Semi-supervised learning on real-world graphs is frequently challenged by heterophily, where the observed graph is unreliable or label-disassortative. Many existing graph neural networks either rely on a fixed adjacency structure or attempt to handle structural noise through regularization. In this work, we explicitly capture structural uncertainty by modeling a posterior distribution over signed adjacency matrices, allowing each edge to be positive, negative, or absent. We propose a sparse signed message passing network that is naturally robust to edge noise and heterophily, which can be interpreted from a Bayesian perspective. By combining (i) posterior marginalization over signed graph structures with (ii) sparse signed message aggregation, our approach offers a principled way to handle both edge noise and heterophily. Experimental results demonstrate that our method outperforms strong baseline models on heterophilic benchmarks under both synthetic and real-world structural noise.
@article{arxiv.2601.01207,
title = {Sparse Bayesian Message Passing under Structural Uncertainty},
author = {Yoonhyuk Choi and Jiho Choi and Chanran Kim and Yumin Lee and Hawon Shin and Yeowon Jeon and Minjeong Kim and Jiwoo Kang},
journal= {arXiv preprint arXiv:2601.01207},
year = {2026}
}