Related papers: A General Framework for tilings, Delone sets, func…

This paper addresses the challenge of establishing a bridge between deep convolutional neural networks and conventional object detection frameworks for accurate and efficient generic object detection. We introduce Dense Neural Patterns,…

This paper introduces Multidimensional Task Learning (MTL), a unified mathematical framework based on Generalized Einstein MLPs (GE-MLPs) that operate directly on tensors via the Einstein product. We argue that current computer vision task…

A 2-dimensional direction-length framework is a collection of points in the plane which are linked by pairwise constraints that fix the direction or length of the line segments joining certain pairs of points. We represent it as a pair…

Neural networks have been shown to frequently fail to learn critical safety and correctness properties purely from data, highlighting the need for training methods that directly integrate logical specifications. While adversarial training…

Metallic spin glass systems, such as dilute magnetic alloys, are characterized by randomly distributed local moments coupled to each other through a long-range electron-mediated effective interaction. We present a scalable machine learning…

This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for…

We discuss the possible set of operators from various boundary conformal field theories to build meaningful correlators that lead via a Loewner type procedure to generalisations of SLE($\kappa,\rho$). We also highlight the necessity of…

Self-similar binary one-dimensional (1D) quasilattices (QLs) are classified into mutual local-derivability (MLD) classes. It is shown that the MLD classification is closely related to the number-theoretical classification of parameters…

Machine learning (ML) is quickly emerging as a powerful tool with diverse applications across an extremely broad spectrum of disciplines and commercial endeavors. Typically, ML is used as a black box that provides little illuminating…

The capacity to generalize beyond the range of training data is a pivotal challenge, often synonymous with a model's utility and robustness. This study investigates the comparative abilities of traditional machine learning (ML) models and…

Classical splines feature prominently in approximation theory and numerical analysis, while GKM theory arises in the study of equivariant cohomology. More recently, generalized splines have been studied which simultaneously generalize both…

We use string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. We obtain concise geometric expressions for the objects describing bulk and boundary…

This paper proposes an attributable visual similarity learning (AVSL) framework for a more accurate and explainable similarity measure between images. Most existing similarity learning methods exacerbate the unexplainability by mapping each…

This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at the (topological) level of filtrations…

We remind how relationality arises as the core insight of general-relativistic gauge field theories from the articulation of the generalised hole and point-coincidence arguments. Hence, a compelling case for a manifestly relational…

Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…

A thermodynamic framework that predicts the thermal conductivity $\lambda$ of simple fluids beyond the dilute-gas limit is introduced. By generalizing the transition-rate approach of particles on a lattice to conserved quantities in…

We define simple tilings in the general context of a $G$-tiling on a Riemannian homogeneous space $M$ to be tilings by Riemannian simplices. As evidence that this definition is natural, we prove that a large class of tilings of $M$ are MLD…

The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…

The local trace function introduced in \cite{Dut} is used to derive equations that relate multiwavelets and multiscaling functions in the context of a generalized multiresolution analysis, without appealing to filters. A construction of…