Depth-Adaptive Graph Neural Networks via Learnable Bakry-'Emery Curvature

Graph Neural Networks (GNNs) have demonstrated strong representation learning capabilities for graph-based tasks. Recent advances on GNNs leverage geometric properties, such as curvature, to enhance its representation capabilities by modeling complex connectivity patterns and information flow within graphs. However, most existing approaches focus solely on discrete graph topology, overlooking diffusion dynamics and task-specific dependencies essential for effective learning. To address this, we propose integrating Bakry-\'Emery curvature, which captures both structural and task-driven aspects of information propagation. We develop an efficient, learnable approximation strategy, making curvature computation scalable for large graphs. Furthermore, we introduce an adaptive depth mechanism that dynamically adjusts message-passing layers per vertex based on its curvature, ensuring efficient propagation. Our theoretical analysis establishes a link between curvature and feature distinctiveness, showing that high-curvature vertices require fewer layers, while low-curvature ones benefit from deeper propagation. Extensive experiments on benchmark datasets validate the effectiveness of our approach, showing consistent performance improvements across diverse graph learning tasks.

Deep Learning Meets Oversampling: A Learning Framework to Handle Imbalanced Classification

Despite extensive research spanning several decades, class imbalance is still considered a profound difficulty for both machine learning and deep learning models. While data oversampling is the foremost technique to address this issue, traditional sampling techniques are often decoupled from the training phase of the predictive model, resulting in suboptimal representations. To address this, we propose a novel learning framework that can generate synthetic data instances in a data-driven manner. The proposed framework formulates the oversampling process as a composition of discrete decision criteria, thereby enhancing the representation power of the model's learning process. Extensive experiments on the imbalanced classification task demonstrate the superiority of our framework over state-of-the-art algorithms.

DeepSN: A Sheaf Neural Framework for Influence Maximization

Influence maximization is key topic in data mining, with broad applications in social network analysis and viral marketing. In recent years, researchers have increasingly turned to machine learning techniques to address this problem. They have developed methods to learn the underlying diffusion processes in a data-driven manner, which enhances the generalizability of the solution, and have designed optimization objectives to identify the optimal seed set. Nonetheless, two fundamental gaps remain unsolved: (1) Graph Neural Networks (GNNs) are increasingly used to learn diffusion models, but in their traditional form, they often fail to capture the complex dynamics of influence diffusion, (2) Designing optimization objectives is challenging due to combinatorial explosion when solving this problem. To address these challenges, we propose a novel framework, DeepSN. Our framework employs sheaf neural diffusion to learn diverse influence patterns in a data-driven, end-to-end manner, providing enhanced separability in capturing diffusion characteristics. We also propose an optimization technique that accounts for overlapping influence between vertices, which helps to reduce the search space and identify the optimal seed set effectively and efficiently. Finally, we conduct extensive experiments on both synthetic and real-world datasets to demonstrate the effectiveness of our framework.

Uplifting the Expressive Power of Graph Neural Networks through Graph Partitioning

Graph Neural Networks (GNNs) have paved its way for being a cornerstone in graph related learning tasks. From a theoretical perspective, the expressive power of GNNs is primarily characterised according to their ability to distinguish non-isomorphic graphs. It is a well-known fact that most of the conventional GNNs are upper-bounded by Weisfeiler-Lehman graph isomorphism test (1-WL). In this work, we study the expressive power of graph neural networks through the lens of graph partitioning. This follows from our observation that permutation invariant graph partitioning enables a powerful way of exploring structural interactions among vertex sets and subgraphs, and can help uplifting the expressive power of GNNs efficiently. Based on this, we first establish a theoretical connection between graph partitioning and graph isomorphism. Then we introduce a novel GNN architecture, namely Graph Partitioning Neural Networks (GPNNs). We theoretically analyse how a graph partitioning scheme and different kinds of structural interactions relate to the k-WL hierarchy. Empirically, we demonstrate its superior performance over existing GNN models in a variety of graph benchmark tasks.