[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82756-en":3,"doc-seo-82756-105":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},82756,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","The Informational Cost of Structure: Representational Complexity in Networked Dynamical Systems","The work quantifies how much information is required to represent a dynamical system using an interaction structure together with an evolution rule. It defines Representational Complexity as the excess description length of a structure-plus-rule model relative to the shortest exact description of the dynamics itself, establishing a universal intrinsic lower bound. When arbitrary rules are allowed, graph, hypergraph, and related formalisms can reach the same bound, so expressiveness alone cannot discriminate them. Meaningful differences arise only under scientific modeling constraints on admissible structures and rules.","arXiv :2607 .03608v 1 [ cs .IT] 3 Jul 2026  \nThe Informational Cost of Structure:  \nRepresentational Complexity in Networked Dynamical Systems  \nCyril Rommens, 1, 2 Pietro Traversa, 1, 2 Guilherme Ferraz de Arruda,3 and Yamir Moreno 1, 2, ∗  \n1 Institute for Biocomputation and Physics of Complex Systems (BIFI),  \nUniversidad de Zaragoza, 50018 Zaragoza, Spain  \n2 Department of Theoretical Physics, University of Zaragoza, 50009 Zaragoza, Spain  \n3 Instituto de F´ısica Gleb Wataghin, Universidade de Campinas (UNICAMP), Campinas, Brazil.  \nHow much information is required to represent a dynamical system in terms of an interaction structure and an evolution rule? We address this question using algorithmic information theory. We introduce Representational Complexity, the excess description length of a structure-plus-rule model relative to the shortest possible description of the dynamics itself. This intrinsic description defines a universal lower bound: no exact structural representation can be more concise. If arbitrary rules are allowed, graphs, hypergraphs, and other formalisms can all reach this bound by shifting information between structure and dynamics, so expressiveness alone cannot distinguish them. Meaningful differences arise only when scientific modeling restricts the admissible structures and rules. Within this setting, we identify conditions under which graph and hypergraph descriptions are informationally equivalent, and show how graph-preferred, hypergraph-preferred, and mixed regimescan emerge when those conditions are relaxed. Because Kolmogorov complexity is not computable, we complement the formal results with explicit description-length estimates. Our framework reframes the choice of network representation as a question of informational cost and mechanistic transparency rather than universal expressive power.  \nI. INTRODUCTION  \nStructural representations pervade complex-systems science [1–6] . The choice of structural language — graph, hypergraph, simplicial complex, etc. [7–14]—is often presented as a question of expressiveness: can the language represent the interactions of interest? A recent preprint by Peixoto et al. [15] argues that graphs are maximally expressive, subsuming hypergraph formulations as constrained special cases, a claim that has been debated on both technical and conceptual grounds [16–18] .  \nWe argue that expressiveness is not the right operational criterion. Any finite Boolean dynamical map is fully specified by its truth table, a finite binary string, and can therefore be encoded exactly within essentially any structural language by absorbing the missing information into the dynamical rule. Expressiveness alone thus cannot motivate a choice between graphs and hypergraphs. A more informative criterion is the informational cost of a representation [19– 21]: given a specific dynamical map F, a structural language, and a class of admissible dynamical rules, how much description length does the resulting representation minimally require?  \nInformational cost is, however, only part of the story. Scientific modeling is not merely the reproduction of input– output relations at minimal bit cost; it is an attempt to identify the relevant degrees of freedom, symmetries, and interaction mechanisms of a system. A fully flexible representation may achieve a short description while concealing the physical hypothesis inside an opaque effective rule. A more constrained representation can be scientifically preferable precisely because it makes that hypothesis explicit and testable. From this viewpoint, hypergraphs are not primarily a claim of greater representational power; they are modeling commitments that declare group-level interactions to be primitive objects [22–24] . The relevant question is therefore not whether a graph with sufficiently flexible node dynamics can emulate a hypergraph model [18], but whether doing so preserves parsimony, interpretability, identifiability, and mechanistic transp","cbCainHLUmICCvRF","https://ap.wps.com/l/cbCainHLUmICCvRF","pdf",561111,1,17,"English","en",105,"# Introduction\n## Representational languages and expressiveness\n## Informational cost as an operational criterion\n## Restricted vs unrestricted modeling\n## Informational equivalence and regime classification","[{\"question\":\"What is Representational Complexity in this framework?\",\"answer\":\"Representational Complexity is defined as the excess description length of a structure-plus-rule model relative to the shortest possible description of the dynamics itself.\"},{\"question\":\"Why does expressiveness alone not determine whether graphs or hypergraphs are better?\",\"answer\":\"With unrestricted dynamical rules, missing interaction information can be absorbed into the rule, so essentially any structural language can encode the dynamics with the same intrinsic lower bound.\"},{\"question\":\"Under what conditions do graph and hypergraph representations become informationally equivalent?\",\"answer\":\"They become informationally equivalent up to additive constants when the higher-order structure is recoverable from the graph through the dynamical rule, and the modeling respects the required admissible 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is Representational Complexity in this framework?","Question",{"text":75,"@type":76},"Representational Complexity is defined as the excess description length of a structure-plus-rule model relative to the shortest possible description of the dynamics itself.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why does expressiveness alone not determine whether graphs or hypergraphs are better?",{"text":80,"@type":76},"With unrestricted dynamical rules, missing interaction information can be absorbed into the rule, so essentially any structural language can encode the dynamics with the same intrinsic lower bound.",{"name":82,"@type":73,"acceptedAnswer":83},"Under what conditions do graph and hypergraph representations become informationally equivalent?",{"text":84,"@type":76},"They become informationally equivalent up to additive constants when the higher-order structure is recoverable from the graph through the dynamical rule, and the modeling respects the required admissible 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