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The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting higher-order structures in the data, especially in topological deep learning (TDL), which designs…

Topological deep learning (TDL) is a rapidly growing field that seeks to leverage topological structure in data and facilitate learning from data supported on topological objects, ranging from molecules to 3D shapes. Most TDL architectures…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent…

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…

Molecular representation learning, a cornerstone for downstream tasks like molecular captioning and molecular property prediction, heavily relies on Graph Neural Networks (GNN). However, GNN suffers from the over-smoothing problem, where…

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation…

Topological deep learning has emerged as a powerful paradigm for modeling higher-order relational structures beyond pairwise interactions that standard graph neural networks fail to capture. While combinatorial complexes (CCs) offer a…

Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry. While extensive research has been done on developing GNN models with superior performance according to a…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Learning disentangled representations is regarded as a fundamental task for improving the generalization, robustness, and interpretability of generative models. However, measuring disentanglement has been challenging and inconsistent, often…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…

Hypergraphs, with their capacity to depict high-order relationships, have emerged as a significant extension of traditional graphs. Although Graph Neural Networks (GNNs) have remarkable performance in graph representation learning, their…

Graph Neural Networks (GNNs) have achieved significant success in learning better representations by performing feature propagation and transformation iteratively to leverage neighborhood information. Nevertheless, iterative propagation…

Graph neural networks (GNNs) have been widely used to learn vector representation of graph-structured data and achieved better task performance than conventional methods. The foundation of GNNs is the message passing procedure, which…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

Graph Neural Networks based on the message-passing (MP) mechanism are a dominant approach for handling graph-structured data. However, they are inherently limited to modeling only pairwise interactions, making it difficult to explicitly…

Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data. Although many different types of GNN models have been developed, with many benchmarking procedures…