arXiv Machine Learning

Topology-Aware Gaussian Graph Repair for Robust Graph Neural Networks

arXiv:2606. 03462v1 Announce Type: new Abstract: Graph neural networks have achieved strong performance on graph-structured data, but their effectiveness depends heavily on the quality of the observed graph.

arXiv Machine Learning
Aug 20

Enhancing Distance-Based Graph Autoencoders with Structural Penalties for Dynamic Graph Embedding

The paper introduces three distance‑based graph autoencoder variants that add structural penalties to the reconstruction loss. All models use a two‑layer Graph Convolutional Network encoder and a Euclidean‑distance decoder, with two node‑level regularizers: a hub penalty based on degree centrality and a penalty based on Natural Community Local Intrinsic Dimensionality (NC‑LID). Experiments on multiple dynamic graph datasets show that incorporating NC‑LID regularization consistently improves reconstruction performance compared to baselines without structural regularization and to the hub‑aware variant.

By Aleksandar Tom\v{c}i\'c, Milo\v{s} Savi\'c, Milo\v{s} Radovanovi\'c
arXiv AI
Sep 25

Reachability-Based Formal Verification of Graph Neural Networks with Node and Edge Features

The paper extends the neural network verification framework to graph neural networks by introducing GraphStar sets, which model uncertainty over both node and edge features. This allows sound propagation of linear message‑passing operations and ReLU nonlinearities for GCN and GINE layers. Experiments on power system tasks (PF, OPF, CFA) and graph classification benchmarks (ENZYMES, PROTEINS) show that the method, called GNNV, yields tighter robustness guarantees than CORA and provides, for the first time, edge‑aware guarantees for GINE‑based models under joint node and edge perturbations.

By Anne M. Tumlin, Ben Wooding, Zhenxuan Shao, Diego Manzanas Lopez, Tyler Derr, Taylor T. Johnson
arXiv Machine Learning
5d ago

Scaffold: Support Graph Theory Based Sparsification for Graph Neural Networks

Scaffold is a new unsupervised graph sparsification framework for graph neural networks that uses support graph theory preconditioners to jointly control dilation and congestion, thereby preserving short communication paths while avoiding bottlenecks. It achieves superior aggregate ranking across 19 homophilic and heterophilic benchmarks, recovering or closely approaching full‑graph GNN performance with only 10%–50% of the original edges. The method reduces memory usage to less than half and cuts end‑to‑end training time, including sparsification overhead.

By Siddhartha Shankar Das, Sai Karthik Navuluru, S M Ferdous, Ryan A. Rossi, Baris Coskunuzer, Lakshman Tamil, Edoardo Serra, Alex Pothen, Robert Rallo, Mahantesh M Halappanavar