# Stuart-Landau Oscillatory Graph Neural Network

arXiv: https://arxiv.org/abs/2511.08094 · HTML: https://mlsanity.com/paper/2511.08094/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 57 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature](https://mlsanity.com/paper/2211.15779/) (2022)
- [Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependencies](https://mlsanity.com/paper/2010.00951/) (2020)
- [UnICORNN: A recurrent model for learning very long time dependencies](https://mlsanity.com/paper/2103.05487/) (2021)
- [GREAD: Graph Neural Reaction-Diffusion Networks](https://mlsanity.com/paper/2211.14208/) (2022)
- [How does over-squashing affect the power of GNNs?](https://mlsanity.com/paper/2306.03589/) (2023)
- [Oscillatory State-Space Models](https://mlsanity.com/paper/2410.03943/) (2024)
- [SVD-GCN: A Simplified Graph Convolution Paradigm for Recommendation](https://mlsanity.com/paper/2208.12689/) (2022)
- [Feature Transportation Improves Graph Neural Networks](https://mlsanity.com/paper/2307.16092/) (2023)
- [Towards Graph Foundation Models for Personalization](https://mlsanity.com/paper/2403.07478/) (2024)
- [Are We Measuring Oversmoothing in Graph Neural Networks Correctly?](https://mlsanity.com/paper/2502.04591/) (2025)
- [Unique Nash equilibrium of a nonlinear model of opinion dynamics on networks with friction-inspired stubbornness](https://mlsanity.com/paper/2304.07556/) (2023)

## Built on by (most cited first, 3 of 3)

- [Beyond ReLU: Bifurcation, Oversmoothing, and Topological Priors](https://mlsanity.com/paper/2602.15634/) (2026)
- [Generative Models on Analog Hardware with Dynamics](https://mlsanity.com/paper/2606.27294/) (2026)
- [Phasor Agents: Oscillatory Graphs with Three-Factor Plasticity and Sleep-Staged Learning](https://mlsanity.com/paper/2601.04362/) (2026)

## Abstract (arXiv)

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 between feature amplitudes and network structure. We conduct extensive experiments across node classification, graph classification, and graph regression tasks, demonstrating that SLGNN outperforms existing OGNNs and establishes a novel, expressive, and theoretically grounded framework for deep oscillatory architectures on graphs.