[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82488-en":3,"doc-seo-82488-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82488,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Multi-Hypothesis Test-Time Adaptation to Mitigate Underspecification","Test-Time Adaptation (TTA) improves robustness under distribution shift by adapting model parameters using unlabeled target data, yet entropy-based TTA is underconstrained: multiple distinct parameter updates can yield similarly low entropy while producing very different decision boundaries, a problem called underspecification. This work reframes TTA via a posterior-inspired view from entropy minimization, defining a pseudo-likelihood over parameters. It proposes a particle-based multi-hypothesis diversification wrapper that jointly explores plausible adaptation trajectories at multiple levels. Experiments on challenging benchmarks show consistent stability and robustness gains (3–4% for mixed shifts, 2–3% with batch size one, 1–2.5% for label shifts).","arXiv :2607 .00259v1 [ cs .CV] 30 Jun 2026  \nMulti-Hypothesis Test-Time Adaptation to Mitigate Underspecification  \nAfshar Shamsi 1 , Xiao-Yu Guo2 , Hamid Alinejad-Rokny3 Arash Mohammadi 1 , Damien Teney4 , and Ehsan Abbasnejad5  \n1 Concordia University, Canada  \n{afshar.shamsi,[arash.mohammadi}@concordia.ca](arash.mohammadi}@concordia.ca)  \n2 Australian Institute for Machine Learning, Australia  \n[xiaoyu.guo@gmail.com](xiaoyu.guo@gmail.com)  \n3 University of New South Wales, Australia  \n[h.alinejad@unsw.edu.au](h.alinejad@unsw.edu.au)  \n4 Idiap Research Institute, Switzerland  \n[damien.teney@idiap.ch](damien.teney@idiap.ch)  \n5 Monash University, Australia  \n[Ehsan.Abbasnejad@monash.edu](Ehsan.Abbasnejad@monash.edu)  \nAbstract. Test-Time Adaptation (TTA) seeks to improve model robustness under distribution shifts by adapting parameters using unlabeled target data. However, in the absence of supervision, entropy-based adaptation is fundamentally underconstrained: multiple distinct parameter updates can achieve similarly low entropy while inducing drastically different decision boundaries. This phenomenon, known as underspecification, renders standard TTA brittle and prone to collapse into spurious modes. In this work, we reinterpret TTA through a posterior-inspired lens induced by entropy minimization, where low-entropy solutions define a pseudo-likelihood over parameters. Instead of committing to a single point estimate, we introduce a particle-based diversification framework that explores multiple plausible adaptation trajectories simultaneously. Our method can be viewed as a structured exploration of multiple plausible adaptation solutions, implemented through multi-level diversification atthe output, parameter, optimizer, and input levels. Crucially, the framework acts as a plug-and-play wrapper compatible with existing TTA methods. Extensive experiments on challenging benchmarks demonstrate consistent gains in stability and robustness, achieving improvements of 3–4% under mixed shifts, 2–3% with batch size one, and 1–2.5% under label shifts, outperforming state-of-the-art baselines. Our results suggest that treating TTA as a multi-hypothesis inference problem, rather thana single-point optimization task, is key to mitigating underspecification and enabling reliable real-world deployment.  \nKeywords: Test-Time Adaptation · Underspecification · Model Diversification  \n2 A. Shamsi et al.  \nNormalization Layers (NLs)  \ny1 = x~~ ~~−~~ ~~EVar~~ ~~x][x+]~~ ~~⋅ γ1 + β1  y2 = x~~ ~~−~~ ~~EVar~~ ~~x][x+]~~ ~~⋅ γ2 + β2   \n =  \ny1 + y2 2  \nFig. 1: Conceptual illustration of multi-hypothesis test-time adaptation. Entropy minimization can yield multiple low-entropy solutions in the adaptation landscape. Standard TTA follows a single trajectory from θ0 , which may converge to a suboptimal decision boundary. Our framework instead maintains multiple adaptation particles (θ1 , θ2 ) by adapting separate normalization parameters. Aggregating their predictions produces amore stable adaptation and mitigates underspecification.  \n1 Introduction  \nDeep learning models have achieved remarkable performance across a range of tasks when training and test data are drawn from the same distribution. However, their performance often degrades sharply when deployed in the wild, where distribution shifts are inevitable [23, 26] . Test-time adaptation (TTA) has emerged as a promising strategy to bridge this train–test gap by adapting the model to the target distribution using only unlabeled test data [31, 33, 34] .  \nDespite its appeal, standard TTA optimizes a single entropy-based objective in the absence of ground-truth supervision. This renders the adaptation process fundamentally underconstrained: multiple parameter configurations can achieve similarly low entropy on the target data while corresponding to qualitatively different decision boundaries. This phenomenon, underspecification, has been shown to induce instability and spurious feature reliance i","cbCaisfyuobp69qZ","https://ap.wps.com/l/cbCaisfyuobp69qZ","pdf",2617700,1,26,"English","en",105,"# Introduction\n## Problem: Underspecification in Standard TTA\n## Proposed approach: Particle-based multi-hypothesis diversification\n## Experimental evaluation and results","[{\"question\":\"What is underspecification in test-time adaptation?\",\"answer\":\"Underspecification refers to the underconstrained nature of entropy-based adaptation: different parameter updates can produce similarly low entropy but lead to qualitatively different decision boundaries.\"},{\"question\":\"How does the proposed method reinterpret TTA?\",\"answer\":\"It reformulates TTA as a posterior-inspired inference process, where entropy minimization induces a pseudo-likelihood over parameters and encourages exploring multiple plausible low-entropy solutions rather than a single trajectory.\"},{\"question\":\"What diversification levels does the framework use?\",\"answer\":\"The method performs multi-level diversification at the output, parameter, optimizer, and input levels, maintaining multiple adaptation particles and regularizing them to avoid premature mode collapse.\"}]",1784180876,66,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"multi-hypothesis-test-time-adaptation-to-mitigate-underspecification","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/multi-hypothesis-test-time-adaptation-to-mitigate-underspecification/82488/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is underspecification in test-time adaptation?","Question",{"text":75,"@type":76},"Underspecification refers to the underconstrained nature of entropy-based adaptation: different parameter updates can produce similarly low entropy but lead to qualitatively different decision boundaries.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method reinterpret TTA?",{"text":80,"@type":76},"It reformulates TTA as a posterior-inspired inference process, where entropy minimization induces a pseudo-likelihood over parameters and encourages exploring multiple plausible low-entropy solutions rather than a single trajectory.",{"name":82,"@type":73,"acceptedAnswer":83},"What diversification levels does the framework use?",{"text":84,"@type":76},"The method performs multi-level diversification at the output, parameter, optimizer, and input levels, maintaining multiple adaptation particles and regularizing them to avoid premature mode 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