Adaptive Multi-view Graph Contrastive Learning via Fractional-order Neural Diffusion Networks

TL;DR

The paper addresses the limitation of fixed handcrafted views in graph contrastive learning by introducing FD-MVGCL, an augmentation-free framework that uses fractional-order diffusion to generate a continuum of views parameterized by the order $α ∈ (0,1]$ with $α$ learned end-to-end. Each view is produced by a dedicated fractional differential equation encoder, and a simple consecutive-view cosine loss aligns neighboring views while regularization and an adaptive view learning algorithm AVLA prevent collapse and reduce redundancy. The authors provide theoretical insights into the distinctness of embeddings across diffusion scales and establish stability bounds under perturbations. Empirically, FD-MVGCL achieves state-of-the-art or competitive results across both homophilic and heterophilic graphs and demonstrates robustness against various adversarial attacks, validating the practicality of multi-scale diffusion based contrastive learning on graphs.

Abstract

Graph contrastive learning (GCL) learns node and graph representations by contrasting multiple views of the same graph. Existing methods typically rely on fixed, handcrafted views-usually a local and a global perspective, which limits their ability to capture multi-scale structural patterns. We present an augmentation-free, multi-view GCL framework grounded in fractional-order continuous dynamics. By varying the fractional derivative order $α\in (0,1]$, our encoders produce a continuous spectrum of views: small $α$ yields localized features, while large $α$ induces broader, global aggregation. We treat $α$ as a learnable parameter so the model can adapt diffusion scales to the data and automatically discover informative views. This principled approach generates diverse, complementary representations without manual augmentations. Extensive experiments on standard benchmarks demonstrate that our method produces more robust and expressive embeddings and outperforms state-of-the-art GCL baselines.

Figures (10)

• Figure 1: t-SNE visualizations of single-class node embeddings from encoders with different FDE orders are shown. Class means are aligned for fair comparison. Results on Cora (homophilic) and Wisconsin and Cornell (heterophilic) reveal distinct embedding behaviors: smaller $\alpha$ values yield compact, core-concentrated clusters, whereas larger $\alpha$ values produce more evenly dispersed feature distributions. Additional visualizations for other classes are provided in \ref{['supp.tsne']}.
• Figure 2: The PCA components of features for different datasets and choices of FDE order parameters. We see that for at least the small order $\alpha_l$, the bar chart is more spread out, which prevents dimension collapse.
• Figure 3: The variation in the ratio $r_c$ during training. Each line plot corresponds to a label class. The ratio $r_c$ for the input features is shown at epoch $0$. We see that the ratio generally increases at the beginning of the training and stabilizes. For example, FD-MVGCL produces higher $r_c$ values than the strong benchmark PolyGCL chen2024polygcl, suggesting better clustered embeddings.
• Figure 4: Overview of the proposed adaptive FD-MVGCL framework. The fractional orders are selected such that $0<\alpha_{1}<\alpha_{2}<\dots<\alpha_{K}$, enabling contrastive learning across multiple distinct views.
• Figure 5: Accuracy vs. training epochs for various loss functions on the Wisconsin and Cora datasets.

Theorems & Definitions (1)

• proof