[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86269-en":3,"doc-seo-86269-105":30,"detail-sidebar-cat-0-en-105":84},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86269,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Structure-Feature Aligned Graph Learning via Alternating Constrained Optimization","Introduces a constrained two-view node prediction framework that aligns structure-conditioned GNN embeddings with a structure-free feature prior learned by an anchor model. Conventional GNNs tightly couple feature transformation with neighborhood aggregation, making them sensitive to topology noise and heterophilous edges. The approach uses an independent anchor network trained via self-supervised feature reconstruction, and proposes CSAG-GNN with channel-split adaptive gating between spectral smoothing and spatial discrimination. A stable cyclic alternating optimization prevents bi-level objective drift, improving performance and structural robustness on homophilous and heterophilous benchmarks.","arXiv :2607 . 1 1577v 1 [ cs .LG] 13 Jul 2026  \nStructure-Feature Aligned Graph Learning via Alternating  \nConstrained Optimization  \nChengcheng Yan ∗†, Qingsong Wang ‡  \nAbstract  \nWe introduce a constrained two-view framework for node prediction that aligns structureconditioned GNN embeddings with a structure-free feature prior learned by an anchor model. Conventional Graph Neural Networks (GNNs) couple feature transformation and neighborhood aggregation, which renders them vulnerable to topology noise and heterophilous connections. To decouple this dependency, our framework utilizes an independent anchor network to capture intrinsic attribute features via a self-supervised reconstruction objective. Furthermore, we propose a Channel-Split Adaptive Gated GNN (CSAG-GNN) that dynamically routes representations between global spectral smoothing and local spatial discrimination through a node-wise gating mechanism. We propose a stable cyclic alternating optimization strategy to solve the resulting coupled bi-level objective, preventing mutual representation drift during training. Empirical results on both homophilous and heterophilous benchmarks show balanced performance gains and structural robustness over competitive baselines.  \nKeywords: Graph Neural Network; Alternating Optimization; Feature-Structure Alignment; Topological Robustness; Representation Learning  \n1 Introduction  \nGraph Neural Networks (GNNs) [4] have emerged as a powerful paradigm for graph representation learning. Given the topological structure A and the node feature matrix X of a graph, the conventional training objective of GNNs is typically formulated as the following unconstrained optimization problem:  \nmin L(Ψ(A, X;θ), Y ), (1)  \nθ  \nwhere Ψ(·;θ) denotes the neural network model for node-level prediction and θ = {W1 , W2 ,..., WL } denotes all trainable parameters of the GNN. Symbol L denotes the task-specific loss function, and Y denotes the labels of nodes. Given an L-layer GNN, for problem (1), Ψ denotes the composition of L message-passing layers defined as follows:  \nΨ(A, X;θ) = HLθ , H0θ = X, Hlθ = σ (AHlθ−1Wl), l = 1 , . . . , L, (2)  \nwhere σ is an activation function, Hlθ denotes the hidden representation at the l-th layer, and Wl are the weight parameters of GNN. By adopting the aggregation operator σ(AHlθ−1Wl ), the model  \n∗ College of Artificial Intelligence, Shaoxing Institute of Technology, Shaoxing, 312000, China. Email: [ycc956176796@gmail.com](ycc956176796@gmail.com)  \n†School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China.  \n‡School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China. Email: [nothing2wang@hotmail.com](nothing2wang@hotmail.com)  \nLegend & Symbols  \n Graph Node  \n Node Feature  \n Node Relation  \n Fixed Weight  \n􀀤 Loss Function  Cyclic Update  \nAggregation  Adaptive Gate  Sigmoid  \n􀀠lθ Middle Feature  \n| \u003Cbr>\u003Cbr> |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| \u003Cbr>Feature-Structure Alignment |  |  |  |  |  |  |  |\n| \u003Cbr> |  |  |  | \u003Cbr>Feature Encoder | \u003Cbr>Feature Decoder |  | \u003Cbr>􀀤 rec |\n|  |  |  |  |  |  |  |  |\n| \u003Cbr>Node Features 􀜺 |  |  |  |  |  | Step 1： Feature View |  |\n\nFigure 1: An overview of the proposed CSAG-GNN framework. The model decouples graph learning into a Feature View (Step 1) and a Structure View (Step 2) optimized via a cyclic alternating scheme. The feature encoder distills a structure-agnostic prior Fϕ , which acts as an alignment anchor (Lalign ) for the intermediate embeddings of the task-driven CSAG-GNN. The embedded CSAG-Layer dynamically balances dual-branch aggregations using an adaptive gating mechanism.  \nperforms spatial smoothing over node representations in the non-Euclidean graph domain. This coupling between neighborhood aggregation and feature transformation enables GNNs’ ability to learn stronger feature representations.  \nHowever, the above procedure implicitly assumes that the","cbCaijWYYpfyQAnC","https://ap.wps.com/l/cbCaijWYYpfyQAnC","pdf",1615308,6,1,18,"English","en",105,"# Introduction\n## Related Background and Motivation\n## Proposed Two-View Framework","[{\"question\":\"Why is cyclic alternating optimization used in training?\",\"answer\":\"It solves the coupled bi-level objective while preventing mutual representation drift between the structure view and the feature prior during training.\"}]",1784209941,45,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":79,"head_meta":81,"extra_data":83,"updated_unix":28},"structure-feature-aligned-graph-learning-via-alternating-constrained-optimization","",{"@graph":36,"@context":78},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"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/structure-feature-aligned-graph-learning-via-alternating-constrained-optimization/86269/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-26","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72],{"name":73,"@type":74,"acceptedAnswer":75},"Why is cyclic alternating optimization used in training?","Question",{"text":76,"@type":77},"It solves the coupled bi-level objective while preventing mutual representation drift between the structure view and the feature prior during training.","Answer","https://schema.org",{"og:url":52,"og:type":80,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":82,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":85},[86,90,94,98,103,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":87,"show_sort_weight":88,"slug":89},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":91,"show_sort_weight":92,"slug":93},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Exam",70,"exam",{"id":99,"doc_module":4,"doc_module_name":46,"category_name":100,"show_sort_weight":101,"slug":102},5,"Comic",60,"comic",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":99,"slug":130},19,"General","general"]