mlsanityData to 7 Oct 2026

Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND

arXiv 2404.17099 ↗First posted 26 Apr 2024cs.LG cs.NEcited by 16

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Abstract (arXiv)

We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process. We demonstrate analytically that oversmoothing can be mitigated in this setting. Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs. The code is available at urlhttps://github.com/zknus/ICLR2024-FROND.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 75 of its 141 references that are in the map. First posted on arXiv 26 Apr 2024.

Builds on

75 of 141 references.

References · 75

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50 most cited of 75 All 75 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 7; 2026: 5.

16 papers.

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  1. 2024On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systemscited by 26
  2. 2024Temporal Graph ODEs for Irregularly-Sampled Time Seriescited by 11
  3. 2024Distributed-Order Fractional Graph Operating Networkcited by 7
  4. 2025Neural Variable-Order Fractional Differential Equation Networkscited by 5
  5. 2024A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systemscited by 3
  6. 2025Efficient Training of Neural Fractional-Order Differential Equation via Adjoint Backpropagationcited by 3
  7. 2025Measuring Over-smoothing beyond Dirichlet energycited by 1
  8. 2025Simplifying Graph Convolutional Networks with Redundancy-Free Neighborscited by 0
  9. 2025Simple Graph Contrastive Learning via Fractional-order Neural Diffusion Networkscited by 0
  10. 2025Adaptive Multi-view Graph Contrastive Learning via Fractional-order Neural Diffusion Networkscited by 0
  11. 2025Solving Oversmoothing in GNNs via Nonlocal Message Passing: Algebraic Smoothing and Depth Scalabilitycited by 0
  12. 2026Lyapunov Stable Graph Neural Flowcited by 0
4 more
  1. 2026Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitionscited by 0
  2. 2026Graph Navier Stokes Networkscited by 0
  3. 2026LongSpike: Fractional Order Spiking State Space Models for Efficient Long Sequence Learningcited by 0
  4. 2026Continuous-Time Quantum Walks based Graph Neural Networkcited by 0