[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120064-en":3,"doc-seo-120064-105":30,"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":4,"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":27,"seo_description":14,"update_tm":28,"read_time":29},120064,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","Homological Neural Networks - A Sparse Architecture for Multivariate Complexity - research paper","Rapid advances in artificial intelligence have produced deep learning models with escalating computational complexity, energy costs, and limited interpretability. This study proposes a new deep neural network unit that uses advanced network-based information filtering to build a sparse higher-order graphical architecture grounded in the homological structure of data. The approach targets two difficult settings: tabular prediction and time-series regression. Results show improvements and the ability to match or surpass state-of-the-art methods with far fewer parameters. Code and data are provided via a public repository.","Homological Neural Networks A Sparse Architecture for Multivariate Complexity  \nYuanrong Wang 1 2 Antonio Briola 1 2 Tomaso Aste 1 2 3  \nAbstract  \nThe rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In this study, we apply advanced networkbased information filtering techniques to design a novel deep neural network unit characterized by a sparse higher-order graphical architecture built over the homological structure of underlying data. We demonstrate its effectiveness in two application domains which are traditionally challenging for deep learning: tabular data and time series regression problems. Results demonstrate the advantages of this novel design which can tie or overcome the results of state-of-the-art machine learning and deep learning models using only a fraction of parameters. The code and the data are available at [https://github.com/](https://github.com/)[ ](https://github.com/)FinancialComputingUCL/HNN.  \n1. Introduction  \nComputational processes can be viewed as mapping operations from points or regions in space into points or regions in another space with different dimensionality and properties. Neural networks process information through stacked layers with different dimensions to efficiently represent the inherent structure of the underlying data. Uncovering this structure is however challenging since it is typically an unknown priori. Nevertheless, studying dependencies among variables in a dataset makes it possible to characterise the  \n1Department of Computer Science, University College London, London, UK 2UCL Centre for Blockchain Technologies, London, UK 3 Systemic Risk Centre, London School of Economics, London, United Kingdom. Correspondence to: Tomaso Aste \u003C[t.aste@ucl.ac.uk](t.aste@ucl.ac.uk)> .  \nProceedings of the 2 nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML) at the 40th International Conference on Machine Learning, Honolulu, Hawaii, USA. 2023. Copyright 2023 by the author(s) .  \nstructural properties of the data and shape ad-hoc deep learning architectures on it. Specifically, the basic operation in deep neural networks consists of aggregating input signals into one output. This operation is most effective in scenarios where the spatial organization of the variables is a good proxy for dependency. However, in several real-world complex systems, modelling dependency structures requires the usage of a complex network representation. Graph Neural Networks have been introduced as one possible way to address this issue (Samek et al., 2021) . However, they present two main limits: (i) they are designed for data defined on nodes of a graph (Yang et al., 2022), and (ii) they usually only explicitly consider low-order interactions as geometric priors (edges connecting two nodes), ignoring higher-order relations (triangles, tetrahedra, ... ) . Instead, dependency isnot simply a bi-variate relation between couples of variablesand involves groups of variables with complex aggregation laws.  \nIn this work, we propose a novel deep learning architecture that keeps into account higher-order interactions in the dependency structure as topological priors. Higher-order graphs are networks that connect not only vertices with edges (i.e. low-order 1-dimensional simplexes) but also higher-order simplexes (Torres & Bianconi, 2020) . Indeed, any higher-order component can be described as a combination of lower-order components (i.e. edges connecting two vertices, triangles connecting three edges, ... ) . The study of networks in terms of the relationship between structures at different dimensionality is a form of homology. In this work, we propose a novel multi-layer deep learning unit capable of fully representing the homological structure of data and we name it Homological Neural Network (HNN) . This ","cbCaiaHJspivYmAv","https://ap.wps.com/l/cbCaiaHJspivYmAv","pdf",1409681,1,13,"English","en",105,"# Introduction\n## Motivation: dependency modeling in complex systems\n## Limits of graph neural networks\n## Proposed approach: Homological Neural Network (HNN)\n## Evaluation in tabular and time-series regression","[{\"question\":\"What problem does the study address in deep learning models?\",\"answer\":\"It addresses challenges created by increasingly complex deep learning models, especially computational complexity, energy efficiency, and interpretability.\"},{\"question\":\"How does the proposed Homological Neural Network (HNN) work?\",\"answer\":\"HNN builds a feed-forward unit whose layers represent homological structures: vertices, edges, triangles, and higher-order simplexes, with information flowing only between connected structures across orders.\"},{\"question\":\"Where is the HNN evaluated, and what are the results?\",\"answer\":\"It is evaluated on tabular data and time-series regression tasks, where it matches or overcomes state-of-the-art approaches while using only a fraction of the parameters.\"}]","Homological Neural Networks - A Sparse Architecture for Multivariate Complexity - research paper | PDF",1785727956,33,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"homological-neural-networks-a-sparse-architecture-for-multivariate-complexity-research-paper","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/homological-neural-networks-a-sparse-architecture-for-multivariate-complexity-research-paper/120064/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the study address in deep learning models?","Question",{"text":75,"@type":76},"It addresses challenges created by increasingly complex deep learning models, especially computational complexity, energy efficiency, and interpretability.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed Homological Neural Network (HNN) work?",{"text":80,"@type":76},"HNN builds a feed-forward unit whose layers represent homological structures: vertices, edges, triangles, and higher-order simplexes, with information flowing only between connected structures across orders.",{"name":82,"@type":73,"acceptedAnswer":83},"Where is the HNN evaluated, and what are the results?",{"text":84,"@type":76},"It is evaluated on tabular data and time-series regression tasks, where it matches or overcomes state-of-the-art approaches while using only a fraction of the parameters.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]