LDC-GAT: A Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization
Graph attention networks are pivotal for modeling non-Euclidean data, yet they face dual challenges: training oscillations induced by projection-based high-dimensional constraints and gradient anomalies due to poor adaptation to heterophilic structure. To address these issues, we propose LDC-GAT (Ly...
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MDPI AG
2025-06-01
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| author | Liping Chen Hongji Zhu Shuguang Han |
| author_facet | Liping Chen Hongji Zhu Shuguang Han |
| author_sort | Liping Chen |
| collection | DOAJ |
| description | Graph attention networks are pivotal for modeling non-Euclidean data, yet they face dual challenges: training oscillations induced by projection-based high-dimensional constraints and gradient anomalies due to poor adaptation to heterophilic structure. To address these issues, we propose LDC-GAT (Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization), which jointly optimizes both forward and backward propagation processes. In the forward path, we introduce Dynamic Residual Graph Filtering, which integrates a tunable self-loop coefficient to balance neighborhood aggregation and self-feature retention. This filtering mechanism, constrained by a lower bound on Dirichlet energy, improves multi-head attention via multi-scale fusion and mitigates overfitting. In the backward path, we design the Fro-FWNAdam, a gradient descent algorithm guided by a learning-rate-aware perceptron. An explicit Frobenius norm bound on weights is derived from Lyapunov theory to form the basis of the perceptron. This stability-aware optimizer is embedded within a Frank–Wolfe framework with Nesterov acceleration, yielding a projection-free constrained optimization strategy that stabilizes training dynamics. Experiments on six benchmark datasets show that LDC-GAT outperforms GAT by 10.54% in classification accuracy, which demonstrates strong robustness on heterophilic graphs. |
| format | Article |
| id | doaj-art-48fc505cd86b446ba02f1c2e7fc76655 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-48fc505cd86b446ba02f1c2e7fc766552025-08-20T03:13:43ZengMDPI AGAxioms2075-16802025-06-0114750410.3390/axioms14070504LDC-GAT: A Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware OptimizationLiping Chen0Hongji Zhu1Shuguang Han2School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaSchool of Computer Science, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaSchool of Science, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaGraph attention networks are pivotal for modeling non-Euclidean data, yet they face dual challenges: training oscillations induced by projection-based high-dimensional constraints and gradient anomalies due to poor adaptation to heterophilic structure. To address these issues, we propose LDC-GAT (Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization), which jointly optimizes both forward and backward propagation processes. In the forward path, we introduce Dynamic Residual Graph Filtering, which integrates a tunable self-loop coefficient to balance neighborhood aggregation and self-feature retention. This filtering mechanism, constrained by a lower bound on Dirichlet energy, improves multi-head attention via multi-scale fusion and mitigates overfitting. In the backward path, we design the Fro-FWNAdam, a gradient descent algorithm guided by a learning-rate-aware perceptron. An explicit Frobenius norm bound on weights is derived from Lyapunov theory to form the basis of the perceptron. This stability-aware optimizer is embedded within a Frank–Wolfe framework with Nesterov acceleration, yielding a projection-free constrained optimization strategy that stabilizes training dynamics. Experiments on six benchmark datasets show that LDC-GAT outperforms GAT by 10.54% in classification accuracy, which demonstrates strong robustness on heterophilic graphs.https://www.mdpi.com/2075-1680/14/7/504LDC-GATDRG-FilteringFro-FWNAdammulti-head weight threshold |
| spellingShingle | Liping Chen Hongji Zhu Shuguang Han LDC-GAT: A Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization Axioms LDC-GAT DRG-Filtering Fro-FWNAdam multi-head weight threshold |
| title | LDC-GAT: A Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization |
| title_full | LDC-GAT: A Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization |
| title_fullStr | LDC-GAT: A Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization |
| title_full_unstemmed | LDC-GAT: A Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization |
| title_short | LDC-GAT: A Lyapunov-Stable Graph Attention Network with Dynamic Filtering and Constraint-Aware Optimization |
| title_sort | ldc gat a lyapunov stable graph attention network with dynamic filtering and constraint aware optimization |
| topic | LDC-GAT DRG-Filtering Fro-FWNAdam multi-head weight threshold |
| url | https://www.mdpi.com/2075-1680/14/7/504 |
| work_keys_str_mv | AT lipingchen ldcgatalyapunovstablegraphattentionnetworkwithdynamicfilteringandconstraintawareoptimization AT hongjizhu ldcgatalyapunovstablegraphattentionnetworkwithdynamicfilteringandconstraintawareoptimization AT shuguanghan ldcgatalyapunovstablegraphattentionnetworkwithdynamicfilteringandconstraintawareoptimization |