{"id":"https://openalex.org/W7164998846","doi":"https://doi.org/10.48550/arxiv.2606.17816","title":"Conservation Laws for Modern Neural Architectures","display_name":"Conservation Laws for Modern Neural Architectures","publication_year":2026,"publication_date":"2026-06-16","ids":{"openalex":"https://openalex.org/W7164998846","doi":"https://doi.org/10.48550/arxiv.2606.17816"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.17816","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.17816","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":"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.2606.17816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111236249","display_name":"Viet-Hoang Tran","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tran, Viet-Hoang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138821195","display_name":"Vinh Khanh Bui","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bui, Vinh Khanh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138801076","display_name":"Tan Lai Ngoc","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ngoc, Tan Lai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138768218","display_name":"Nam Nguyen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nguyen, Nam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061282536","display_name":"Tuan Dam","orcid":"https://orcid.org/0000-0001-7422-139X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dam, Tuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138806871","display_name":"Tan M. Nguyen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nguyen, Tan M.","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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.21570000052452087,"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"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.21570000052452087,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.20229999721050262,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.17440000176429749,"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/conservation-law","display_name":"Conservation law","score":0.7361000180244446},{"id":"https://openalex.org/keywords/feed-forward","display_name":"Feed forward","score":0.5322999954223633},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4683000147342682},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4580000042915344},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.43070000410079956},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.3474000096321106}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.7361000180244446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6245999932289124},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.5322999954223633},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4683000147342682},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4580000042915344},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44269999861717224},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.43070000410079956},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3474000096321106},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.30160000920295715},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28870001435279846},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.27880001068115234},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C194583477","wikidata":"https://www.wikidata.org/wiki/Q408891","display_name":"Physical law","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.25189998745918274},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.17816","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.17816","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":"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.2606.17816","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.17816","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":"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":[{"score":0.6286070942878723,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Understanding":[0],"gradient":[1,21],"descent":[2],"dynamics":[3],"is":[4],"key":[5],"to":[6,47],"explaining":[7],"the":[8,87],"success":[9],"of":[10],"over-parameterized":[11],"models,":[12,53],"where":[13],"implicit":[14],"bias":[15],"manifests":[16],"through":[17],"conservation":[18,49],"laws":[19,25,50],"in":[20],"flow.":[22],"While":[23],"such":[24],"are":[26,81],"well":[27],"understood":[28],"for":[29,38,51],"linear":[30],"and":[31,60,67,71],"ReLU":[32],"networks,":[33],"they":[34],"remain":[35],"largely":[36],"unexplored":[37],"modern":[39],"architectures.":[40],"This":[41],"work":[42],"develops":[43],"a":[44],"unified":[45],"framework":[46],"characterize":[48],"contemporary":[52],"including":[54],"feedforward":[55],"networks":[56],"with":[57,65],"GELU,":[58],"SiLU,":[59],"SwiGLU":[61],"activations,":[62],"multihead":[63],"attention":[64],"sinusoidal":[66],"rotary":[68],"positional":[69],"encodings,":[70],"Mixture-of-Experts":[72],"architectures":[73],"under":[74],"diverse":[75],"gating":[76],"designs.":[77],"Our":[78],"theoretical":[79],"findings":[80],"supported":[82],"by":[83],"experiments":[84],"that":[85],"validate":[86],"predicted":[88],"invariants.":[89]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-18T00:00:00"}
