{"id":"https://openalex.org/W7154222555","doi":"https://doi.org/10.48550/arxiv.2604.10727","title":"Tail-Aware Information-Theoretic Generalization for RLHF and SGLD","display_name":"Tail-Aware Information-Theoretic Generalization for RLHF and SGLD","publication_year":2026,"publication_date":"2026-04-12","ids":{"openalex":"https://openalex.org/W7154222555","doi":"https://doi.org/10.48550/arxiv.2604.10727"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.10727","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.10727","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.2604.10727","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100655848","display_name":"Huiming Zhang","orcid":"https://orcid.org/0000-0001-7300-6348"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Huiming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133618900","display_name":"Binghan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Binghan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128486202","display_name":"Wan Tian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tian, Wan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133613304","display_name":"Qiang Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Qiang","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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.33730000257492065,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.33730000257492065,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.18459999561309814,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.09849999845027924,"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/generalization","display_name":"Generalization","score":0.6592000126838684},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5716000199317932},{"id":"https://openalex.org/keywords/chaining","display_name":"Chaining","score":0.520799994468689},{"id":"https://openalex.org/keywords/langevin-dynamics","display_name":"Langevin dynamics","score":0.4964999854564667},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.43619999289512634},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.4268999993801117},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4066999852657318},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.39489999413490295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7459999918937683},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6592000126838684},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5716000199317932},{"id":"https://openalex.org/C49020025","wikidata":"https://www.wikidata.org/wiki/Q1059099","display_name":"Chaining","level":2,"score":0.520799994468689},{"id":"https://openalex.org/C2780004032","wikidata":"https://www.wikidata.org/wiki/Q6485978","display_name":"Langevin dynamics","level":2,"score":0.4964999854564667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47440001368522644},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.43619999289512634},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.4268999993801117},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4066999852657318},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.39489999413490295},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.32330000400543213},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.298799991607666},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29510000348091125},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.2644999921321869},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2565999925136566},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25619998574256897},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2517000138759613}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.10727","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.10727","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.2604.10727","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.10727","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Classical":[0],"information-theoretic":[1,58,152],"generalization":[2,7,146],"bounds":[3,94],"typically":[4],"control":[5],"the":[6,22,64,69,112,163],"gap":[8],"through":[9],"KL-based":[10,51],"mutual":[11,159],"information":[12],"and":[13,36,40,45,79,120,137,143,171],"therefore":[14],"rely":[15],"on":[16,156],"boundedness":[17],"or":[18],"sub-Gaussian":[19],"tails":[20],"via":[21],"moment":[23],"generating":[24],"function":[25],"(MGF).":[26],"In":[27],"many":[28],"modern":[29],"pipelines,":[30],"such":[31],"as":[32,135,148,150],"robust":[33],"learning,":[34],"RLHF,":[35],"stochastic":[37,173],"optimization,":[38],"losses":[39],"rewards":[41,170],"can":[42],"be":[43],"heavy-tailed,":[44],"MGFs":[46],"may":[47],"not":[48],"exist,":[49],"rendering":[50],"tools":[52,140],"ineffective.":[53],"We":[54,161],"develop":[55],"a":[56,90,98,121],"tail-dependent":[57],"framework":[59],"for":[60,125],"sub-Weibull":[61,126],"data,":[62],"where":[63],"tail":[65,70,129],"parameter":[66],"$\u03b8$":[67],"controls":[68],"heaviness:":[71],"$\u03b8=2$":[72],"corresponds":[73],"to":[74,77,81,105],"sub-Gaussian,":[75],"$\u03b8=1$":[76],"sub-exponential,":[78],"$0&lt;\u03b8&lt;1$":[80],"genuinely":[82],"heavy":[83],"tails.":[84],"Our":[85],"key":[86],"technical":[87],"ingredient":[88],"is":[89],"decorrelation":[91],"lemma":[92],"that":[93],"change-of-measure":[95],"expectations":[96],"using":[97],"shifted-log":[99],"$f_\u03b8$-divergence,":[100],"which":[101],"admits":[102],"explicit":[103],"comparisons":[104],"R\u00e9nyi":[106,158],"divergence":[107],"without":[108],"MGF":[109],"arguments.":[110],"On":[111],"empirical-process":[113],"side,":[114],"we":[115],"establish":[116],"sharp":[117],"maximal":[118],"inequalities":[119],"Dudley-type":[122],"chaining":[123,153],"bound":[124],"processes":[127],"with":[128,132,177],"index":[130],"$\u03b8$,":[131],"complexity":[133],"scaling":[134],"$\\log^{1/\u03b8}$":[136],"entropy$^{1/\u03b8}$.":[138],"These":[139],"yield":[141],"expected":[142],"high-probability":[144],"PAC-Bayes":[145],"bounds,":[147],"well":[149],"an":[151],"inequality":[154],"based":[155],"multiscale":[157],"information.":[160],"illustrate":[162],"consequences":[164],"in":[165,172],"R\u00e9nyi-regularized":[166],"RLHF":[167],"under":[168],"heavy-tailed":[169,178],"gradient":[174,179],"Langevin":[175],"dynamics":[176],"noise.":[180]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-15T00:00:00"}
