Related papers: Heat Kernel Goes Topological

Binarization is an attractive strategy for implementing lightweight Deep Convolutional Neural Networks (CNNs). Despite the unquestionable savings offered, memory footprint above all, it may induce an excessive accuracy loss that prevents a…

Self-Organized Operational Neural Networks (Self-ONNs) have recently been proposed as new-generation neural network models with nonlinear learning units, i.e., the generative neurons that yield an elegant level of diversity; however, like…

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…

Convolutional Neural Networks (CNNs) excel at extracting local features hierarchically, but their performance in capturing complex correlations hinges heavily on deep architectures, which are usually computationally demanding and difficult…

Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and…

During the past decade, Deep Learning (DL) algorithms, programming systems and hardware have converged with the High Performance Computing (HPC) counterparts. Nevertheless, the programming methodology of DL and HPC systems is stagnant,…

Tabular foundation models like TabPFN and TabICL achieve state-of-the-art performance through in-context learning, yet their architectures remain fundamentally opaque. We introduce KernelICL, a framework to enhance tabular foundation models…

We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…

We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from…

The rapid development of reliable Quantum Processing Units (QPU) opens up novel computational opportunities for machine learning. Here, we introduce a procedure for measuring the similarity between graph-structured data, based on the…

Group convolution works well with many deep convolutional neural networks (CNNs) that can effectively compress the model by reducing the number of parameters and computational cost. Using this operation, feature maps of different group…

Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion).…

Learning from structured data is a core machine learning task. Commonly, such data is represented as graphs, which normally only consider (typed) binary relationships between pairs of nodes. This is a substantial limitation for many domains…

Given a graph where every node has certain attributes associated with it and some nodes have labels associated with them, Collective Classification (CC) is the task of assigning labels to every unlabeled node using information from the node…

Non-Hermitian topological phases can produce some remarkable properties, compared with their Hermitian counterpart, such as the breakdown of conventional bulk-boundary correspondence and the non-Hermitian topological edge mode. Here, we…

Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

Convolutional Neural Networks, as most artificial neural networks, are commonly viewed as methods different in essence from kernel-based methods. We provide a systematic translation of Convolutional Neural Networks (ConvNets) into their…

In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…