{"id":"https://openalex.org/W7135183809","doi":"https://doi.org/10.48550/arxiv.2603.11396","title":"Harnessing Data Asymmetry: Manifold Learning in the Finsler World","display_name":"Harnessing Data Asymmetry: Manifold Learning in the Finsler World","publication_year":2026,"publication_date":"2026-03-12","ids":{"openalex":"https://openalex.org/W7135183809","doi":"https://doi.org/10.48550/arxiv.2603.11396"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.11396","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11396","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":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.2603.11396","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128977866","display_name":"Thomas Dag\u00e8s","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dag\u00e8s, Thomas","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128978645","display_name":"Simon Weber","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weber, Simon","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087710605","display_name":"Daniel Cremers","orcid":"https://orcid.org/0000-0002-3079-7984"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cremers, Daniel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5122358157","display_name":"Ron Kimmel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kimmel, Ron","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5128977866"],"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/T12417","display_name":"Morphological variations and asymmetry","score":0.7843000292778015,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.7843000292778015,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.041999999433755875,"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/T11448","display_name":"Face recognition and analysis","score":0.022600000724196434,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/pairwise-comparison","display_name":"Pairwise comparison","score":0.6330999732017517},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5899999737739563},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5889999866485596},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.5464000105857849},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5371999740600586},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.4900999963283539},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4885999858379364},{"id":"https://openalex.org/keywords/asymmetry","display_name":"Asymmetry","score":0.4584999978542328},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.4578999876976013}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6330999732017517},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5899999737739563},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5889999866485596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5547999739646912},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.5464000105857849},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5371999740600586},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.4900999963283539},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4885999858379364},{"id":"https://openalex.org/C38976095","wikidata":"https://www.wikidata.org/wiki/Q752641","display_name":"Asymmetry","level":2,"score":0.4584999978542328},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.4578999876976013},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4189999997615814},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3774999976158142},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3747999966144562},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.352400004863739},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C153120616","wikidata":"https://www.wikidata.org/wiki/Q17068315","display_name":"Manifold alignment","level":4,"score":0.3061000108718872},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28349998593330383},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2615000009536743},{"id":"https://openalex.org/C2776145971","wikidata":"https://www.wikidata.org/wiki/Q30673951","display_name":"Labeled data","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C169316501","wikidata":"https://www.wikidata.org/wiki/Q2498782","display_name":"Finsler manifold","level":4,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.11396","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11396","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":"doi:10.48550/arxiv.2603.11396","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11396","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Manifold":[0],"learning":[1,86],"is":[2],"a":[3,83,95],"fundamental":[4],"task":[5],"at":[6],"the":[7,18,59,101,150],"core":[8],"of":[9,22,61,78,103],"data":[10,25,62,110],"analysis":[11],"and":[12,44,81,92,129,135,156],"visualisation.":[13],"It":[14],"aims":[15],"to":[16,58,66,72,111,124],"capture":[17],"simple":[19],"underlying":[20],"structure":[21],"complex":[23],"high-dimensional":[24],"by":[26,70,119],"preserving":[27],"pairwise":[28],"dissimilarities":[29,43,91],"in":[30,52,94,149],"low-dimensional":[31],"embeddings.":[32],"Traditional":[33],"methods":[34,123],"rely":[35],"on":[36],"symmetric":[37,42],"Riemannian":[38,79],"geometry,":[39,74,80],"thus":[40],"forcing":[41],"embedding":[45],"spaces,":[46],"e.g.":[47,153],"Euclidean.":[48],"However,":[49],"this":[50,68],"discards":[51],"practice":[53],"valuable":[54,146],"asymmetric":[55,76,90,105,117,143],"information":[56,147],"inherent":[57],"non-uniformity":[60],"samples.":[63],"We":[64,114],"suggest":[65],"harness":[67],"asymmetry":[69],"switching":[71],"Finsler":[73,84,96,127,130],"an":[75],"generalisation":[77],"propose":[82],"manifold":[85],"pipeline":[87,144],"that":[88,141],"constructs":[89],"embeds":[93],"space.":[97],"This":[98],"greatly":[99],"broadens":[100],"applicability":[102],"existing":[104],"embedders":[106,118],"beyond":[107],"traditionally":[108],"directed":[109],"any":[112],"data.":[113],"also":[115],"modernise":[116],"generalising":[120],"current":[121],"reference":[122],"asymmetry,":[125],"like":[126],"t-SNE":[128],"Umap.":[131],"On":[132],"controlled":[133],"synthetic":[134],"large":[136],"real":[137],"datasets,":[138],"we":[139],"show":[140],"our":[142],"reveals":[145],"lost":[148],"traditional":[151],"pipeline,":[152],"density":[154],"hierarchies,":[155],"consistently":[157],"provides":[158],"superior":[159],"quality":[160],"embeddings":[161],"than":[162],"their":[163],"Euclidean":[164],"counterparts.":[165]},"counts_by_year":[],"updated_date":"2026-03-14T06:46:50.379900","created_date":"2026-03-14T00:00:00"}