{"id":"https://openalex.org/W4382766245","doi":"https://doi.org/10.48550/arxiv.2306.16951","title":"Applying language models to algebraic topology: generating simplicial cycles using multi-labeling in Wu's formula","display_name":"Applying language models to algebraic topology: generating simplicial cycles using multi-labeling in Wu's formula","publication_year":2023,"publication_date":"2023-06-01","ids":{"openalex":"https://openalex.org/W4382766245","doi":"https://doi.org/10.48550/arxiv.2306.16951"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2306.16951","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2306.16951","pdf_url":"https://arxiv.org/pdf/2306.16951","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2306.16951","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092277208","display_name":"Kirill Brilliantov","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Brilliantov, Kirill","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108685387","display_name":"Fedor Pavutnitskiy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pavutnitskiy, Fedor","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001372309","display_name":"Dmitry Pasechnyuk","orcid":"https://orcid.org/0000-0002-1208-1659"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pasechnyuk, Dmitry","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045654177","display_name":"German Magai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Magai, German","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5092277208"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9697999954223633,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9697999954223633,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10181","display_name":"Natural Language Processing Techniques","score":0.96670001745224,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9509000182151794,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algebraic-topology","display_name":"Algebraic topology","score":0.7920241355895996},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.7093276977539062},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6412745118141174},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.5884173512458801},{"id":"https://openalex.org/keywords/abstract-simplicial-complex","display_name":"Abstract simplicial complex","score":0.5678128004074097},{"id":"https://openalex.org/keywords/simplicial-approximation-theorem","display_name":"Simplicial approximation theorem","score":0.563113808631897},{"id":"https://openalex.org/keywords/homotopy-group","display_name":"Homotopy group","score":0.5440269708633423},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5087006688117981},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5038933157920837},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4912697672843933},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45969831943511963},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4241664707660675},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4083205461502075},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3930487036705017},{"id":"https://openalex.org/keywords/simplicial-set","display_name":"Simplicial set","score":0.345670223236084},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3070813715457916},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24183526635169983},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20620214939117432}],"concepts":[{"id":"https://openalex.org/C145054310","wikidata":"https://www.wikidata.org/wiki/Q212803","display_name":"Algebraic topology","level":3,"score":0.7920241355895996},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.7093276977539062},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6412745118141174},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.5884173512458801},{"id":"https://openalex.org/C146867743","wikidata":"https://www.wikidata.org/wiki/Q4669959","display_name":"Abstract simplicial complex","level":3,"score":0.5678128004074097},{"id":"https://openalex.org/C64245159","wikidata":"https://www.wikidata.org/wiki/Q3983972","display_name":"Simplicial approximation theorem","level":5,"score":0.563113808631897},{"id":"https://openalex.org/C147688034","wikidata":"https://www.wikidata.org/wiki/Q1626416","display_name":"Homotopy group","level":3,"score":0.5440269708633423},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5087006688117981},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5038933157920837},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4912697672843933},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45969831943511963},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4241664707660675},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4083205461502075},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3930487036705017},{"id":"https://openalex.org/C155366967","wikidata":"https://www.wikidata.org/wiki/Q1467124","display_name":"Simplicial set","level":4,"score":0.345670223236084},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3070813715457916},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24183526635169983},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20620214939117432},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2306.16951","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2306.16951","pdf_url":"https://arxiv.org/pdf/2306.16951","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2306.16951","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2306.16951","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2306.16951","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2306.16951","pdf_url":"https://arxiv.org/pdf/2306.16951","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4382766245.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2133717328","https://openalex.org/W2103738419","https://openalex.org/W3033469176","https://openalex.org/W4288359443","https://openalex.org/W2943582562","https://openalex.org/W2969857904","https://openalex.org/W2011162705","https://openalex.org/W4380352139","https://openalex.org/W2126991673","https://openalex.org/W2982149580"],"abstract_inverted_index":{"Computing":[0],"homotopy":[1,46],"groups":[2,47],"of":[3,36,41,44,52,61,68,75,80],"spheres":[4],"has":[5],"long":[6],"been":[7,20],"a":[8,31,73],"fundamental":[9],"objective":[10],"in":[11,56],"algebraic":[12],"topology.":[13],"Various":[14],"theoretical":[15],"and":[16,89,107],"algorithmic":[17,81],"approaches":[18,93],"have":[19],"developed":[21],"to":[22,84],"tackle":[23],"this":[24,27],"problem.":[25],"In":[26],"paper":[28],"we":[29,64],"take":[30],"step":[32],"towards":[33],"the":[34,38,42,50,57,66,78,103],"goal":[35],"comprehending":[37],"group-theoretic":[39,105],"structure":[40],"generators":[43],"these":[45],"by":[48],"leveraging":[49],"power":[51],"machine":[53],"learning.":[54],"Specifically,":[55],"simplicial":[58,70],"group":[59],"setting":[60],"Wu's":[62],"formula,":[63],"reformulate":[65],"problem":[67,74],"generating":[69],"cycles":[71],"as":[72],"sampling":[76],"from":[77],"intersection":[79],"datasets":[82],"related":[83],"Dyck":[85],"languages.":[86],"We":[87],"present":[88],"evaluate":[90],"language":[91],"modelling":[92],"that":[94],"employ":[95],"multi-label":[96],"information":[97],"for":[98],"input":[99],"sequences,":[100],"along":[101],"with":[102],"necessary":[104],"toolkit":[106],"non-neural":[108],"baselines.":[109]},"counts_by_year":[],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2023-07-01T00:00:00"}