Related papers: Interpretable Discovery of One-parameter Subgroups…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically…

Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…

Hypergraphs are useful mathematical representations of overlapping and nested subsets of interacting units, including groups of genes or brain regions, economic cartels, political or military coalitions, and groups of products that are…

Understanding the intricate mappings between visual stimuli and neural responses is a fundamental challenge in cognitive neuroscience. While current approaches predominantly align images and functional magnetic resonance imaging (fMRI)…

Uniform and smooth data collection is often infeasible in real-world scenarios. In this paper, we propose an identification framework to effectively handle the so-called non-uniform observations, i.e., data scenarios that include missing…

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically…

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in…

The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…

In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…

We introduce a machine-learning approach (denoted Symmetry Seeker Neural Network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that…

We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…

Hyperbolic rotation is commonly used to effectively model knowledge graphs and their inherent hierarchies. However, existing hyperbolic rotation models rely on logarithmic and exponential mappings for feature transformation. These models…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

This monograph presents a geometric modeling method nonlinear dynamical systems from experimental data . basis method is a qualitative approach to the analysis of linear models and construction of the symmetry groups of attractors of…

Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical…

This paper develops a new mathematical framework that enables nonparametric joint semantic and geometric representation of continuous functions using data. The joint embedding is modeled by representing the processes in a reproducing kernel…

Symmetry is widely applied in problems such as the design of equivariant networks and the discovery of governing equations, but in complex scenarios, it is not known in advance. Most previous symmetry discovery methods are limited to linear…

This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…