# Graph Spring Neural ODEs for Link Sign Prediction

arXiv: https://arxiv.org/abs/2412.12916 · HTML: https://mlsanity.com/paper/2412.12916/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 51 references that are in the map.
- First posted on arXiv 17 Dec 2024.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [Signed Graph Attention Networks](https://mlsanity.com/paper/1906.10958/) (2019)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [GREAD: Graph Neural Reaction-Diffusion Networks](https://mlsanity.com/paper/2211.14208/) (2022)
- [SDGNN: Learning Node Representation for Signed Directed Networks](https://mlsanity.com/paper/2101.02390/) (2021)
- [Distributed Representations of Signed Networks](https://mlsanity.com/paper/1702.06819/) (2017)
- [Signed Graph Diffusion Network](https://mlsanity.com/paper/2012.14191/) (2020)
- [Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks](https://mlsanity.com/paper/2305.18965/) (2023)
- [Learning Representations of Bi-level Knowledge Graphs for Reasoning beyond Link Prediction](https://mlsanity.com/paper/2302.02601/) (2023)
- [Spear and Shield: Adversarial Attacks and Defense Methods for Model-Based Link Prediction on Continuous-Time Dynamic Graphs](https://mlsanity.com/paper/2308.10779/) (2023)
- [Force2Vec: Parallel force-directed graph embedding](https://mlsanity.com/paper/2009.10035/) (2020)
- [A Signed Subgraph Encoding Approach via Linear Optimization for Link Sign Prediction](https://mlsanity.com/paper/2305.09869/) (2023)
- [Force-directed graph embedding with hops distance](https://mlsanity.com/paper/2309.05865/) (2023)
- [On Manipulating Weight Predictions in Signed Weighted Networks](https://mlsanity.com/paper/2302.02687/) (2023)

## Abstract (arXiv)

Signed graphs allow for encoding positive and negative relations between nodes and are used to model various online activities. Node representation learning for signed graphs is a well-studied task with important applications such as sign prediction. While the size of datasets is ever-increasing, recent methods often sacrifice scalability for accuracy. We propose a novel message-passing layer architecture called Graph Spring Network (GSN) modeled after spring forces. We combine it with a Graph Neural Ordinary Differential Equations (ODEs) formalism to optimize the system dynamics in embedding space to solve a downstream prediction task. Once the dynamics is learned, embedding generation for novel datasets is done by solving the ODEs in time using a numerical integration scheme. Our GSN layer leverages the fast-to-compute edge vector directions and learnable scalar functions that only depend on nodes' distances in latent space to compute the nodes' positions. Conversely, Graph Convolution and Graph Attention Network layers rely on learnable vector functions that require the full positions of input nodes in latent space. We propose a specific implementation called Spring-Neural-Network (SPR-NN) using a set of small neural networks mimicking attracting and repulsing spring forces that we train for link sign prediction. Experiments show that our method achieves accuracy close to the state-of-the-art methods with node generation time speedup factors of up to 28,000 on large graphs.