[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118268-en":3,"doc-seo-118268-105":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},118268,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Future Directions in the Theory of Graph Machine Learning","Graph machine learning on graph neural networks (GNNs) has advanced rapidly due to the growing availability of graph-structured data across life, social, and engineering sciences. Despite strong empirical performance, theoretical understanding remains incomplete, especially regarding how expressive power, generalization, and optimization interact under stochastic first-order training. Recent theory mainly analyzes coarse expressive limits using combinatorial tools, which can mismatch real training behavior. This position paper argues for a more balanced framework that links expressivity with generalization guarantees and optimization dynamics for practical GNNs.","arXiv :2402 .02287v4 [ cs .LG] 14 Jun 2024  \nFuture Directions in the Theory of Graph Machine Learning  \nChristopher Morris 1 , Fabrizio Frasca2 , Nadav Dym2 , Haggai Maron2,3 ,İsmail İlkan Ceylan4 , Ron Levie2 , Derek Lim5 , Michael Bronstein4 , Martin Grohe 1 , and Stefanie Jegelka5,6  \n1RWTH Aachen University  \n2Technion-Israel Institute of Technology  \n3NVIDIA Research  \n4University of Oxford  \n5MIT  \n6TU Munich  \nMachine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across abroad spectrum of disciplines, from life to social and engineering sciences. Despite their practical success, our theoretical understanding of the properties of GNNs remains highly incomplete. Recent theoretical advancements primarily focus on elucidating the coarse-grained expressive power of GNNs, predominantly employing combinatorial techniques. However, these studies do not perfectly align with practice, particularly in understanding the generalization behavior of GNNs when trained with stochastic first-order optimization techniques. In this position paper, we argue that the graph machine learning community needs to shift its attention to developing a balanced theory of graph machine learning, focusing on a more thorough understanding of the interplay of expressive power, generalization, and optimization.  \n1 Introduction  \nGraphs serve as powerful mathematical representations, adept at capturing intricate interactions among entities across a spectrum of disciplines, spanning from life [Wong et al., 2023] to social sciences [Easley and Kleinberg, 2010] and optimization [Cappart et al., 2021] . This diversity underscores the critical demand for specialized machine-learning methods that extract valuable patterns from complex graph data.  \nHence, in recent years, neural networks capable of handling graph-structured data received alot of attention in the machine learning community, especially messsage-passing graph neural  \nFigure 1 : Interactions of the four challenges within graph machine learning: Fine-grained expressivity, generalization, optimization, applications, and their interactions. The green boxes architectural choices (hyperparameter and other design choices like normalization layers), model parameters, and graph classes (different types of graphs) represent aspects of all four challenges.  \nnetworks (MPNNs) [Gilmer et al., 2017, Scarselli et al., 2009] .1 Nowadays, MPNNs, or, more generally, GNNs, are among the most prominent topics at top-tier machine learning conferences,2 and have showcased promising outcomes across diverse domains, including breakthroughs in discovering new antibiotics [Stokes et al., 2020, Wong et al., 2023] .  \nWhile GNNs are successful in practice and are making real-world impact, their theoretical properties are understood to a lesser extent. That is, only GNNs’ expressive power, i.e., their ability to separate graphs and express functions over graphs is understood to some extent [Azizian and Lelarge, 2021, Geerts and Reutter, 2022, Morris et al., 2019, 2021, Xu et al., 2019] . However, most current analyses heavily rely on combinatorial techniques, such as the 1-dimensional Weisfeiler– Leman algorithm (1-WL), a well-studied heuristic for the graph isomorphism problem [Grohe, 2017, Weisfeiler and Leman, 1968, Weisfeiler, 1976] . While the graph isomorphism perspective has helped the community understand GNNs’ ultimate limitations in capturing graph structure, it is inherently binary. For example, it does not give insights into the degree of similarity between two given graphs, prohibiting a more fine-grained analysis. While some recent works [Böker et al., 2023, Chen et al., 2022] aim at a more fine-grained analysis, they still have strong limitations, such as not considering continuous node and edge features. A second limitation of current GNN expressivity results is that they are fairly specific. They are tailored to par","cbCaivBwdsYBbGJG","https://ap.wps.com/l/cbCaivBwdsYBbGJG","pdf",429571,1,23,"English","en",105,"# Introduction\n## Graphs as mathematical representations\n## Expressive power and 1-WL limitations\n## Fine-grained expressivity gaps\n## Generalization and optimization challenges","[{\"question\":\"为什么需要对图机器学习的理论做出新的关注？\",\"answer\":\"尽管GNN在实践中效果显著，但其理论理解仍不完整，尤其是表达能力、泛化行为与随机一阶优化之间的相互作用尚缺乏系统刻画。\"},{\"question\":\"现有GNN表达能力理论主要依赖哪些方法？\",\"answer\":\"许多分析使用组合技术，例如1维Weisfeiler–Leman算法（1-WL）来研究图同构相关的表达极限。\"},{\"question\":\"作者认为当前泛化与优化研究存在哪些不足？\",\"answer\":\"关于MPNN泛化的工作多使用VC维度等经典均匀泛化界，往往导致常数较大且不能反映深度学习在图上的典型偏差-方差经验；关于优化的研究也常带有过强假设或忽略图结构影响。\"}]","Future Directions in the Theory of Graph Machine Learning | PDF",1785682730,58,{"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},"future-directions-in-the-theory-of-graph-machine-learning","",{"@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/future-directions-in-the-theory-of-graph-machine-learning/118268/",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","2026-08-02",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},"为什么需要对图机器学习的理论做出新的关注？","Question",{"text":75,"@type":76},"尽管GNN在实践中效果显著，但其理论理解仍不完整，尤其是表达能力、泛化行为与随机一阶优化之间的相互作用尚缺乏系统刻画。","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"现有GNN表达能力理论主要依赖哪些方法？",{"text":80,"@type":76},"许多分析使用组合技术，例如1维Weisfeiler–Leman算法（1-WL）来研究图同构相关的表达极限。",{"name":82,"@type":73,"acceptedAnswer":83},"作者认为当前泛化与优化研究存在哪些不足？",{"text":84,"@type":76},"关于MPNN泛化的工作多使用VC维度等经典均匀泛化界，往往导致常数较大且不能反映深度学习在图上的典型偏差-方差经验；关于优化的研究也常带有过强假设或忽略图结构影响。","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"]