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[2511.08094] Stuart-Landau Oscillatory Graph Neural Network
Summary
The paper introduces the Stuart-Landau Oscillatory Graph Neural Network (SLGNN), a novel architecture that addresses oversmoothing and vanishing gradient issues in deep graph neural networks using complex-valued dynamics.
Why It Matters
This research is significant as it presents a new approach to enhance the performance of graph neural networks, particularly in tasks like node classification and graph regression. By leveraging the dynamics of Stuart-Landau oscillators, the SLGNN offers a theoretically grounded method that could lead to advancements in various applications, including neuroscience and complex systems modeling.
Key Takeaways
- SLGNN mitigates oversmoothing and vanishing gradient problems in GNNs.
- The architecture allows dynamic evolution of node feature amplitudes.
- Extensive experiments show SLGNN outperforms existing oscillatory GNNs.
- The model is grounded in Stuart-Landau oscillator dynamics, enhancing theoretical understanding.
- Tunable hyperparameters provide additional control over network behavior.
Computer Science > Machine Learning arXiv:2511.08094 (cs) [Submitted on 11 Nov 2025 (v1), last revised 20 Feb 2026 (this version, v2)] Title:Stuart-Landau Oscillatory Graph Neural Network Authors:Kaicheng Zhang, David N. Reynolds, Piero Deidda, Francesco Tudisco View a PDF of the paper titled Stuart-Landau Oscillatory Graph Neural Network, by Kaicheng Zhang and 3 other authors View PDF HTML (experimental) Abstract:Oscillatory Graph Neural Networks (OGNNs) are an emerging class of physics-inspired architectures designed to mitigate oversmoothing and vanishing gradient problems in deep GNNs. In this work, we introduce the Complex-Valued Stuart-Landau Graph Neural Network (SLGNN), a novel architecture grounded in Stuart-Landau oscillator dynamics. Stuart-Landau oscillators are canonical models of limit-cycle behavior near Hopf bifurcations, which are fundamental to synchronization theory and are widely used in e.g. neuroscience for mesoscopic brain modeling. Unlike harmonic oscillators and phase-only Kuramoto models, Stuart-Landau oscillators retain both amplitude and phase dynamics, enabling rich phenomena such as amplitude regulation and multistable synchronization. The proposed SLGNN generalizes existing phase-centric Kuramoto-based OGNNs by allowing node feature amplitudes to evolve dynamically according to Stuart-Landau dynamics, with explicit tunable hyperparameters (such as the Hopf-parameter and the coupling strength) providing additional control over the interplay be...
