# DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equation

arXiv: https://arxiv.org/abs/2411.10000 · HTML: https://mlsanity.com/paper/2411.10000/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 68 references that are in the map.
- First posted on arXiv 15 Nov 2024.

## Builds on (most cited first, 30 of 44)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Not too little, not too much: a theoretical analysis of graph (over)smoothing](https://mlsanity.com/paper/2205.12156/) (2022)
- [Merging Multi-Task Models via Weight-Ensembling Mixture of Experts](https://mlsanity.com/paper/2402.00433/) (2024)
- [How would Stance Detection Techniques Evolve after the Launch of ChatGPT?](https://mlsanity.com/paper/2212.14548/) (2022)
- [On Second Order Behaviour in Augmented Neural ODEs](https://mlsanity.com/paper/2006.07220/) (2020)
- [Equivariant Graph Mechanics Networks with Constraints](https://mlsanity.com/paper/2203.06442/) (2022)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [Equivariant Flows: sampling configurations for multi-body systems with symmetric energies](https://mlsanity.com/paper/1910.00753/) (2019)
- [Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks](https://mlsanity.com/paper/2003.08414/) (2020)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [A new perspective on building efficient and expressive 3D equivariant graph neural networks](https://mlsanity.com/paper/2304.04757/) (2023)

## Built on by (most cited first, 6 of 6)

- [SGAC: A Graph Neural Network Framework for Imbalanced and Structure-Aware AMP Classification](https://mlsanity.com/paper/2412.16276/) (2024)
- [ProtoMol: Enhancing Molecular Property Prediction via Prototype-Guided Multimodal Learning](https://mlsanity.com/paper/2510.16824/) (2025)
- [DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation](https://mlsanity.com/paper/2602.00656/) (2026)
- [MOLAR: Learning Multimodal Molecular Representations from Noisy Labels](https://mlsanity.com/paper/2606.18390/) (2026)
- [Cross-Attention Graph Neural Networks for Inferring Gene Regulatory Networks with Skewed Degree Distribution](https://mlsanity.com/paper/2412.16220/) (2024)
- [Data-Efficient Agentic Graph Domain Adaptation via Reliability-Aware Prototype Learning](https://mlsanity.com/paper/2609.14045/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) with equivariant properties have achieved significant success in modeling complex dynamic systems and molecular properties. However, their expressiveness ability is limited by: (1) Existing methods often overlook the over-smoothing issue caused by traditional GNN models, as well as the gradient explosion or vanishing problems in deep GNNs. (2) Most models operate on first-order information, neglecting that the real world often consists of second-order systems, which further limits the model's representation capabilities. To address these issues, we propose the Dual Second-order Equivariant Graph Ordinary Differential Equation (method) for equivariant representation. Specifically, method apply the dual second-order equivariant graph ordinary differential equations (Graph ODEs) on graph embeddings and node coordinates, simultaneously. Theoretically, we first prove that method maintains the equivariant property. Furthermore, we provide theoretical insights showing that method effectively alleviates the over-smoothing problem in both feature representation and coordinate update. Additionally, we demonstrate that the proposed method mitigates the exploding and vanishing gradients problem, facilitating the training of deep multi-layer GNNs. Extensive experiments on benchmark datasets validate the superiority of the proposed method compared to baselines.