Distributed-Order Fractional Graph Operating Network
This work addresses a bottleneck in graph learning for researchers and practitioners by offering a more flexible and powerful continuous GNN framework, though it appears incremental as it builds on existing continuous GNNs with fractional calculus.
The paper tackles the problem of modeling complex graph feature updating dynamics in continuous Graph Neural Networks (GNNs) by introducing DRAGON, a framework that uses distributed-order fractional calculus with learnable derivative orders, resulting in superior performance compared to traditional continuous GNN models across various graph learning tasks.
We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize integer-order or single fractional-order differential equations, DRAGON uses a learnable probability distribution over a range of real numbers for the derivative orders. By allowing a flexible and learnable superposition of multiple derivative orders, our framework captures complex graph feature updating dynamics beyond the reach of conventional models. We provide a comprehensive interpretation of our framework's capability to capture intricate dynamics through the lens of a non-Markovian graph random walk with node feature updating driven by an anomalous diffusion process over the graph. Furthermore, to highlight the versatility of the DRAGON framework, we conduct empirical evaluations across a range of graph learning tasks. The results consistently demonstrate superior performance when compared to traditional continuous GNN models. The implementation code is available at \url{https://github.com/zknus/NeurIPS-2024-DRAGON}.