{"id":"https://openalex.org/W7138306419","doi":"https://doi.org/10.48550/arxiv.2603.13663","title":"PDE-SSM: A Spectral State Space Approach to Spatial Mixing in Diffusion Transformers","display_name":"PDE-SSM: A Spectral State Space Approach to Spatial Mixing in Diffusion Transformers","publication_year":2026,"publication_date":"2026-03-14","ids":{"openalex":"https://openalex.org/W7138306419","doi":"https://doi.org/10.48550/arxiv.2603.13663"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.13663","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13663","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.13663","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110168314","display_name":"Eli Gal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gal, Eshed","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064732307","display_name":"Moshe Eliasof","orcid":"https://orcid.org/0000-0002-1780-2312"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eliasof, Moshe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031763340","display_name":"Siddharth Rout","orcid":"https://orcid.org/0000-0003-0865-0916"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rout, Siddharth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5021978302","display_name":"Eldad Haber","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haber, Eldad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"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":0.7239000201225281,"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":0.7239000201225281,"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":0.09269999712705612,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.024299999698996544,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/quadratic-equation","display_name":"Quadratic equation","score":0.5271000266075134},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.4140999913215637},{"id":"https://openalex.org/keywords/granularity","display_name":"Granularity","score":0.41019999980926514},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.3779999911785126},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.35179999470710754},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.34360000491142273},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.32359999418258667},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.31279999017715454}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5271000266075134},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44920000433921814},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4260999858379364},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.4140999913215637},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.41019999980926514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40799999237060547},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3779999911785126},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.35179999470710754},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.34360000491142273},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.32359999418258667},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.31279999017715454},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3050999939441681},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2806999981403351},{"id":"https://openalex.org/C2985909886","wikidata":"https://www.wikidata.org/wiki/Q193147","display_name":"Spatial coherence","level":3,"score":0.2793000042438507},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27810001373291016},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2572000026702881},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.25189998745918274},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.25130000710487366},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.13663","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13663","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.13663","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13663","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":"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":{"The":[0],"success":[1],"of":[2,18,70,104],"vision":[3,134],"transformers-especially":[4],"for":[5,132],"generative":[6,88],"modeling-is":[7],"limited":[8],"by":[9,44],"the":[10,58,61,92,102],"quadratic":[11],"cost":[12],"and":[13,77],"weak":[14],"spatial":[15,24,42],"inductive":[16],"bias":[17],"self-attention.":[19],"We":[20,82],"propose":[21],"PDE-SSM,":[22],"a":[23,31,40,75,86],"state-space":[25],"block":[26],"that":[27],"replaces":[28],"attention":[29],"with":[30,67],"learnable":[32],"convection-diffusion-reaction":[33],"partial":[34],"differential":[35],"equation.":[36],"This":[37],"operator":[38],"encodes":[39],"strong":[41],"prior":[43],"modeling":[45],"information":[46],"flow":[47],"via":[48],"physically":[49],"grounded":[50],"dynamics":[51],"rather":[52],"than":[53],"all-to-all":[54],"token":[55],"interactions.":[56],"Solving":[57],"PDE":[59,125],"in":[60],"Fourier":[62],"domain":[63],"yields":[64],"global":[65],"coupling":[66],"near-linear":[68],"complexity":[69],"$O(N":[71],"\\log":[72],"N)$,":[73],"delivering":[74],"principled":[76],"scalable":[78],"alternative":[79],"to":[80,90,117],"attention.":[81],"integrate":[83],"PDE-SSM":[84],"into":[85],"flow-matching":[87],"model":[89],"obtain":[91],"PDE-based":[93],"Diffusion":[94,106],"Transformer":[95],"PDE-SSM-DiT.":[96],"Empirically,":[97],"PDE-SSM-DiT":[98],"matches":[99],"or":[100],"exceeds":[101],"performance":[103],"state-of-the-art":[105],"Transformers":[107],"while":[108],"substantially":[109],"reducing":[110],"compute.":[111],"Our":[112],"results":[113],"show":[114],"that,":[115],"analogous":[116],"1D":[118],"settings":[119],"where":[120],"SSMs":[121],"supplant":[122],"attention,":[123],"multi-dimensional":[124],"operators":[126],"provide":[127],"an":[128],"efficient,":[129],"inductive-bias-rich":[130],"foundation":[131],"next-generation":[133],"models.":[135]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-18T00:00:00"}