[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-148436-105":59,"doc-detail-148436-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","pathgcn-learning-general-graph-spatial-operators-from-paths","pathGCN - Learning General Graph Spatial Operators from Paths","","Graph Convolutional Networks (GCNs) typically rely on two components: a spatial operator and point-wise convolutions. Unlike CNNs, where both spatial and point-wise filters are learned, many GCNs use a fixed spatial operator derived from the graph Laplacian, which limits expressiveness and can cause over-smoothing. This paper introduces pathGCN, learning the spatial operator from random paths, analyzing convergence, comparing to existing methods, and showing improved performance while mitigating over-smoothing.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/pathgcn-learning-general-graph-spatial-operators-from-paths/148436/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/pathgcn-learning-general-graph-spatial-operators-from-paths/148436.png","ImageObject",300,407,{"name":92,"@type":93},"Noah","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-04","2026-08-26",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What limitation do existing GCNs face with predetermined graph Laplacian spatial operators?","Question",{"text":112,"@type":113},"They restrict network expressiveness because only point-wise operations are learnable, and repeated Laplacian smoothing can lead to over-smoothing and shallow effective representations.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does pathGCN learn spatial operators?",{"text":117,"@type":113},"pathGCN learns a spatial operator by aggregating information from random paths defined over graph vertices, enabling more expressive kernels than fixed Laplacian-based operators.",{"name":119,"@type":110,"acceptedAnswer":120},"What analysis and experimental results are presented for pathGCN?",{"text":121,"@type":113},"The work analyzes convergence and behavior, discusses options for combining the learned spatial operator with point-wise convolutions, and reports extensive experiments showing improved state-of-the-art accuracy and inherent avoidance of over-smoothing.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},148436,1787779783,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},8796095462418,"https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780","pathGCN: Learning General Graph Spatial Operators from Paths  \nMoshe Eliasof 1 Eldad Haber 2 Eran Treister 1  \nAbstract  \nGraph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations-spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the convergence of our method and its difference from existing GCNs.  \nFurthermore, we discuss several options of combining our learnt spatial operator with point-wise convolutions. Our extensive experiments on numerous datasets suggest that by properly learning both the spatial and point-wise convolutions, phenomena like over-smoothing can be inherently avoided, and new state-of-the-art performance is achieved.  \n1. Introduction  \nThe study of Graph Convolutional Networks (GCNs) has gained large popularity in recent years (Bruna et al., 2013 ; Defferrard et al., 2016 ; Kipf & Welling, 2016 ; Bronstein et al., 2017 ; Monti et al., 2017) in a wide variety of fields and applications such as computer graphics and vision (Boscainiet al., 2016 ; Monti et al., 2017 ; Wang et al., 2018 ; Eliasof & Treister, 2020), Bioinformatics (Strokach et al., 2020 ; Jumper et al., 2021), node classification (Kipf & Welling, 2016 ; Chen et al., 2020 ; Chamberlain et al., 2021) and others. The common ingredient that most of the methods share  \n1Department of Computer Science, Ben-Gurion University, Israel. 2Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Canada.. Correspondence to: Moshe Eliasof \u003C[eliasof@post.bgu.ac.il](eliasof@post.bgu.ac.il)>, Eran Treister \u003Cer[ant@cs.bgu.ac.il](ant@cs.bgu.ac.il)>.  \nProceedings of the 39 th International Conference on Machine Learning, Baltimore, Maryland, USA, PMLR 162, 2022 . Copyright 2022 by the author(s) .  \nFigure 1 . The spatial operator induced by a smoothing kernel on different graphs. The vertex with dashed outline is the path origin.  \nis the use of a pre-determined spatial operator, often times based on the graph Laplacian. While this choice is intuitive and effective, it induces limitations on the behaviour of GCNs. First, it is limited in the aspect of the expressiveness of the networks. Unlike CNNs (Krizhevsky et al., 2012 ; He et al., 2016 ; Howard et al., 2017), where both the spatial filters (e.g., 3 × 3 depth-wise convolutions) and point-wise (1 × 1) convolutions are learnt, here only the latter are left to be determined. Secondly, it is well known (Wu et al., 2019) that the Laplacian operator, when applied as in (Kipf & Welling, 2016) smooths the input features, and therefore a recurrent application of it may lead to over-smoothing, resulting in typically shallow networks. This phenomenon is well documented and studied in the field of GCNs (Wu et al., 2019 ; Zhao & Akoglu, 2020 ; Chen et al., 2020 ; Chamberlain et al., 2021 ; Eliasof et al., 2021) . In this work we propose pathGCN – a novel approach that overcomes the limitations above, based on aggregation from random paths defined over the graph vertices. We show that using this approach it is possible to define spatial operators similarly to the ones used in 2D convolutions on images. Such operators have variable aperture and coefficients that may increase the expressiveness of GCNs. In addition, since the coefficients of the operator are learnt, its eigenvalues can be rather different than those of the graph Laplacian. This implies that the learnt kernels can take different roles, from smoothing to edge-detecting (or sharpening) operators. An example of the effective spatial operators that are indu","cbCaiheG8UaovPXj","https://ap.wps.com/l/cbCaiheG8UaovPXj","pdf",2042643,14,"English","# Abstract\n# 1. Introduction\n## 2.1. Graph convolutional networks\n# 2. Related work","[{\"question\":\"What limitation do existing GCNs face with predetermined graph Laplacian spatial operators?\",\"answer\":\"They restrict network expressiveness because only point-wise operations are learnable, and repeated Laplacian smoothing can lead to over-smoothing and shallow effective representations.\"},{\"question\":\"How does pathGCN learn spatial operators?\",\"answer\":\"pathGCN learns a spatial operator by aggregating information from random paths defined over graph vertices, enabling more expressive kernels than fixed Laplacian-based operators.\"},{\"question\":\"What analysis and experimental results are presented for pathGCN?\",\"answer\":\"The work analyzes convergence and behavior, discusses options for combining the learned spatial operator with point-wise convolutions, and reports extensive experiments showing improved state-of-the-art accuracy and inherent avoidance of over-smoothing.\"}]","pathGCN - Learning General Graph Spatial Operators from Paths | PDF",35]