{"id":"https://openalex.org/W7166857058","doi":"https://doi.org/10.48550/arxiv.2606.31588","title":"Power law scaling for classification accuracy in physical neural networks","display_name":"Power law scaling for classification accuracy in physical neural networks","publication_year":2026,"publication_date":"2026-06-30","ids":{"openalex":"https://openalex.org/W7166857058","doi":"https://doi.org/10.48550/arxiv.2606.31588"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.31588","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.31588","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.2606.31588","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139757442","display_name":"Andrei V. Ermolaev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ermolaev, Andrei V.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019842884","display_name":"Mathilde Hary","orcid":"https://orcid.org/0000-0002-5338-113X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hary, Mathilde","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016230147","display_name":"Anas Skalli","orcid":"https://orcid.org/0000-0002-7039-926X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Skalli, Anas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090288277","display_name":"Go\u00ebry Genty","orcid":"https://orcid.org/0000-0002-0768-3663"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Genty, Go\u00ebry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070560787","display_name":"Marcin G\u0119bski","orcid":"https://orcid.org/0000-0002-7307-1761"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gebski, Marcin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125504309","display_name":"Tomasz Czyszanowski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Czyszanowski, Tomasz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139724468","display_name":"Stephan Reitzenstein","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reitzenstein, Stephan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013873343","display_name":"James A. Lott","orcid":"https://orcid.org/0000-0003-4094-499X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lott, James A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066619471","display_name":"J. M. Dudley","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dudley, John M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139761506","display_name":"Daniel Brunner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brunner, Daniel","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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.9861999750137329,"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":0.9861999750137329,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.002199999988079071,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.0019000000320374966,"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/benchmark","display_name":"Benchmark (surveying)","score":0.6148999929428101},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5947999954223633},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5845999717712402},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5559999942779541},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.5164999961853027},{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.510200023651123},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.45570001006126404},{"id":"https://openalex.org/keywords/calibration","display_name":"Calibration","score":0.4032000005245209}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.644599974155426},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6148999929428101},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5947999954223633},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5845999717712402},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5559999942779541},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5178999900817871},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.5164999961853027},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.510200023651123},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.45570001006126404},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4034000039100647},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.4032000005245209},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3337000012397766},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3321000039577484},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.2913999855518341},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.31588","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.31588","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.2606.31588","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.31588","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":[{"id":"https://metadata.un.org/sdg/16","score":0.40634360909461975,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Physical":[0],"neural":[1,13],"networks":[2],"(PNNs)":[3],"harness":[4],"the":[5,46,131,135,170,196,218],"intrinsic":[6],"complexity":[7],"of":[8,54,91,158,179,210],"physical":[9],"systems":[10,122],"to":[11,22,164,229],"perform":[12],"computation,":[14],"potentially":[15],"at":[16],"speeds":[17],"and":[18,32,83,110,116,160,214],"energy":[19],"efficiencies":[20],"inaccessible":[21],"conventional":[23],"digital":[24],"hardware.":[25],"Yet,":[26],"a":[27,51,97,125,155,176,207,222],"principled":[28],"framework":[29],"for":[30,88,108,112,212],"quantifying":[31],"predicting":[33],"their":[34],"computing":[35],"accuracy":[36],"across":[37,75,151],"diverse":[38],"substrates":[39],"has":[40],"remained":[41],"elusive.":[42],"Here":[43],"we":[44],"introduce":[45],"Hotelling":[47],"Trace":[48],"Criterion":[49],"(HTC),":[50],"task-conditioned":[52],"measure":[53],"PNN-":[55],"state":[56],"separability":[57],"that":[58,66,144],"can":[59,192],"be":[60,193],"evaluated":[61],"without":[62],"training.":[63],"We":[64],"demonstrate":[65],"it":[67],"predicts":[68],"PNN":[69,152],"classification":[70],"performance":[71,185,191,231],"with":[72,102],"high":[73],"fidelity":[74],"highly":[76],"nonlinear":[77,85],"optical":[78],"fibres,":[79],"vertical-cavity":[80],"surface-emitting":[81],"lasers,":[82],"coupled":[84],"oscillator":[86],"networks,":[87],"benchmark":[89],"tasks":[90],"different":[92],"difficulty.":[93],"Classification":[94],"loss":[95,166],"follows":[96],"power":[98],"law":[99],"in":[100],"HTC,":[101],"Pearson":[103],"correlation":[104],"coefficients":[105],"exceeding":[106],"0.99":[107],"MNIST":[109],"$\\approx$0.97":[111],"Fashion-MNIST,":[113],"noteworthy":[114],"experimental":[115],"simulated":[117],"data":[118],"from":[119,175,195],"physically":[120],"distinct":[121],"collapse":[123],"onto":[124],"single":[126],"scaling":[127,171,215,234],"curve":[128],"determined":[129],"by":[130],"task":[132,230],"rather":[133],"than":[134],"substrate.":[136],"Applying":[137],"HTC":[138,200,205],"layer-by-layer":[139],"during":[140],"training":[141,159,189],"further":[142,184,220],"reveals":[143],"gradient-based":[145],"optimisation":[146],"distributes":[147],"representational":[148],"capacity":[149],"unevenly":[150],"layers,":[153],"providing":[154],"quantitative":[156],"diagnostic":[157],"architecture":[161],"efficiency":[162],"invisible":[163],"standard":[165],"monitoring.":[167],"Crucially,":[168],"once":[169],"exponent":[172],"is":[173],"established":[174],"small":[177],"number":[178],"trained":[180],"calibration":[181],"systems,":[182],"all":[183],"predictions":[186],"require":[187],"no":[188],"since":[190],"derived":[194],"much":[197],"more":[198],"efficient":[199],"measurement.":[201],"These":[202],"results":[203],"establish":[204],"as":[206],"substrate-agnostic":[208],"figure":[209],"merit":[211],"comparing":[213],"PNNs,":[216],"advancing":[217],"field":[219],"towards":[221],"complete":[223],"theory":[224],"connecting":[225],"fundamental":[226],"hardware":[227],"parameters":[228],"through":[232],"universal":[233],"laws.":[235]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-02T00:00:00"}
