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Graph neural networks (GNNs) have been widely used in deep learning on graphs. They can learn effective node representations that achieve superior performances in graph analysis tasks such as node classification and node clustering.…
Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known…
Networks with higher-order interactions, prevalent in biological, social, and information systems, are naturally represented as hypergraphs, yet their structural complexity poses fundamental challenges for geometric characterization. While…
Hierarchical abstractions are a methodology for solving large-scale graph problems in various disciplines. Coarsening is one such approach: it generates a pyramid of graphs whereby the one in the next level is a structural summary of the…
Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of…
Medical image segmentation, which is essential for many clinical applications, has achieved almost human-level performance via data-driven deep learning technologies. Nevertheless, its performance is predicated upon the costly process of…
The burgeoning presence of Large Language Models (LLM) is propelling the development of personalized recommender systems. Most existing LLM-based methods fail to sufficiently explore the multi-view graph structure correlations inherent in…
Ordinal regression is a classification task where classes have an order and prediction error increases the further the predicted class is from the true class. The standard approach for modeling ordinal data involves fitting parallel…
Recently, topological data analysis has become a trending topic in data science and engineering. However, the key technique of topological data analysis, i.e., persistent homology, is defined on point cloud data, which does not work…
Solving robotic navigation tasks via reinforcement learning (RL) is challenging due to their sparse reward and long decision horizon nature. However, in many navigation tasks, high-level (HL) task representations, like a rough floor plan,…
Graph Neural Networks (GNNs) are currently dominating in modeling graph-structure data, while their high reliance on graph structure for inference significantly impedes them from widespread applications. By contrast, Graph-regularized MLPs…
Graph clustering is a fundamental task in graph analysis, and recent advances in utilizing graph neural networks (GNNs) have shown impressive results. Despite the success of existing GNN-based graph clustering methods, they often overlook…
Black-box algorithms are designed to optimize functions without relying on their underlying analytical structure or gradient information, making them essential when gradients are inaccessible or difficult to compute. Traditional methods for…
This paper addresses theory and applications of $\ell_p$-based Laplacian regularization in semi-supervised learning. The graph $p$-Laplacian for $p>2$ has been proposed recently as a replacement for the standard ($p=2$) graph Laplacian in…
Deep Reinforcement Learning (Deep RL) has been receiving increasingly more attention thanks to its encouraging performance on a variety of control tasks. Yet, conventional regularization techniques in training neural networks (e.g., $L_2$…
Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the…
Higher-order network analysis uses the ideas of hypergraphs, simplicial complexes, multilinear and tensor algebra, and more, to study complex systems. These are by now well established mathematical abstractions. What's new is that the ideas…
In order to evaluate the invulnerability of networks against various types of attacks and provide guidance for potential performance enhancement as well as controllability maintenance, network controllability robustness (NCR) has attracted…
Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image…
Standard deep learning architectures used for classification generate label predictions with a projection head and softmax activation function. Although successful, these methods fail to leverage the relational information between samples…