Heterophily is a prevalent property of real-world graphs and is well known to impair the performance of homophilic Graph Neural Networks (GNNs). Prior work has attempted to adapt GNNs to heterophilic graphs through non-local neighbor extension or architecture refinement. However, the fundamental reasons behind misclassifications remain poorly understood. In this work, we take a novel perspective by examining recurring inductive subgraphs, empirically and theoretically showing that they act as spurious shortcuts that mislead GNNs and reinforce non-causal correlations in heterophilic graphs. To address this, we adopt a causal inference perspective to analyze and correct the biased learning behavior induced by shortcut inductive subgraphs. We propose a debiased causal graph that explicitly blocks confounding and spillover paths responsible for these shortcuts. Guided by this causal graph, we introduce Causal Disentangled GNN (CD-GNN), a principled framework that disentangles spurious inductive subgraphs from true causal subgraphs by explicitly blocking non-causal paths. By focusing on genuine causal signals, CD-GNN substantially improves the robustness and accuracy of node classification in heterophilic graphs. Extensive experiments on real-world datasets not only validate our theoretical findings but also demonstrate that our proposed CD-GNN outperforms state-of-the-art heterophily-aware baselines.

Generative adversarial network (GAN) has achieved remarkable success in generating high-quality synthetic data by learning the underlying distributions of target data. Recent efforts have been devoted to utilizing optimal transport (OT) to tackle the gradient vanishing and instability issues in GAN. They use the Wasserstein distance as a metric to measure the discrepancy between the generator distribution and the real data distribution. However, most optimal transport GANs define loss functions in Euclidean space, which limits their capability in handling high-order statistics that are of much interest in a variety of practical applications. In this article, we propose a computational framework to alleviate this issue from both theoretical and practical perspectives. Particularly, we generalize the optimal transport-based GAN from Euclidean space to the reproducing kernel Hilbert space (RKHS) and propose Hilbert Optimal Transport GAN (HOT-GAN). First, we design HOT-GAN with a Hilbert embedding that allows the discriminator to tackle more informative and high-order statistics in RKHS. Second, we prove that HOT-GAN has a closed-form kernel reformulation in RKHS that can achieve a tractable objective under the GAN framework. Third, HOT-GAN's objective enjoys the theoretical guarantee of differentiability with respect to generator parameters, which is beneficial to learn powerful generators via adversarial kernel learning. Extensive experiments are conducted, showing that our proposed HOT-GAN consistently outperforms the representative GAN works.

Abstract Artificial neural networks ( $${{{\texttt {ANN}}}}$$ ANN ) are widely used machine learning models. Their widespread use has attracted a lot of interest in their robustness. Many studies show that ’s performance can be highly vulnerable to input manipulation such as adversarial attacks and covariate drift. Therefore, various techniques that focus on improving $${{{\texttt {ANN}}}}$$ ANN ’s robustness have been proposed in the last few years. However, most of these works have mostly focused on image data. In this paper, we investigate the role of discretization in improving $${{{\texttt {ANN}}}}$$ ANN ’s robustness on tabular datasets. Two custom $${{{\texttt {ANN}}}}$$ ANN layers– and (collectively called ) are proposed. The two layers integrate discretization during the training phase to improve $${{{\texttt {ANN}}}}$$ ANN ’s ability to defend against adversarial attacks. Additionally, integrates dynamic discretization during testing phase as well, to provide a unified strategy to handle adversarial attacks and covariate drift. The experimental results on 24 publicly available datasets show that our proposed add much-needed robustness to $${{{\texttt {ANN}}}}$$ ANN for tabular datasets.