{"id":"https://openalex.org/W7160824374","doi":"https://doi.org/10.48550/arxiv.2605.08037","title":"Beyond Pairs: Your Language Model is Secretly Optimizing a Preference Graph","display_name":"Beyond Pairs: Your Language Model is Secretly Optimizing a Preference Graph","publication_year":2026,"publication_date":"2026-05-08","ids":{"openalex":"https://openalex.org/W7160824374","doi":"https://doi.org/10.48550/arxiv.2605.08037"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.08037","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08037","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.2605.08037","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135877720","display_name":"Ning Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Ning","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087094568","display_name":"Chuanneng Sun","orcid":"https://orcid.org/0000-0001-7524-9044"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Chuanneng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135899733","display_name":"Kristina Klinkner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Klinkner, Kristina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059403175","display_name":"Shervin Malmasi","orcid":"https://orcid.org/0000-0001-6250-5571"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Malmasi, Shervin","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/T11273","display_name":"Advanced Graph Neural Networks","score":0.1868000030517578,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.1868000030517578,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.10890000313520432,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.040300000458955765,"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/pairwise-comparison","display_name":"Pairwise comparison","score":0.8324999809265137},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.5205000042915344},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.5004000067710876},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.47760000824928284},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45170000195503235},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.4399000108242035},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.42829999327659607},{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.4223000109195709}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.8324999809265137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5950000286102295},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5205000042915344},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.5004000067710876},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.49790000915527344},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.47760000824928284},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45170000195503235},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.4399000108242035},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.42829999327659607},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.4223000109195709},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4000999927520752},{"id":"https://openalex.org/C181204326","wikidata":"https://www.wikidata.org/wiki/Q7239820","display_name":"Preference learning","level":3,"score":0.3734000027179718},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3483999967575073},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C195818886","wikidata":"https://www.wikidata.org/wiki/Q5421724","display_name":"Expressive power","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27619999647140503},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2680000066757202},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.25369998812675476},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.08037","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08037","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.2605.08037","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08037","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":{"Direct":[0,69],"Preference":[1,70],"Optimization":[2,71],"(DPO)":[3],"aligns":[4],"language":[5],"models":[6],"using":[7],"pairwise":[8,42,208],"preference":[9,39,83,199],"comparisons,":[10],"offering":[11],"a":[12,73,97,114,202],"simple":[13],"and":[14,60,95,136,172,189,204,209],"effective":[15],"alternative":[16,206],"to":[17,45,63,207],"Reinforcement":[18],"Learning":[19],"(RL)":[20],"from":[21],"human":[22],"feedback.":[23],"However,":[24],"in":[25],"many":[26],"practical":[27],"settings,":[28],"training":[29,180],"data":[30,49],"consists":[31],"of":[32,76],"multiple":[33],"rollouts":[34],"per":[35],"prompt,":[36],"inducing":[37],"rich":[38],"structure":[40],"that":[41,78,101,177,197],"DPO":[43,77,112],"fails":[44],"exploit.":[46],"Collapsing":[47],"such":[48],"into":[50],"independent":[51],"pairs":[52],"discards":[53],"transitivity,":[54],"introduces":[55],"redundant":[56],"or":[57,120],"conflicting":[58],"supervision,":[59],"can":[61],"lead":[62],"unstable":[64],"optimization.":[65],"We":[66,159],"propose":[67],"Graph":[68],"(GraphDPO),":[72],"principled":[74],"generalization":[75],"operates":[79],"over":[80,104],"directed":[81],"acyclic":[82],"graphs":[84],"induced":[85],"by":[86,165],"rollout":[87],"rankings.":[88],"GraphDPO":[89,150],"encodes":[90],"dominance":[91],"relations":[92],"as":[93,113,169],"edges":[94,138],"optimizes":[96],"graph-structured":[98,198],"Plackett--Luce-inspired":[99],"objective":[100],"aggregates":[102],"supervision":[103],"graph":[105,134,148],"neighborhoods,":[106],"enforcing":[107],"transitivity":[108],"while":[109,181],"recovering":[110],"standard":[111],"special":[115],"case.":[116],"To":[117],"handle":[118],"discrete":[119],"sparse":[121],"signals,":[122],"we":[123],"introduce":[124],"an":[125,174],"equivalence-class":[126],"construction":[127],"where":[128],"responses":[129],"with":[130],"identical":[131],"preferences":[132],"form":[133],"layers,":[135],"intra-layer":[137],"contribute":[139],"zero":[140],"loss,":[141],"preventing":[142],"spurious":[143],"gradients.":[144],"Despite":[145],"leveraging":[146],"full":[147],"structure,":[149],"maintains":[151],"linear":[152],"per-prompt":[153],"complexity":[154],"via":[155],"efficient":[156],"log-sum-exp":[157],"aggregation.":[158],"further":[160],"incorporate":[161],"optional":[162],"ground-truth":[163],"anchoring":[164],"inserting":[166],"verified":[167],"solutions":[168],"dominant":[170],"nodes":[171],"applying":[173],"annealed":[175],"schedule":[176],"stabilizes":[178],"early":[179],"gradually":[182],"relaxing":[183],"oracle":[184],"supervision.":[185],"Experiments":[186],"on":[187],"reasoning":[188],"program":[190],"synthesis":[191],"tasks":[192],"demonstrate":[193],"superior":[194],"performance,":[195],"suggesting":[196],"modeling":[200],"is":[201],"scalable":[203],"robust":[205],"listwise":[210],"alignment":[211],"objectives.":[212]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-12T00:00:00"}