbital Polar Embeddings for Hierarchical Concept Learning","display_name":"Polaris: Coupled Orbital Polar Embeddings for Hierarchical Concept Learning","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7160027026","doi":"https://doi.org/10.48550/arxiv.2605.00265"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.00265","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00265","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.00265","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048570466","display_name":"Sahil Mishra","orcid":"https://orcid.org/0000-0001-5477-9003"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mishra, Sahil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101476712","display_name":"Srinitish Srinivasan","orcid":"https://orcid.org/0009-0007-0122-8890"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Srinivasan, Srinitish","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017847295","display_name":"Sourish Dasgupta","orcid":"https://orcid.org/0000-0003-0507-6824"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dasgupta, Sourish","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135244930","display_name":"Tanmoy Chakraborty","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chakraborty, Tanmoy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048570466"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.7153000235557556,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.7153000235557556,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.0885000005364418,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11550","display_name":"Text and Document Classification Technologies","score":0.03099999949336052,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6062999963760376},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.5135999917984009},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.46459999680519104},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.4203000068664551},{"id":"https://openalex.org/keywords/outer-product","display_name":"Outer product","score":0.4043000042438507},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4025999903678894},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.33709999918937683},{"id":"https://openalex.org/keywords/inner-product-space","display_name":"Inner product space","score":0.3174000084400177}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6062999963760376},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.5135999917984009},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.46459999680519104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4489000141620636},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42989999055862427},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4203000068664551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4154999852180481},{"id":"https://openalex.org/C180623205","wikidata":"https://www.wikidata.org/wiki/Q1268589","display_name":"Outer product","level":3,"score":0.4043000042438507},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4025999903678894},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3781999945640564},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.322299987077713},{"id":"https://openalex.org/C91855343","wikidata":"https://www.wikidata.org/wiki/Q214159","display_name":"Inner product space","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3001999855041504},{"id":"https://openalex.org/C40069579","wikidata":"https://www.wikidata.org/wiki/Q62494","display_name":"Polar coordinate system","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2937999963760376},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C161301231","wikidata":"https://www.wikidata.org/wiki/Q3478658","display_name":"Knowledge representation and reasoning","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2547999918460846},{"id":"https://openalex.org/C48164120","wikidata":"https://www.wikidata.org/wiki/Q4491893","display_name":"Concept learning","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.00265","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00265","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.00265","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00265","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Real-world":[0],"knowledge":[1],"is":[2,20],"often":[3],"organized":[4],"as":[5,8],"hierarchies":[6],"such":[7],"product":[9],"taxonomies,":[10],"medical":[11],"ontologies,":[12],"and":[13,26,45,52,78,98,136,150],"label":[14],"trees,":[15,133],"yet":[16],"learning":[17,49],"hierarchical":[18],"representations":[19,81],"challenging":[21],"due":[22],"to":[23,66,113,144,152],"asymmetric":[24,100],"structure":[25,53],"noisy":[27],"semantics.":[28],"We":[29,122],"introduce":[30],"Polaris,":[31],"a":[32],"polar":[33],"hyperspherical":[34],"embedding":[35],"framework":[36],"that":[37,94,102],"separates":[38],"semanticity":[39],"from":[40],"hierarchy":[41],"using":[42,82],"angular":[43],"geometry":[44],"radius,":[46],"enabling":[47],"the":[48,61,67,71,75],"of":[50,128,142],"meaning":[51],"without":[54],"interference.":[55],"To":[56],"map":[57],"latent":[58],"representation":[59],"onto":[60],"sphere,":[62],"we":[63],"project":[64],"it":[65],"tangent":[68],"space":[69],"at":[70],"north":[72],"pole,":[73],"apply":[74],"exponential":[76],"map,":[77],"learn":[79],"unit-norm":[80],"spherical":[83],"linear":[84],"layers.":[85],"Polaris":[86,109,124],"then":[87],"combines":[88],"robust":[89],"local":[90],"constraints,":[91],"global":[92],"regularization":[93],"prevents":[95],"geometric":[96],"collapse,":[97],"uncertainty-aware":[99],"objectives":[101],"encourage":[103],"directional":[104],"containment.":[105],"At":[106],"inference":[107],"time,":[108],"uses":[110],"structure-guided":[111],"retrieval":[112,149],"efficiently":[114],"narrow":[115],"down":[116],"candidate":[117],"parents":[118],"before":[119],"final":[120],"ranking.":[121],"evaluate":[123],"on":[125],"different":[126],"settings":[127],"taxonomy":[129],"expansion":[130],"-":[131],"spanning":[132],"multi-parent":[134],"DAGs,":[135],"multimodal":[137],"hierarchies,":[138],"showing":[139],"consistent":[140],"improvements":[141],"up":[143,151],"~19":[145],"points":[146],"in":[147,155],"top-K":[148],"~60%":[153],"reduction":[154],"mean":[156],"rank":[157],"over":[158],"fourteen":[159],"strong":[160],"baselines.":[161]},"counts_by_year":[],"updated_date":"2026-05-05T06:12:25.323381","created_date":"2026-05-05T00:00:00"}
