{"id":"https://openalex.org/W7163320473","doi":"https://doi.org/10.48550/arxiv.2606.02841","title":"Learning Coherent Representations: A Topological Approach to Interpretability","display_name":"Learning Coherent Representations: A Topological Approach to Interpretability","publication_year":2026,"publication_date":"2026-06-01","ids":{"openalex":"https://openalex.org/W7163320473","doi":"https://doi.org/10.48550/arxiv.2606.02841"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.02841","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.02841","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.02841","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119811154","display_name":"Sigurd Gaukstad","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gaukstad, Sigurd","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137738487","display_name":"Melvin Vaupel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vaupel, Melvin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5096084665","display_name":"Valdemar Karg\u00e5rd Olsen","orcid":"https://orcid.org/0009-0007-7077-7404"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olsen, Valdemar Karg\u00e5rd","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036785568","display_name":"Erik Hermansen","orcid":"https://orcid.org/0000-0001-9624-4349"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hermansen, Erik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137754180","display_name":"Benjamin Dunn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dunn, Benjamin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.6693999767303467,"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":0.6693999767303467,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.06549999862909317,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.05939999967813492,"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/interpretability","display_name":"Interpretability","score":0.6862999796867371},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5264999866485596},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5192000269889832},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4999000132083893},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4650999903678894},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4569999873638153},{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.4377000033855438},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.42890000343322754},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.42419999837875366},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4174000024795532}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.6862999796867371},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5264999866485596},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5192000269889832},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4999000132083893},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47380000352859497},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4650999903678894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4575999975204468},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4526999890804291},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.4377000033855438},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.42419999837875366},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4174000024795532},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40049999952316284},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.39910000562667847},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.38909998536109924},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3817000091075897},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.3314000070095062},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C28034677","wikidata":"https://www.wikidata.org/wiki/Q17092530","display_name":"Interleaving","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C70437156","wikidata":"https://www.wikidata.org/wiki/Q7228652","display_name":"Pooling","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28760001063346863},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.02841","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.02841","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.02841","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.02841","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"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":{"Deep":[0],"neural":[1,29],"networks":[2],"learn":[3],"representations":[4],"where":[5,34],"individual":[6],"features":[7,126,177],"often":[8],"lack":[9],"interpretable":[10,176,180],"meaning;":[11],"a":[12,24,93,123,137,157,197],"single":[13],"neuron":[14],"may":[15],"activate":[16],"for":[17],"scattered,":[18],"unrelated":[19],"inputs.":[20],"We":[21,87,134,183],"introduce":[22,135],"coherence,":[23],"geometric":[25,113,166],"property":[26],"inspired":[27],"by":[28,76,84],"coding":[30],"in":[31,69,186,196],"the":[32,97],"brain,":[33],"neurons":[35],"like":[36],"grid":[37],"cells":[38,42],"and":[39,65,68,79,102,191,195],"head":[40],"direction":[41],"respond":[43],"to":[44,60],"contiguous":[45,132],"regions":[46],"of":[47,100,200],"state":[48],"space.":[49,182],"A":[50],"non-negative":[51],"matrix":[52],"is":[53,73,82],"coherent":[54,90,125],"if":[55,119],"each":[56],"row":[57],"(sample)":[58],"attends":[59],"geometrically":[61],"clustered":[62],"columns":[63],"(features)":[64],"vice":[66],"versa,":[67],"addition":[70],"every":[71,80],"sample":[72],"well":[74],"described":[75],"some":[77,85],"feature":[78,81,158,181],"needed":[83],"sample.":[86],"prove":[88],"that":[89,105,129,145],"matrices":[91],"induce":[92],"bounded":[94],"interleaving":[95],"between":[96],"Vietoris-Rips":[98],"filtrations":[99],"samples":[101,156],"features,":[103],"guaranteeing":[104],"both":[106],"spaces":[107],"share":[108],"compatible":[109],"topological":[110],"structure.":[111],"This":[112,172],"constraint":[114],"facilitates":[115],"interpretability.":[116],"For":[117],"example,":[118],"data":[120],"lies":[121],"on":[122,142],"circle,":[124],"must":[127],"tile":[128],"circle":[130],"into":[131],"arcs.":[133],"Coh,":[136],"differentiable":[138],"objective":[139],"function":[140],"based":[141],"Fr\u00e9chet":[143],"variance":[144],"enforces":[146],"coherence":[147,161],"during":[148],"training.":[149],"Unlike":[150],"sparsity,":[151],"which":[152,163],"bounds":[153,162],"how":[154],"many":[155],"activates":[159],"on,":[160],"samples,":[164],"requiring":[165],"connectivity":[167],"rather":[168],"than":[169],"only":[170],"rarity.":[171],"yields":[173],"not":[174],"just":[175],"but":[178],"an":[179,187],"validate":[184],"Coh":[185],"auto-encoder":[188],"using":[189,202],"synthetic":[190],"rotated":[192],"MNIST":[193],"datasets":[194],"token":[198],"embedding":[199],"BERT":[201],"language":[203],"data.":[204]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-04T00:00:00"}
