# Simple Graph Contrastive Learning via Fractional-order Neural Diffusion Networks

arXiv: https://arxiv.org/abs/2504.16748 · HTML: https://mlsanity.com/paper/2504.16748/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 53 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 30 of 36)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Large-Scale Representation Learning on Graphs via Bootstrapping](https://mlsanity.com/paper/2102.06514/) (2021)
- [SimGRACE: A Simple Framework for Graph Contrastive Learning without Data Augmentation](https://mlsanity.com/paper/2202.03104/) (2022)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Augmentation-Free Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2112.02472/) (2021)
- [Fast Training of Convolutional Networks through FFTs](https://mlsanity.com/paper/1312.5851/) (2013)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [Revisiting Graph Contrastive Learning from the Perspective of Graph Spectrum](https://mlsanity.com/paper/2210.02330/) (2022)
- [Simple and Asymmetric Graph Contrastive Learning without Augmentations](https://mlsanity.com/paper/2310.18884/) (2023)
- [On the Robustness of Graph Neural Diffusion to Topology Perturbations](https://mlsanity.com/paper/2209.07754/) (2022)
- [Graph Neural Convection-Diffusion with Heterophily](https://mlsanity.com/paper/2305.16780/) (2023)
- [Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND](https://mlsanity.com/paper/2404.17099/) (2024)

## Abstract (arXiv)

Graph Contrastive Learning (GCL) has recently made progress as an unsupervised graph representation learning paradigm. GCL approaches can be categorized into augmentation-based and augmentation-free methods. The former relies on complex data augmentations, while the latter depends on encoders that can generate distinct views of the same input. Both approaches may require negative samples for training. In this paper, we introduce a novel augmentation-free GCL framework based on graph neural diffusion models. Specifically, we utilize learnable encoders governed by Fractional Differential Equations (FDE). Each FDE is characterized by an order parameter of the differential operator. We demonstrate that varying these parameters allows us to produce learnable encoders that generate diverse views, capturing either local or global information, for contrastive learning. Our model does not require negative samples for training and is applicable to both homophilic and heterophilic datasets. We demonstrate its effectiveness across various datasets, achieving state-of-the-art performance.