[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85600-en":3,"doc-seo-85600-105":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},85600,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Learning Developmental Scaffoldings to Guide Self-Organisation","Self-organisation creates global biological structure through local interactions, yet much of the information that drives development is offloaded to initial conditions rather than generated by the self-organising dynamics alone. The work studies this informational offloading by jointly learning self-organisation rules and developmental pre-patterns under controlled variation. A Neural Cellular Automaton is paired with a learned coordinate-based pattern generator, trained together, with information-theoretic analyses showing improved robustness, encoding capacity, and symmetry breaking.","Learning Developmental Scaffoldings to Guide Self-Organisation  \nMilton L. Montero 1 , Elias Najarro 1 , Jakob Schauser2 and Sebastian Risi 1 ,3  \n1IT University of Copenhagen, Denmark  \n2University of Copenhagen, Denmark  \n3 Sakana AI, Japan  \n{mlle,enaj,[sebr](sebr}@itu.dk)[}](sebr}@itu.dk)[@itu.dk](sebr}@itu.dk), [jakob.schauser@nbi.ku.dk](jakob.schauser@nbi.ku.dk)  \narXiv :2605 . 14998v4 [ cs .AI] 13 Jul 2026  \nAbstract  \nFrom subcellular structures to entire organisms, many natural systems generate complex organisation through selforganisation: local interactions that collectively give rise to global structure without any blueprint of the outcome. Yet a significant portion of the information driving such processes is not produced by self-organisation itself, instead, it is often offloaded to initial conditions of the system, analogous to a memory-compute trade-off in computational systems. Biological development is a prime example, where maternal pre-patterns encode positional and symmetry-breaking information that scaffolds the self-organising process. In this work, we study this offloading phenomenon by introducing a model that jointly learns both the self-organisation rules and the pre-patterns, allowing their interplay to be varied and measured under controlled conditions: a Neural Cellular Automaton (NCA) paired with a learned coordinate-based pattern generator (SIREN), both trained simultaneously to generate a set of patterns. We provide information-theoretic analyses of how information is distributed between pre-patterns and the self-organising process, and show that jointly learning both components yields improvements in robustness, encoding capacity, and symmetry breaking over purely selforganising alternatives. Our analysis further suggests that effective pre-patterns do not simply approximate their targets; rather, they bias the developmental dynamics in ways that facilitate convergence, pointing to a non-trivial relationship between the structure of initial conditions and the dynamics of self-organisation.  \nData/Code available at: [https://github.com/](https://github.com/)[ ](https://github.com/)[miltonllera/siren-growth](miltonllera/siren-growth.)[.](miltonllera/siren-growth.)  \nIntroduction  \nSelf-organisation is widely regarded as one of the fundamental concepts in the study of complex systems [Weber, 1998] . It describes how global structure and function canemerge from local interactions between components, without the need for a central controller or explicit blueprint. A fundamental, yet often under explored, question in the study of self-organising systems is: where does the information  \n©2026 [AUTHORS’ NAMES] . Published under a Creative Commons Attribution 4 .0 International (CC BY 4 .0) license.  \nthat drives this process come from? In many natural systems, that information is not generated entirely by the selforganising process itself, instead, some of it is offloaded to the system’s initial conditions.  \nBiological development is a classical example of this phenomenon. Cell division, differentiation, and morphogenesis are all governed by local cell-cell interactions, yet this process does not operate in an informational vacuum. In many species, a substantial portion of the organisational information guiding development is instantiated via the initial conditions of the developmental substrate in the form of spatially structured pre-patterns: morphogenetic gradients, maternally provided mRNAs, and localised protein concentrations created by the parent organism prior to or during early development, which provide initial organisational information in the form of maternal effect genes [Gilbert, 2000], body-axes specification [Lander, 2007], and tissue level processes such as gastrulation [Inomata, 2017] and limb formation [Raspopovic et al., 2014, Meinhardt, 1983](see [Meinhardt, 2008] for a broader overview) .  \nIn all these cases morphogenetic gradients provide organisational information by enabling","cbCaimxxKzXGTELM","https://ap.wps.com/l/cbCaimxxKzXGTELM","pdf",3252466,1,10,"English","en",105,"# Abstract\n# Introduction\n## Self-organisation and information origin\n## Biological development as offloading\n## Modeling and controlled quantitative study\n## Model overview and example results","[{\"question\":\"What phenomenon does the paper focus on in self-organisation systems?\",\"answer\":\"The paper focuses on how key information can be offloaded from self-organisation dynamics into the system’s initial conditions, rather than being produced entirely by the self-organising process itself.\"},{\"question\":\"How does the proposed model jointly learn developmental scaffolding and self-organisation?\",\"answer\":\"It couples a Neural Cellular Automaton with a learned coordinate-based pattern generator, training both simultaneously so that their interaction can be varied and measured while generating target patterns.\"},{\"question\":\"What are the main reported benefits of learning both pre-patterns and self-organisation together?\",\"answer\":\"Joint learning improves robustness, increases encoding capacity, and enhances symmetry breaking compared with approaches that rely on self-organisation 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phenomenon does the paper focus on in self-organisation systems?","Question",{"text":75,"@type":76},"The paper focuses on how key information can be offloaded from self-organisation dynamics into the system’s initial conditions, rather than being produced entirely by the self-organising process itself.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed model jointly learn developmental scaffolding and self-organisation?",{"text":80,"@type":76},"It couples a Neural Cellular Automaton with a learned coordinate-based pattern generator, training both simultaneously so that their interaction can be varied and measured while generating target patterns.",{"name":82,"@type":73,"acceptedAnswer":83},"What are the main reported benefits of learning both pre-patterns and self-organisation together?",{"text":84,"@type":76},"Joint learning improves robustness, increases encoding capacity, and enhances symmetry breaking compared with approaches that rely on self-organisation 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