Yoon-Hyuk Choi

Yoonhyuk Choi, Jiho Choi, Taewook Ko et al.

Traditional Graph Neural Networks (GNNs) rely on network homophily, which can lead to performance degradation due to over-smoothing in many real-world heterophily scenarios. Recent studies analyze the smoothing effect (separability) after message-passing (MP), depending on the expectation of node features. Regarding separability gain, they provided theoretical backgrounds on over-smoothing caused by various propagation schemes, including positive, signed, and blocked MPs. More recently, by extending these theorems, some works have suggested improvements in signed propagation under multiple classes. However, prior works assume that the error ratio of all propagation schemes is fixed, failing to investigate this phenomenon correctly. To solve this problem, we propose a novel method for estimating homophily and edge error ratio, integrated with dynamic selection between blocked and signed propagation during training. Our theoretical analysis, supported by extensive experiments, demonstrates that blocking MP can be more effective than signed propagation under high edge error ratios, improving the performance in both homophilic and heterophilic graphs.

Yoonhyuk Choi, Chong-Kwon Kim

Graph Neural Networks (GNNs) excel on homophilous graphs but often fail under heterophily due to self-reinforcing and phase-inconsistent signals. We propose a Gauge-Equivariant Graph Network with Self-Interference Cancellation (GESC), which replaces additive aggregation with a projection-based interference mechanism. Unlike prior magnetic or gauge-equivariant GNNs that typically focus on phase handling in spectral filtering while largely relying on scalar weighting, GESC introduces a $\mathrm{U}(1)$ phase connection followed by a rank-1 projection that attenuates self-parallel components before attention. A sign- and phase-aware gate further regulates neighbor influence, attenuating components aligned with current node states and acting as a local notch on low-frequency modes. Across diverse graph benchmarks, our method consistently outperforms recent state-of-the-art models while offering a unified, interference-aware view of message passing. Our code is available at \href{here}{https://anonymous.4open.science/r/GESC-1B22}.

Yoonhyuk Choi, Jiho Choi, Chong-Kwon Kim

Over-smoothing in Graph Neural Networks (GNNs) causes collapse in distinct node features, particularly on heterophilic graphs where adjacent nodes often have dissimilar labels. Although sheaf neural networks partially mitigate this problem, they typically rely on static or heavily parameterized sheaf structures that hinder generalization and scalability. Existing sheaf-based models either predefine restriction maps or introduce excessive complexity, yet fail to provide rigorous stability guarantees. In this paper, we introduce a novel scheme called SGPC (Sheaf GNNs with PAC-Bayes Calibration), a unified architecture that combines cellular-sheaf message passing with several mechanisms, including optimal transport-based lifting, variance-reduced diffusion, and PAC-Bayes spectral regularization for robust semi-supervised node classification. We establish performance bounds theoretically and demonstrate that end-to-end training in linear computational complexity can achieve the resulting bound-aware objective. Experiments on nine homophilic and heterophilic benchmarks show that SGPC outperforms state-of-the-art spectral and sheaf-based GNNs while providing certified confidence intervals on unseen nodes. The code and proofs are in https://github.com/ChoiYoonHyuk/SGPC.

Yoonhyuk Choi, Jiho Choi, Taewook Ko et al.

The issue of data sparsity poses a significant challenge to recommender systems. In response to this, algorithms that leverage side information such as review texts have been proposed. Furthermore, Cross-Domain Recommendation (CDR), which captures domain-shareable knowledge and transfers it from a richer domain (source) to a sparser one (target), has received notable attention. Nevertheless, the majority of existing methodologies assume a Euclidean embedding space, encountering difficulties in accurately representing richer text information and managing complex interactions between users and items. This paper advocates a hyperbolic CDR approach based on review texts for modeling user-item relationships. We first emphasize that conventional distance-based domain alignment techniques may cause problems because small modifications in hyperbolic geometry result in magnified perturbations, ultimately leading to the collapse of hierarchical structures. To address this challenge, we propose hierarchy-aware embedding and domain alignment schemes that adjust the scale to extract domain-shareable information without disrupting structural forms. The process involves the initial embedding of review texts in hyperbolic space, followed by feature extraction incorporating degree-based normalization and structure alignment. We conducted extensive experiments to substantiate the efficiency, robustness, and scalability of our proposed model in comparison to state-of-the-art baselines.

Yoonhyuk Choi, Jiho Choi, Taewook Ko et al.

Recent research on graph neural networks (GNNs) has explored mechanisms for capturing local uncertainty and exploiting graph hierarchies to mitigate data sparsity and leverage structural properties. However, the synergistic integration of these two approaches remains underexplored. This work introduces a novel architecture, the Hierarchical Uncertainty-Aware Graph Neural Network (HU-GNN), which unifies multi-scale representation learning, principled uncertainty estimation, and self-supervised embedding diversity within a single end-to-end framework. Specifically, HU-GNN adaptively forms node clusters and estimates uncertainty at multiple structural scales from individual nodes to higher levels. These uncertainty estimates guide a robust message-passing mechanism and attention weighting, effectively mitigating noise and adversarial perturbations while preserving predictive accuracy on semi-supervised classification tasks. We also offer key theoretical contributions, including a probabilistic formulation, rigorous uncertainty-calibration guarantees, and formal robustness bounds. Extensive experiments on standard benchmarks demonstrate that our model achieves state-of-the-art robustness and interpretability.

Yoonhyuk Choi, Jiho Choi, Chong-Kwon Kim

Recent Graph Neural Networks (GNNs) combine spectral-spatial architectures for enhanced representation learning. However, limited attention has been paid to certified robustness, particularly regarding training strategies and underlying rationale. In this paper, we explicitly specialize each branch: the spectral network is trained to withstand l0 edge flips and capture homophilic structures, while the spatial part is designed to resist linf feature perturbations and heterophilic patterns. A context-aware gating network adaptively fuses the two representations, dynamically routing each node's prediction to the more reliable branch. This specialized adversarial training scheme uses branch-specific inner maximization (structure vs feature attacks) and a unified alignment objective. We provide theoretical guarantees: (i) expressivity of the gating mechanism beyond 1-WL, (ii) spectral-spatial frequency bias, and (iii) certified robustness with trade-off. Empirically, SpecSphere attains state-of-the-art node classification accuracy and offers tighter certified robustness on real-world benchmarks.