{"id":"https://openalex.org/W7220917153","doi":"https://doi.org/10.48550/arxiv.2610.09886","title":"Sparsifying Stochasticity, Not Capacity: Partial Stochasticity via Deep Weight Factorization of Prior Scales","display_name":"Sparsifying Stochasticity, Not Capacity: Partial Stochasticity via Deep Weight Factorization of Prior Scales","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220917153","doi":"https://doi.org/10.48550/arxiv.2610.09886"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09886","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09886","pdf_url":"https://arxiv.org/pdf/2610.09886","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.09886","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120532823","display_name":"Marius P. Linhard","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Linhard, Marius P","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes , France","institution_ids":["https://openalex.org/I899635006"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021162375","display_name":"Maurizio Filippone","orcid":"https://orcid.org/0000-0001-7294-472X","observed_orcids":["https://orcid.org/0000-0001-7294-472X"]},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Filippone, Maurizio","raw_affiliation_strings":["KAUST , Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KAUST , Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9980000257492065,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9980000257492065,"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/T10320","display_name":"Neural Networks and Applications","score":0.0006000000284984708,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.00019999999494757503,"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/bayesian-neural-networks","display_name":"Bayesian neural networks","score":0.9430000185966492},{"id":"https://openalex.org/keywords/maximum-mean-discrepancy","display_name":"maximum mean discrepancy","score":0.6729999780654907},{"id":"https://openalex.org/keywords/gaussian-process-priors","display_name":"Gaussian process priors","score":0.746999979019165},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"stochastic approximation","score":0.5049999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.621999979019165},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4830000102519989},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.47760000824928284},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4569999873638153},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4496999979019165},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.43479999899864197},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4074999988079071},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.38019999861717224},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3368000090122223},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.32659998536109924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3222000002861023},{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.31119999289512634},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.29019999504089355},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2782999873161316},{"id":"https://openalex.org/C91716921","wikidata":"https://www.wikidata.org/wiki/Q1289366","display_name":"Scale parameter","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.2590999901294708},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.2590000033378601},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.25130000710487366},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09886","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09886","pdf_url":"https://arxiv.org/pdf/2610.09886","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.09886","doi":"https://doi.org/10.48550/arxiv.2610.09886","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09886","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09886","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09886","pdf_url":"https://arxiv.org/pdf/2610.09886","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220917153.pdf","grobid_xml":"https://content.openalex.org/works/W7220917153.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W4387221896","https://openalex.org/W6888914244","https://openalex.org/W6888926718","https://openalex.org/W6888945715","https://openalex.org/W6907693833","https://openalex.org/W6945636699","https://openalex.org/W6963913421","https://openalex.org/W6963942687"],"related_works":["https://openalex.org/W4309047569","https://openalex.org/W4399151408","https://openalex.org/W4391631484","https://openalex.org/W7104025611","https://openalex.org/W2149991584","https://openalex.org/W3132413728","https://openalex.org/W3064582752","https://openalex.org/W3130823131","https://openalex.org/W4386075730","https://openalex.org/W2995393114"],"abstract_inverted_index":{"Bayesian":[0],"neural":[1],"networks":[2],"need":[3],"not":[4,145],"be":[5,9,21],"fully":[6,204],"stochastic":[7,124,205],"to":[8,32,50,161,171,189],"universal":[10,89],"conditional":[11,90],"density":[12,91],"approximators,":[13],"but":[14],"it":[15,105],"remains":[16],"open":[17],"which":[18,36],"parameters":[19,118,213],"should":[20],"stochastic.":[22],"We":[23,84,107],"learn":[24],"this":[25],"split":[26,158],"by":[27,187],"applying":[28],"deep":[29],"weight":[30],"factorization":[31],"the":[33,38,42,47,77,111,121,148,156,172,179],"prior":[34,49,63,181],"scales,":[35],"are":[37,185],"standard":[39],"deviations":[40],"of":[41,115,192,211],"parameter":[43,61],"priors,":[44],"while":[45,174,207],"fitting":[46],"functional":[48],"a":[51,55,67,86,101,127,130,140,153,203],"Gaussian":[52],"process":[53],"with":[54,100,202],"maximum":[56,129],"mean":[57],"discrepancy":[58],"objective.":[59],"A":[60],"whose":[62],"scale":[64],"falls":[65],"below":[66],"cutoff":[68],"becomes":[69],"deterministic":[70],"and":[71,119,133,168],"is":[72,94,123,169],"optimized":[73],"during":[74],"inference,":[75],"so":[76],"regularizer":[78],"sparsifies":[79],"stochasticity":[80],"rather":[81],"than":[82],"capacity.":[83],"give":[85],"certificate":[87],"for":[88,126],"approximation":[92,125],"that":[93,110,134,143,177],"checkable":[95],"in":[96],"linear":[97],"time,":[98],"together":[99],"minimal":[102],"repair":[103],"when":[104],"fails.":[106],"further":[108],"show":[109],"common":[112],"hybrid":[113],"scheme":[114],"sampling":[116],"some":[117],"optimizing":[120],"others":[122],"type-II":[128],"posteriori":[131],"objective,":[132],"coupled":[135],"step":[136,149],"sizes":[137],"can":[138],"leave":[139],"tracking":[141],"error":[142],"does":[144],"vanish":[146],"as":[147],"size":[150],"shrinks.":[151],"On":[152,194],"bimodal":[154],"target,":[155],"learned":[157],"stays":[159],"close":[160],"an":[162],"unconstrained":[163],"reference":[164],"across":[165,183],"all":[166],"budgets":[167],"insensitive":[170],"cutoff,":[173],"random":[175],"masks":[176],"distribute":[178],"same":[180],"scales":[182],"layers":[184],"worse":[186],"up":[188],"two":[190],"orders":[191],"magnitude.":[193],"UCI":[195],"benchmarks,":[196],"our":[197],"method":[198],"performs":[199],"on":[200],"par":[201],"network":[206],"keeping":[208],"about":[209],"half":[210],"its":[212],"deterministic.":[214]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}