Related papers: Hyperbolic Deep Neural Networks: A Survey

In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and…

The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable attention in the realm of representation learning. Current endeavors in hyperbolic representation largely presuppose that the underlying hierarchies can be…

Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains…

Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…

Hyperbox-based classification has been seen as a promising technique in which decisions on the data are represented as a series of orthogonal, multidimensional boxes (i.e., hyperboxes) that are often interpretable and human-readable.…

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…

The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However,…

Hyperbolic geometry have shown significant potential in modeling complex structured data, particularly those with underlying tree-like and hierarchical structures. Despite the impressive performance of various hyperbolic neural networks…

Hyperbolic embeddings have recently gained attention in machine learning due to their ability to represent hierarchical data more accurately and succinctly than their Euclidean analogues. However, multi-relational knowledge graphs often…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

Hyperdimensional Computing (HDC) has obtained abundant attention as an emerging non von Neumann computing paradigm. Inspired by the way human brain functions, HDC leverages high dimensional patterns to perform learning tasks. Compared to…

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…

In recent years, Dynamic Graph (DG) representations have been increasingly used for modeling dynamic systems due to their ability to integrate both topological and temporal information in a compact representation. Dynamic graphs allow to…

Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The…

Hierarchical data is common in many domains like life sciences and e-commerce, and its embeddings often play a critical role. While hyperbolic embeddings offer a theoretically grounded approach to representing hierarchies in low-dimensional…

Hyperbolic cross approximation is a special type of multivariate approximation. Recently, driven by applications in engineering, biology, medicine and other areas of science new challenging problems have appeared. The common feature of…

Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain…

3D-aware visual pretraining has proven effective in improving the performance of downstream robotic manipulation tasks. However, existing methods are constrained to Euclidean embedding spaces, whose flat geometry limits their ability to…

This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such…

The extensive adoption of Deep Neural Networks has led to their increased utilization in challenging scientific visualization tasks. Recent advancements in building compressed data models using implicit neural representations have shown…