{"id":"https://openalex.org/W4415182850","doi":"https://doi.org/10.48550/arxiv.2510.15998","title":"AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM","display_name":"AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM","publication_year":2025,"publication_date":"2025-10-14","ids":{"openalex":"https://openalex.org/W4415182850","doi":"https://doi.org/10.48550/arxiv.2510.15998"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2510.15998","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.15998","pdf_url":"https://arxiv.org/pdf/2510.15998","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.15998","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115505239","display_name":"Nilo Schwencke","orcid":null},"institutions":[{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4387152856","display_name":"Laboratoire Interdisciplinaire des Sciences du Num\u00e9rique","ror":"https://ror.org/00rd81916","country_code":null,"type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4387152856"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Schwencke, Nilo","raw_affiliation_strings":["LISN, TAU","LISN - Laboratoire Interdisciplinaire des Sciences du Num\u00e9rique (Campus Universitaire b\u00e2t 507\r\nRue du Belv\u00e9d\u00e8re\r\n91405 Orsay cedex\r\net \r\nCampus Universitaire b\u00e2t 640\r\n1 rue Raimond Castaing\r\n91190 Gif-sur-Yvette - France)","TAU - TAckling the Underspecified (Universit\u00e9 Paris Saclay\r\nB\u00e2timent 660 - Shannon ; \r\n91405 Orsay Cedex - France)"],"affiliations":[{"raw_affiliation_string":"LISN, TAU","institution_ids":[]},{"raw_affiliation_string":"LISN - Laboratoire Interdisciplinaire des Sciences du Num\u00e9rique (Campus Universitaire b\u00e2t 507\r\nRue du Belv\u00e9d\u00e8re\r\n91405 Orsay cedex\r\net \r\nCampus Universitaire b\u00e2t 640\r\n1 rue Raimond Castaing\r\n91190 Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I4387152856"]},{"raw_affiliation_string":"TAU - TAckling the Underspecified (Universit\u00e9 Paris Saclay\r\nB\u00e2timent 660 - Shannon ; \r\n91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I277688954"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105103095","display_name":"Cyriaque Rousselot","orcid":null},"institutions":[{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210126360","display_name":"Inria Saclay - \u00cele de France","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4387152856","display_name":"Laboratoire Interdisciplinaire des Sciences du Num\u00e9rique","ror":"https://ror.org/00rd81916","country_code":null,"type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4387152856"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Rousselot, Cyriaque","raw_affiliation_strings":["TAU, LISN","Centre Inria de Saclay (1 rue Honor\u00e9 d'Estienne d'Orves\r\n\r\nB\u00e2timent Alan Turing\r\n\r\nCampus de l'\u00c9cole Polytechnique\r\n\r\n91120 Palaiseau - France)","LISN - Laboratoire Interdisciplinaire des Sciences du Num\u00e9rique (Campus Universitaire b\u00e2t 507\r\nRue du Belv\u00e9d\u00e8re\r\n91405 Orsay cedex\r\net \r\nCampus Universitaire b\u00e2t 640\r\n1 rue Raimond Castaing\r\n91190 Gif-sur-Yvette - France)","TAU - TAckling the Underspecified (Universit\u00e9 Paris Saclay\r\nB\u00e2timent 660 - Shannon ; \r\n91405 Orsay Cedex - France)"],"affiliations":[{"raw_affiliation_string":"TAU, LISN","institution_ids":[]},{"raw_affiliation_string":"Centre Inria de Saclay (1 rue Honor\u00e9 d'Estienne d'Orves\r\n\r\nB\u00e2timent Alan Turing\r\n\r\nCampus de l'\u00c9cole Polytechnique\r\n\r\n91120 Palaiseau - France)","institution_ids":["https://openalex.org/I4210126360","https://openalex.org/I4210139461"]},{"raw_affiliation_string":"LISN - Laboratoire Interdisciplinaire des Sciences du Num\u00e9rique (Campus Universitaire b\u00e2t 507\r\nRue du Belv\u00e9d\u00e8re\r\n91405 Orsay cedex\r\net \r\nCampus Universitaire b\u00e2t 640\r\n1 rue Raimond Castaing\r\n91190 Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I4387152856"]},{"raw_affiliation_string":"TAU - TAckling the Underspecified (Universit\u00e9 Paris Saclay\r\nB\u00e2timent 660 - Shannon ; \r\n91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I277688954"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008247659","display_name":"Alena Shilova","orcid":"https://orcid.org/0000-0002-1795-8421"},"institutions":[{"id":"https://openalex.org/I4387152856","display_name":"Laboratoire Interdisciplinaire des Sciences du Num\u00e9rique","ror":"https://ror.org/00rd81916","country_code":null,"type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4387152856"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Shilova, Alena","raw_affiliation_strings":["TAU, LISN","TAU - TAckling the Underspecified (Universit\u00e9 Paris Saclay\r\nB\u00e2timent 660 - Shannon ; \r\n91405 Orsay Cedex - France)","LISN - Laboratoire Interdisciplinaire des Sciences du Num\u00e9rique (Campus Universitaire b\u00e2t 507\r\nRue du Belv\u00e9d\u00e8re\r\n91405 Orsay cedex\r\net \r\nCampus Universitaire b\u00e2t 640\r\n1 rue Raimond Castaing\r\n91190 Gif-sur-Yvette - France)"],"affiliations":[{"raw_affiliation_string":"TAU, LISN","institution_ids":[]},{"raw_affiliation_string":"TAU - TAckling the Underspecified (Universit\u00e9 Paris Saclay\r\nB\u00e2timent 660 - Shannon ; \r\n91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I277688954"]},{"raw_affiliation_string":"LISN - Laboratoire Interdisciplinaire des Sciences du Num\u00e9rique (Campus Universitaire b\u00e2t 507\r\nRue du Belv\u00e9d\u00e8re\r\n91405 Orsay cedex\r\net \r\nCampus Universitaire b\u00e2t 640\r\n1 rue Raimond Castaing\r\n91190 Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I4387152856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001525923","display_name":"Cyril Furtlehner","orcid":"https://orcid.org/0000-0002-3986-2076"},"institutions":[{"id":"https://openalex.org/I4210126360","display_name":"Inria Saclay - \u00cele de France","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]},{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Furtlehner, Cyril","raw_affiliation_strings":["LRI, TAU","TAU - TAckling the Underspecified (Universit\u00e9 Paris-Saclay;\r\nB\u00e2timent 660 - Shannon ; \r\n91405 Orsay Cedex - France)","Centre Inria de Saclay (1 rue Honor\u00e9 d'Estienne d'Orves\r\n\r\nB\u00e2timent Alan Turing\r\n\r\nCampus de l'\u00c9cole Polytechnique\r\n\r\n91120 Palaiseau - France)","LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Saclay 91405 Orsay Cedex - France)"],"affiliations":[{"raw_affiliation_string":"LRI, TAU","institution_ids":[]},{"raw_affiliation_string":"TAU - TAckling the Underspecified (Universit\u00e9 Paris-Saclay;\r\nB\u00e2timent 660 - Shannon ; \r\n91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I277688954"]},{"raw_affiliation_string":"Centre Inria de Saclay (1 rue Honor\u00e9 d'Estienne d'Orves\r\n\r\nB\u00e2timent Alan Turing\r\n\r\nCampus de l'\u00c9cole Polytechnique\r\n\r\n91120 Palaiseau - France)","institution_ids":["https://openalex.org/I4210126360","https://openalex.org/I4210139461"]},{"raw_affiliation_string":"LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Saclay 91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I277688954","https://openalex.org/I4210144804"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5115505239"],"corresponding_institution_ids":["https://openalex.org/I277688954","https://openalex.org/I4387152856"],"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/T12288","display_name":"Optimization and Search Problems","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9914000034332275,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5457000136375427},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5238000154495239},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.5177000164985657},{"id":"https://openalex.org/keywords/cutoff","display_name":"Cutoff","score":0.4747999906539917},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.4526999890804291},{"id":"https://openalex.org/keywords/anagram","display_name":"Anagram","score":0.4092000126838684},{"id":"https://openalex.org/keywords/adaptation","display_name":"Adaptation (eye)","score":0.36469998955726624},{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.3499000072479248}],"concepts":[{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5673999786376953},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5645999908447266},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5457000136375427},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5238000154495239},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.5177000164985657},{"id":"https://openalex.org/C2778217198","wikidata":"https://www.wikidata.org/wiki/Q556977","display_name":"Cutoff","level":2,"score":0.4747999906539917},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4526999890804291},{"id":"https://openalex.org/C2777996765","wikidata":"https://www.wikidata.org/wiki/Q122981","display_name":"Anagram","level":3,"score":0.4092000126838684},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.37610000371932983},{"id":"https://openalex.org/C139807058","wikidata":"https://www.wikidata.org/wiki/Q352374","display_name":"Adaptation (eye)","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34360000491142273},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.2856999933719635},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.28060001134872437},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.2802000045776367},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27619999647140503},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2669000029563904},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2597000002861023}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2510.15998","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.15998","pdf_url":"https://arxiv.org/pdf/2510.15998","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05245453v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05245453","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ENUMATH 2025 - MS31 \u2013 Geometric Optimization Methods for Scientific Machine Learning, Marius Zeinhofer; Johannes M\u00fcller, Sep 2025, Heidelberg, Germany","raw_type":"Conference papers"},{"id":"pmh:oai:HAL:hal-05302122v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05302122","pdf_url":null,"source":{"id":"https://openalex.org/S4406922454","display_name":"SPIRE - Sciences Po Institutional REpository","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2025","raw_type":"Preprints, Working Papers, ..."},{"id":"doi:10.48550/arxiv.2510.15998","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.15998","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":"pmh:oai:arXiv.org:2510.15998","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.15998","pdf_url":"https://arxiv.org/pdf/2510.15998","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Recent":[0],"works":[1],"have":[2],"shown":[3,97],"that":[4,52,88],"natural":[5],"gradient":[6],"methods":[7],"can":[8],"significantly":[9],"outperform":[10],"standard":[11],"optimizers":[12],"when":[13],"training":[14,25],"physics-informed":[15],"neural":[16],"networks":[17],"(PINNs).":[18],"In":[19],"this":[20,44],"paper,":[21],"we":[22,46,80],"analyze":[23],"the":[24,62,90],"dynamics":[26],"of":[27,64,92],"PINNs":[28],"optimized":[29],"with":[30,39,99],"ANaGRAM,":[31],"a":[32,48,82],"natural-gradient-inspired":[33],"approach":[34],"employing":[35],"singular":[36],"value":[37],"decomposition":[38],"cutoff":[40],"regularization.":[41],"Building":[42],"on":[43,58,73,85],"analysis,":[45],"propose":[47],"multi-cutoff":[49],"adaptation":[50],"strategy":[51],"further":[53],"enhances":[54],"ANaGRAM's":[55],"performance.":[56],"Experiments":[57],"benchmark":[59],"PDEs":[60],"validate":[61],"effectiveness":[63],"our":[65],"method,":[66],"which":[67],"allows":[68],"to":[69],"reach":[70],"machine":[71],"precision":[72],"some":[74],"experiments.":[75],"To":[76],"provide":[77],"theoretical":[78],"grounding,":[79],"develop":[81],"framework":[83],"based":[84],"spectral":[86],"theory":[87],"explains":[89],"necessity":[91],"regularization":[93],"and":[94],"extend":[95],"previous":[96],"connections":[98],"Green's":[100],"functions":[101],"theory.":[102]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-15T00:00:00"}