[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86408-en":3,"doc-seo-86408-105":30,"detail-sidebar-cat-0-en-105":92},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86408,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","From Performance to Representational Adequacy A Representational Bootstrap Framework for Adaptive Biological Systems","Observable performance is widely used to characterize biological systems, yet adaptive settings can leave aggregated outputs unable to uniquely resolve observational conditions, while multivariate representations may still be ambiguous. This article introduces a representational bootstrap framework where new analytical levels emerge when the current active representation becomes insufficient for the posed question. The framework proceeds through five successive levels, forming a progressive sequence for constructing increasingly adequate analyses, and is illustrated on gait–occlusion studies as a methodological case sequence.","arXiv :2606 .0 1374v 3 [ cs .LG] 13 Jul 2026  \nFrom Performance to Representational Adequacy: A Representational Bootstrap Framework for Adaptive Biological Systems  \nJacques Raynal 1 , ∗ , Pierre Slangen2 , Elsa Raynal3 , Jacques Margerit4  \n1Laboratory of Bioengineering and Nanosciences (LBN), University of Montpellier, France  \n2EuroMov Digital Health in Motion, University of Montpellier, IMT Mines Alès, Alès, France  \n3 Certified Sophrologist and Dental Assistant, Sensorimotor Practice, Montpellier, France  \n4Emeritus Professor, University of Montpellier, France  \n∗ Corresponding author: [raynal.cab@gmail.com](raynal.cab@gmail.com)  \nAbstract  \nObservable performance is commonly used to characterize biological systems. In adaptive systems, however, aggregated outputs may remain insufficient for uniquely resolving observational conditions, and richer multivariate representations may themselves retain substantial ambiguity.  \nThis article proposes a representational bootstrap framework for adaptive biological systems.  \nThe term bootstrap is used here in a methodological and epistemological sense, not in the statistical resampling sense. New analytical levels emerge progressively when the active representation becomes insufficient for the question under investigation.  \nThe framework is organized around five successive analytical levels: observable performance, conceptual dynamic organization, exploratory multivariate representation, observed longitudinal centroid displacement, and internal approximation of observed longitudinal displacement. These levels are not independent tools, but a progressive sequence through which increasingly adequate analytical representations can be constructed.  \nThe framework is illustrated by three previously reported gait–occlusion studies, used here as a methodological case sequence rather than as new experimental evidence. In the revised first study, neither the aggregated scalar score nor the static exploratory embedding uniquely resolved the occlusal observational probes. The second study therefore shifted the analysis from static representational nonidentifiability to longitudinal centroid displacement within a common PCA representation. The third study examined whether this observed representation-dependent transformation could be internally approximated by a supervised model.  \nThe contribution of this article is not a new algorithm, clinical protocol, or dataset. It is the formalization of a bootstrap methodology in which persistent explanatory insufficiency motivates changes in the analytical question and the emergence of new representational levels.  \nKeywords: representation learning; exploratory multivariate representation; representational nonidentifiability; adaptive biological systems; longitudinal centroid displacement; internal approximation; gait analysis; occlusal observational probes; biomechanics; representational bootstrap; scientific inquiry.  \n1 Introduction  \nBiological systems are often evaluated through observable performance. In biomechanics, physiology, rehabilitation, and clinical assessment, measurable outputs such as speed, symmetry, stability, pressure distribution, postural variables, physiological markers, or composite scores are commonly used to characterize the functional state of a system.  \nThe present work addresses a recurrent problem in representation learning: the progressive emergence of analytical levels when an available representation remains insufficient for the question under investigation.  \nIn adaptive biological systems, aggregated observable variables may fail to uniquely resolve experimental or clinical conditions. Introducing a multivariate representation may preserve relationships that are lost through scalar aggregation, but it does not necessarily produce clearly separated or physiologically interpretable states.  \nObservable analysis remains necessary. Observable variables provide reproducible descriptors, allow comparisons across cond","cbCaiga5Rk8nOO9G","https://ap.wps.com/l/cbCaiga5Rk8nOO9G","pdf",200805,5,1,23,"English","en",105,"# Abstract\n# Introduction\n## Observable performance and representation insufficiency\n## Constraints and longitudinal questions\n## Representational bootstrap framework overview","[{\"question\":\"Why can observable performance be insufficient for adaptive biological systems?\",\"answer\":\"In adaptive settings, aggregated outputs may not uniquely resolve observational conditions, and even richer multivariate embeddings can retain substantial ambiguity.\"},{\"question\":\"What does “bootstrap” mean in this framework?\",\"answer\":\"Bootstrap is used methodologically and epistemologically: new analytical levels emerge progressively when the active representation becomes insufficient, not primarily as statistical resampling.\"},{\"question\":\"How are the five analytical levels organized in the proposed framework?\",\"answer\":\"They form a progressive sequence: observable performance, conceptual dynamic organization, exploratory multivariate representation, observed longitudinal centroid displacement, and internal approximation of the longitudinal 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