{"id":"https://openalex.org/W4416377069","doi":"https://doi.org/10.48550/arxiv.2511.07892","title":"A Generalized Spectral Framework to Expain Neural Scaling and Compression Dynamics","display_name":"A Generalized Spectral Framework to Expain Neural Scaling and Compression Dynamics","publication_year":2025,"publication_date":"2025-11-11","ids":{"openalex":"https://openalex.org/W4416377069","doi":"https://doi.org/10.48550/arxiv.2511.07892"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2511.07892","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.07892","pdf_url":"https://arxiv.org/pdf/2511.07892","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":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/2511.07892","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100643387","display_name":"Yizhou Zhang","orcid":"https://orcid.org/0000-0001-9154-0085"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhang, Yizhou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5100643387"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10581","display_name":"Neural dynamics and brain function","score":0.15870000422000885,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.15870000422000885,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.10660000145435333,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.10559999942779541,"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/scaling","display_name":"Scaling","score":0.6539000272750854},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.47540000081062317},{"id":"https://openalex.org/keywords/compression","display_name":"Compression (physics)","score":0.4487999975681305},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43970000743865967},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.42320001125335693},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4203999936580658},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3982999920845032},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3831000030040741}],"concepts":[{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6539000272750854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5436000227928162},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.47540000081062317},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.4487999975681305},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43970000743865967},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.42320001125335693},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4203999936580658},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.398499995470047},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36090001463890076},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.35830000042915344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3492000102996826},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3310999870300293},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31630000472068787},{"id":"https://openalex.org/C2988430800","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Scaling law","level":3,"score":0.30469998717308044},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.30230000615119934},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C89735579","wikidata":"https://www.wikidata.org/wiki/Q6795894","display_name":"Maximum entropy spectral estimation","level":3,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2511.07892","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.07892","pdf_url":"https://arxiv.org/pdf/2511.07892","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2511.07892","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.07892","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.07892","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.07892","pdf_url":"https://arxiv.org/pdf/2511.07892","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":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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4416377069.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Empirical":[0],"scaling":[1,29],"laws":[2,21],"describe":[3],"how":[4],"test":[5],"loss":[6],"and":[7,17,62,100,106,113],"other":[8],"performance":[9],"metrics":[10],"depend":[11],"on":[12],"model":[13,39],"size,":[14,16],"dataset":[15],"compute.":[18],"While":[19],"such":[20,37],"are":[22],"consistent":[23],"within":[24],"specific":[25],"regimes,":[26],"apparently":[27],"distinct":[28],"behaviors":[30],"have":[31],"been":[32],"reported":[33],"for":[34],"related":[35],"settings":[36],"as":[38,103],"compression.":[40],"Motivated":[41],"by":[42,89],"recent":[43],"progress":[44],"in":[45],"spectral":[46,56,73],"analyses":[47],"of":[48],"neural":[49],"representations,":[50],"this":[51],"paper":[52],"develops":[53],"a":[54,66],"\\emph{generalized":[55],"framework}":[57],"that":[58],"unifies":[59],"learning":[60,112],"dynamics":[61],"compression":[63,114],"phenomena":[64],"under":[65],"common":[67],"functional":[68],"ansatz.":[69],"We":[70],"generalize":[71],"the":[72,77],"evolution":[74],"function":[75,86],"from":[76],"linear":[78],"kernel":[79],"form":[80],"$g(\u03bbt)=\u03bbt$":[81],"to":[82],"an":[83,90,108],"asymptotically":[84],"polynomial":[85],"$g(\u03bb,t;\u03b2)$,":[87],"characterized":[88],"effective":[91],"spectral--temporal":[92],"elasticity":[93],"$\u03c1(\u03b2)$.":[94],"This":[95],"framework":[96],"recovers":[97],"existing":[98],"lazy":[99],"feature-learning":[101],"theories":[102],"special":[104],"cases":[105],"yields":[107],"invariant":[109],"relation":[110],"between":[111]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-11-13T00:00:00"}