Chuan Shi, Meiqi Zhu, Yue Yu, Xiao Wang, Junping Du
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Actually, the optimization framework can not only help understand the propagation mechanisms of GNNs, but also open up opportunities for flexibly designing new GNNs. Through analyzing the general solutions of the optimization framework, we provide a more convenient way for deriving corresponding propagation results of GNNs. We further discover that existing works usually utilize naïve graph convolutional kernels for feature fitting function, or just utilize one-hop structural information (original topology graph) for graph regularization term. Correspondingly, we develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities and one novel objective function considering high-order structural information during propagation respectively. Extensive experiments on benchmark datasets clearly show that the newly proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with the generalized unified optimization framework.","PeriodicalId":5,"journal":{"name":"ACS Applied Materials & Interfaces","volume":"15 8","pages":""},"PeriodicalIF":8.3000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unifying Graph Neural Networks with a Generalized Optimization Framework\",\"authors\":\"Chuan Shi, Meiqi Zhu, Yue Yu, Xiao Wang, Junping Du\",\"doi\":\"10.1145/3660852\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism, which has been demonstrated effective, is the most fundamental part of GNNs. Although most of the GNNs basically follow a message passing manner, little effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with an optimization problem. We show that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solutions of a generalized optimization framework with a flexible feature fitting function and a generalized graph regularization term. Actually, the optimization framework can not only help understand the propagation mechanisms of GNNs, but also open up opportunities for flexibly designing new GNNs. Through analyzing the general solutions of the optimization framework, we provide a more convenient way for deriving corresponding propagation results of GNNs. We further discover that existing works usually utilize naïve graph convolutional kernels for feature fitting function, or just utilize one-hop structural information (original topology graph) for graph regularization term. Correspondingly, we develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities and one novel objective function considering high-order structural information during propagation respectively. 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Unifying Graph Neural Networks with a Generalized Optimization Framework
Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism, which has been demonstrated effective, is the most fundamental part of GNNs. Although most of the GNNs basically follow a message passing manner, little effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with an optimization problem. We show that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solutions of a generalized optimization framework with a flexible feature fitting function and a generalized graph regularization term. Actually, the optimization framework can not only help understand the propagation mechanisms of GNNs, but also open up opportunities for flexibly designing new GNNs. Through analyzing the general solutions of the optimization framework, we provide a more convenient way for deriving corresponding propagation results of GNNs. We further discover that existing works usually utilize naïve graph convolutional kernels for feature fitting function, or just utilize one-hop structural information (original topology graph) for graph regularization term. Correspondingly, we develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities and one novel objective function considering high-order structural information during propagation respectively. Extensive experiments on benchmark datasets clearly show that the newly proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with the generalized unified optimization framework.
期刊介绍:
ACS Applied Materials & Interfaces is a leading interdisciplinary journal that brings together chemists, engineers, physicists, and biologists to explore the development and utilization of newly-discovered materials and interfacial processes for specific applications. Our journal has experienced remarkable growth since its establishment in 2009, both in terms of the number of articles published and the impact of the research showcased. We are proud to foster a truly global community, with the majority of published articles originating from outside the United States, reflecting the rapid growth of applied research worldwide.