{"id":"https://openalex.org/W7129669520","doi":"https://doi.org/10.48550/arxiv.2602.14729","title":"Scale redundancy and soft gauge fixing in positively homogeneous neural networks","display_name":"Scale redundancy and soft gauge fixing in positively homogeneous neural networks","publication_year":2026,"publication_date":"2026-02-16","ids":{"openalex":"https://openalex.org/W7129669520","doi":"https://doi.org/10.48550/arxiv.2602.14729"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.14729","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126232712","display_name":"Rodrigo Carmo Terin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Terin, Rodrigo Carmo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5126232712"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20377959,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.3605000078678131,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.3605000078678131,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.1362999975681305,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.06889999657869339,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.6593999862670898},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.6362000107765198},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5719000101089478},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5047000050544739},{"id":"https://openalex.org/keywords/gauge","display_name":"Gauge (firearms)","score":0.5031999945640564},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4869999885559082},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.42820000648498535},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.41040000319480896},{"id":"https://openalex.org/keywords/scale-invariance","display_name":"Scale invariance","score":0.4043000042438507}],"concepts":[{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.6593999862670898},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.6362000107765198},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5719000101089478},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C40976572","wikidata":"https://www.wikidata.org/wiki/Q2330873","display_name":"Gauge (firearms)","level":2,"score":0.5031999945640564},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4869999885559082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4830999970436096},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.42820000648498535},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.41040000319480896},{"id":"https://openalex.org/C135593079","wikidata":"https://www.wikidata.org/wiki/Q1750766","display_name":"Scale invariance","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.390500009059906},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.38339999318122864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37880000472068787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3686000108718872},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C31593994","wikidata":"https://www.wikidata.org/wiki/Q832289","display_name":"Gauge fixing","level":4,"score":0.35589998960494995},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33250001072883606},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3203999996185303},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C147247565","wikidata":"https://www.wikidata.org/wiki/Q5527635","display_name":"Gauge symmetry","level":3,"score":0.30090001225471497},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C135854075","wikidata":"https://www.wikidata.org/wiki/Q1421688","display_name":"Relaxation oscillator","level":4,"score":0.28679999709129333},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2831999957561493},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C94906876","wikidata":"https://www.wikidata.org/wiki/Q1132952","display_name":"Homogeneous function","level":3,"score":0.2630999982357025},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.14729","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.14729","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.14729","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":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.14729","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","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":{"Neural":[0],"networks":[1],"with":[2],"positively":[3],"homogeneous":[4],"activations":[5],"exhibit":[6],"an":[7],"exact":[8],"continuous":[9],"reparametrization":[10],"symmetry:":[11],"neuron-wise":[12],"rescalings":[13],"generate":[14],"parameter-space":[15],"orbits":[16],"along":[17],"which":[18],"the":[19,75,85],"input--output":[20],"function":[21],"is":[22],"invariant.":[23],"We":[24,62],"interpret":[25],"this":[26,81],"symmetry":[27],"as":[28],"a":[29,51,99,109],"gauge":[30,44],"redundancy":[31],"and":[32,39,89,105,115],"introduce":[33,50],"gauge-adapted":[34],"coordinates":[35],"that":[36,65],"separate":[37],"invariant":[38],"scale-imbalance":[40],"directions.":[41],"Inspired":[42],"by":[43],"fixing":[45],"in":[46],"field":[47],"theory,":[48],"we":[49],"soft":[52],"orbit-selection":[53,82],"(norm-balancing)":[54],"functional":[55],"acting":[56],"only":[57],"on":[58],"redundant":[59],"scale":[60,91],"coordinates.":[61],"show":[63],"analytically":[64],"it":[66],"induces":[67],"dissipative":[68],"relaxation":[69],"of":[70],"imbalance":[71],"modes":[72],"to":[73],"preserve":[74],"realized":[76],"function.":[77],"In":[78],"controlled":[79],"experiments,":[80],"penalty":[83],"expands":[84],"stable":[86],"learning-rate":[87],"regime":[88],"suppresses":[90],"drift":[92],"without":[93],"changing":[94],"expressivity.":[95],"These":[96],"results":[97],"establish":[98],"structural":[100],"link":[101],"between":[102,112],"gauge-orbit":[103],"geometry":[104],"optimization":[106],"conditioning,":[107],"providing":[108],"concrete":[110],"connection":[111],"gauge-theoretic":[113],"concepts":[114],"machine":[116],"learning.":[117]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2026-02-18T00:00:00"}