Related papers: Shadow Cones: A Generalized Framework for Partial …

How can we represent hierarchical information present in large type inventories for entity typing? We study the ability of hyperbolic embeddings to capture hierarchical relations between mentions in context and their target types in a…

Spatio-temporal data is intrinsically high dimensional, so unsupervised modeling is only feasible if we can exploit structure in the process. When the dynamics are local in both space and time, this structure can be exploited by splitting…

The paper deals with topical issues of modern mathematical theory of dynamical chaos and its applications. At present, it is customary to assume that dynamical chaos in finitedimensional smooth systems can exist in three different forms.…

This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…

Contract theories have been proposed to formally support distributed and decentralized system design while ensuring safe system integration. In this paper we propose hypercontracts, a generic model with a richer structure for its underlying…

The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying natural assumptions (satisfied, for example, by mapping class…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…

We consider the task of inferring is-a relationships from large text corpora. For this purpose, we propose a new method combining hyperbolic embeddings and Hearst patterns. This approach allows us to set appropriate constraints for…

We provide a framework to classify hyperbolic monopoles with continuous symmetries and find a Structure Theorem, greatly simplifying the construction of all those with spherically symmetry. In doing so, we reduce the problem of finding…

We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its…

Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, and ultrametric complete spaces. We develop a theory of shifts of finite type for infinite alphabets. We call…

In this work, we explore the task of hierarchical distance-based speech separation defined on a hyperbolic manifold. Based on the recent advent of audio-related tasks performed in non-Euclidean spaces, we propose to make use of the…

Real-world knowledge is often organized as hierarchies such as product taxonomies, medical ontologies, and label trees, yet learning hierarchical representations is challenging due to asymmetric structure and noisy semantics. We introduce…

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…

While Vision-Language Models (VLMs) have achieved remarkable performance, their Euclidean embeddings remain limited in capturing hierarchical relationships such as part-to-whole or parent-child structures, and often face challenges in…

Hyperbolic neural networks have been popular in the recent past due to their ability to represent hierarchical data sets effectively and efficiently. The challenge in developing these networks lies in the nonlinearity of the embedding space…

The importance of higher-order relations is widely recognized in a large number of real-world systems. However, annotating them is a tedious and sometimes impossible task. Consequently, current approaches for data modelling either ignore…

Time-delay embedding is an increasingly popular starting point for data-driven reduced-order modeling efforts. In particular, the singular value decomposition (SVD) of a block Hankel matrix formed from successive delay embeddings of the…

Recently, Hyperbolic Spaces in the context of Non-Euclidean Deep Learning have gained popularity because of their ability to represent hierarchical data. We propose that it is possible to take advantage of the hierarchical characteristic…