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Without references, judges may rely on parametric knowledge and hallucinate, or use tool augmentation at added cost. The paper introduces a risk-controlled selective evaluation framework that calibrates uncertainty thresholds using finite-sample guarantees, routing uncertain cases to retrieval with a second calibrated threshold.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/judge-retrieve-or-abstain-uncertainty-guarded-llm-judging-with-provable-risk-guarantees/273547/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/judge-retrieve-or-abstain-uncertainty-guarded-llm-judging-with-provable-risk-guarantees/273547.png","ImageObject",300,407,{"name":92,"@type":93},"Maeve","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":46},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What reliability problem arises when LLMs judge without reference answers?","Question",{"text":112,"@type":113},"Reference-free judging forces the judge to assess correctness using parametric knowledge or tool evidence. Parametric knowledge can be insufficient or lead to hallucinated, confident verdicts, and tool use requires reliable criteria for when evidence is needed.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the proposed method control risk among accepted judgments?",{"text":117,"@type":113},"It calibrates uncertainty thresholds on a held-out set so the false discovery rate among accepted verdicts stays below a user-specified level with high probability. It uses finite-sample Clopper–Pearson intervals for formal control.",{"name":119,"@type":110,"acceptedAnswer":120},"What happens when the judge is uncertain in Mode 1?",{"text":121,"@type":113},"In Mode 1, if the parametric judge is confident the verdict is accepted; if uncertain, the instance is routed to Mode 2. Mode 2 retrieves web evidence and re-evaluates under a second calibrated threshold, abstaining if uncertainty persists.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},273547,1789472000,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":46,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144,"preview_page_count":4},5909877438554,"https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272","arXiv : 2608 . 17994v 1 [cs .CL] 18 Aug 2026  \nJudge, Retrieve, or Abstain: Uncertainty-Guarded LLM Judging with Provable Risk Guarantees  \nSher Badshah1,2, Ali Emami3, Hassan Sajjad1,2  \n1Dalhousie University 2New York University Abu Dhabi 3Emory University {sh545346,[hsajjad](hsajjad}@dal.ca)[}](hsajjad}@dal.ca)[@dal.ca](hsajjad}@dal.ca)  \n[ali.emami@emory.edu](ali.emami@emory.edu)  \nAbstract  \nUsing LLMs as judges has become standard practice for evaluating model outputs at scale. This is particularly common for subjective, open-ended tasks such as assessing helpfulness or alignment, where no single reference answer exists. However, objective tasks introduce a distinct reliability challenge for reference-free LLM judging. In the absence of a reference answer, the judge evaluates factual correctness either through its parametric knowledge or through tool augmentation. Although the former enables efficient evaluation, the judge may hallucinate or lack sufficient evidence for its verdict. Conversely, tool augmentation can provide additional evidence but introduces extra computational cost and requires an appropriate mechanism to determine when and how that evidence should be used reliably.  \nMore importantly, neither approach alone provides formal control over the risk of accepted verdicts or guarantees their reliability at a specified level. We propose a risk-controlled framework that calibrates uncertainty thresholds on a held-out set so that the false discovery rate among accepted verdicts remains below a user-specified level α with high probability, using finite-sample Clopper–Pearson intervals. When the parametric mode isnot sufficiently confident, the instance is routed to a retrieval-augmented mode, where the judge gathers web evidence and re-evaluates the instance under a second calibrated threshold. The finite-sample guarantee carries over to this two-threshold routing without additional assumptions. Across open-domain QA benchmarks and judges of varying scales, the framework maintains the target error rate while achieving substantially higher coverage than single-mode baselines.  \n1 Introduction  \nLLM-as-a-judge has emerged as a scalable alternative to human evaluation for assessing language model outputs (Zheng et al., 2023) . It enables practitioners to evaluate thousands of model outputs at a fraction of the cost and time required for human annotation (Gu et al., 2024; Tan et al., 2025) . However, most existing work employs LLM judges for subjective evaluation (Badshah et al., 2025), such as scoring outputs for helpfulness, harmlessness, or style in reward modeling, where no single correct answer exists and approximate agreement suffices (Yuan et al., 2024; Liu et al., 2023) . Extending LLM-as-a-judge to objective, factual evaluation remains an open challenge.  \nIn factual and open-domain QA, answers are either correct or incorrect, and the judge must make this determination reliably. However, obtaining g˜round-truth annotations  \nfor this purpose is expensive at scale (Chiang & Lee, 2023; Manas et al., 2024), requires domain expertise for specialized questions, and is entirely infeasible when LLMs operate as autonomous agents answering open-ended queries in real-world environments where no pre-collected labels exist. LLM-as-a-judge offers a reference-free alternative that eliminates this dependency. Nevertheless, utilizing LLM judges to assess correctness without explicit references introduces two key reliability challenges (Schroeder & Wood-Doughty, 2025; Badshah & Sajjad, 2025) .  \nFirst, LLM judges are bounded by their training data and may lack knowledge of recent events, rare entities, or specialized domains (Wen et al., 2025) . Such limitations can prevent reliable distinction between correct answers and plausible fabrications. Second, even if the judge has the relevant knowledge, hallucinations may still cause it to produce confident but incorrect verdicts (Huang et al., 2025) . In both cases, the failures","cbCaidFv8SfJJY9N","https://ap.wps.com/l/cbCaidFv8SfJJY9N","pdf",454251,25,"English","# Abstract\n# 1 Introduction\n## LLM-as-a-judge for objective evaluation\n## Reliability challenges in reference-free judging\n## Selective evaluation and risk-controlled thresholds\n## Proposed two-mode risk-controlled framework","[{\"question\":\"What reliability problem arises when LLMs judge without reference answers?\",\"answer\":\"Reference-free judging forces the judge to assess correctness using parametric knowledge or tool evidence. Parametric knowledge can be insufficient or lead to hallucinated, confident verdicts, and tool use requires reliable criteria for when evidence is needed.\"},{\"question\":\"How does the proposed method control risk among accepted judgments?\",\"answer\":\"It calibrates uncertainty thresholds on a held-out set so the false discovery rate among accepted verdicts stays below a user-specified level with high probability. It uses finite-sample Clopper–Pearson intervals for formal control.\"},{\"question\":\"What happens when the judge is uncertain in Mode 1?\",\"answer\":\"In Mode 1, if the parametric judge is confident the verdict is accepted; if uncertain, the instance is routed to Mode 2. Mode 2 retrieves web evidence and re-evaluates under a second calibrated threshold, abstaining if uncertainty persists.\"}]","Judge, Retrieve, or Abstain - Uncertainty-Guarded LLM Judging with Provable Risk Guarantees | PDF",63]