{"id":"https://openalex.org/W7154743487","doi":"https://doi.org/10.48550/arxiv.2604.15149","title":"LLMs Gaming Verifiers: RLVR can Lead to Reward Hacking","display_name":"LLMs Gaming Verifiers: RLVR can Lead to Reward Hacking","publication_year":2026,"publication_date":"2026-04-16","ids":{"openalex":"https://openalex.org/W7154743487","doi":"https://doi.org/10.48550/arxiv.2604.15149"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.15149","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.15149","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.2604.15149","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092171975","display_name":"Lukas Helff","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Helff, Lukas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059077091","display_name":"Quentin Delfosse","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Delfosse, Quentin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133872602","display_name":"David Steinmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steinmann, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133903131","display_name":"Ruben H\u00e4rle","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H\u00e4rle, Ruben","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063339544","display_name":"Hikaru Shindo","orcid":"https://orcid.org/0000-0001-7129-6118"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shindo, Hikaru","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133861454","display_name":"Patrick Schramowski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schramowski, Patrick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034737333","display_name":"Wolfgang Stammer","orcid":"https://orcid.org/0000-0003-3793-8046"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stammer, Wolfgang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133878599","display_name":"Kristian Kersting","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kersting, Kristian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133870962","display_name":"Felix Friedrich","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Friedrich, Felix","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":9,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.33000001311302185,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.33000001311302185,"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":0.17440000176429749,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.12470000237226486,"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/correctness","display_name":"Correctness","score":0.766700029373169},{"id":"https://openalex.org/keywords/imperfect","display_name":"Imperfect","score":0.6414999961853027},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.5047000050544739},{"id":"https://openalex.org/keywords/extensional-definition","display_name":"Extensional definition","score":0.48840001225471497},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.4603999853134155},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.436599999666214},{"id":"https://openalex.org/keywords/incentive","display_name":"Incentive","score":0.40720000863075256},{"id":"https://openalex.org/keywords/coin-flipping","display_name":"Coin flipping","score":0.37959998846054077},{"id":"https://openalex.org/keywords/lead","display_name":"Lead (geology)","score":0.3522999882698059}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.766700029373169},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.6414999961853027},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6118999719619751},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C136137745","wikidata":"https://www.wikidata.org/wiki/Q19515659","display_name":"Extensional definition","level":3,"score":0.48840001225471497},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.4603999853134155},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.436599999666214},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4156000018119812},{"id":"https://openalex.org/C29122968","wikidata":"https://www.wikidata.org/wiki/Q1414816","display_name":"Incentive","level":2,"score":0.40720000863075256},{"id":"https://openalex.org/C97399411","wikidata":"https://www.wikidata.org/wiki/Q825367","display_name":"Coin flipping","level":2,"score":0.37959998846054077},{"id":"https://openalex.org/C180747234","wikidata":"https://www.wikidata.org/wiki/Q23373","display_name":"Cognitive psychology","level":1,"score":0.36230000853538513},{"id":"https://openalex.org/C2777093003","wikidata":"https://www.wikidata.org/wiki/Q6508345","display_name":"Lead (geology)","level":2,"score":0.3522999882698059},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.3206999897956848},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C51234621","wikidata":"https://www.wikidata.org/wiki/Q2149495","display_name":"Testability","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C2781198186","wikidata":"https://www.wikidata.org/wiki/Q701521","display_name":"Collusion","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C2777179996","wikidata":"https://www.wikidata.org/wiki/Q911222","display_name":"Mistake","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.2802000045776367},{"id":"https://openalex.org/C166151441","wikidata":"https://www.wikidata.org/wiki/Q4923601","display_name":"Causation","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.274399995803833},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.273499995470047},{"id":"https://openalex.org/C159032336","wikidata":"https://www.wikidata.org/wiki/Q2488768","display_name":"Non-monotonic logic","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C151913843","wikidata":"https://www.wikidata.org/wiki/Q3454555","display_name":"Dominance (genetics)","level":3,"score":0.26579999923706055},{"id":"https://openalex.org/C45493050","wikidata":"https://www.wikidata.org/wiki/Q7884934","display_name":"Unified Model","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C2777152325","wikidata":"https://www.wikidata.org/wiki/Q108163","display_name":"Proposition","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2526000142097473},{"id":"https://openalex.org/C2781466463","wikidata":"https://www.wikidata.org/wiki/Q621695","display_name":"Blame","level":2,"score":0.25110000371932983},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.25}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.15149","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.15149","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.2604.15149","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.15149","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5090734362602234}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"As":[0],"reinforcement":[1],"Learning":[2],"with":[3,175],"Verifiable":[4],"Rewards":[5],"(RLVR)":[6],"has":[7],"become":[8],"the":[9,74,79,131,215],"dominant":[10],"paradigm":[11],"for":[12],"scaling":[13],"reasoning":[14,32,157],"capabilities":[15],"in":[16,164],"LLMs,":[17],"a":[18,88,93,120],"new":[19],"failure":[20,89],"mode":[21],"emerges:":[22],"LLMs":[23],"gaming":[24],"verifiers.":[25],"We":[26,42,81,148],"study":[27],"this":[28,84],"phenomenon":[29],"on":[30],"inductive":[31],"tasks,":[33],"where":[34,130],"models":[35,46,158,166],"must":[36],"induce":[37],"and":[38,127,162,178],"output":[39,123],"logical":[40],"rules.":[41],"find":[43,149],"that":[44,69,83,100,150,199],"RLVR-trained":[45,156],"systematically":[47],"abandon":[48],"rule":[49,141],"induction.":[50],"Instead":[51],"of":[52,90,95],"learning":[53],"generalizable":[54],"patterns":[55,76],"(e.g.,":[56,159,167],"``trains":[57],"carrying":[58],"red":[59],"cars":[60],"go":[61],"east''),":[62],"they":[63],"enumerate":[64],"instance-level":[65],"labels,":[66],"producing":[67],"outputs":[68],"pass":[70],"verifiers":[71,99],"without":[72],"capturing":[73],"relational":[75],"required":[77],"by":[78,212],"task.":[80],"show":[82,198],"behavior":[85,152],"is":[86,153],"not":[87,205],"understanding":[91],"but":[92,210],"form":[94],"reward":[96,203],"hacking:":[97],"imperfect":[98],"check":[101],"only":[102,206],"extensional":[103,126,185],"correctness":[104],"admit":[105],"false":[106],"positives.":[107],"To":[108],"detect":[109],"such":[110],"shortcuts,":[111],"we":[112],"introduce":[113],"Isomorphic":[114],"Perturbation":[115],"Testing":[116],"(IPT),":[117],"which":[118],"evaluates":[119],"single":[121],"model":[122],"under":[124,135],"both":[125],"isomorphic":[128,137,192],"verification,":[129],"latter":[132],"enforces":[133],"invariance":[134],"logically":[136],"tasks.":[138],"While":[139],"genuine":[140],"induction":[142],"remains":[143],"invariant,":[144],"shortcut":[145,151,172,189],"strategies":[146],"fail.":[147],"specific":[154],"to":[155,218],"GPT-5,":[160],"Olmo3)":[161],"absent":[163],"non-RLVR":[165],"GPT-4o,":[168],"GPT-4.5,":[169],"Ministral).":[170],"Moreover,":[171],"prevalence":[173],"increases":[174],"task":[176],"complexity":[177],"inference-time":[179],"compute.":[180],"In":[181],"controlled":[182],"training":[183],"experiments,":[184],"verification":[186,193],"directly":[187],"induces":[188],"strategies,":[190],"while":[191],"eliminates":[194],"them.":[195],"These":[196],"results":[197],"RLVR":[200],"can":[201],"incentivize":[202],"hacking":[204],"through":[207],"overt":[208],"manipulation":[209],"also":[211],"exploiting":[213],"what":[214],"verifier":[216],"fails":[217],"enforce.":[219]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-18T00:00:00"}