Related papers: A General Framework for Relational Parametricity
This paper investigates regularity, controllability and observability for a networked dynamic system (NDS) with its subsystems being described in a descriptor form and system matrices of each subsystem being represented by a generalized…
We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…
Foundation Models (FMs) have demonstrated remarkable insights into the relational dynamics of the world, leading to the crucial question: how do these models acquire an understanding of world hybrid relations? Traditional statistical…
We present a formalization of a version of Abadi and Plotkin's logic for parametricity for a polymorphic dual intuitionistic/linear type theory with fixed points, and show, following Plotkin's suggestions, that it can be used to define a…
Assessing fit in common factor models solely through the lens of mean and covariance structures, as is commonly done with conventional goodness-of-fit (GOF) assessments, may overlook critical aspects of misfit, potentially leading to…
We investigate parametrized variational problems where for each parameter the solution may originate from a different parameter-dependent function space. Our main motivation is the theory of Friedrichs' systems, a large abstract class of…
While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
Symmetry reduction is a well-known approach for alleviating the state explosion problem in model checking. Automatically identifying symmetries in concurrent systems, however, is computationally expensive. We propose a symbolic framework…
Semi-simplicial and semi-cubical sets are commonly defined as presheaves over respectively, the semi-simplex or semi-cube category. Homotopy Type Theory then popularized an alternative definition, where the set of n-simplices or n-cubes are…
Modern order and lattice theory provides convenient mathematical tools for pattern mining, in particular for condensed irredundant representations of pattern spaces and their efficient generation. Formal Concept Analysis (FCA) offers a…
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…
We treat Mechanics as a 1-dimensional general-relativistic gauge field theory, Mechanical Field Theory (MFT), introducing what we call the Mechanical Field Space (MFS) and exploiting its bundle geometry. The diffeomorphism covariance of MFT…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
Pretrained (language) embeddings are versatile, task-agnostic feature representations of entities, like words, that are central to many machine learning applications. These representations can be enriched through retrofitting, a class of…
Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly…
We propose a method for inferring \emph{parameterized regular types} for logic programs as solutions for systems of constraints over sets of finite ground Herbrand terms (set constraint systems). Such parameterized regular types generalize…
We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a functor F into the syntax is stable over the codomain of F. We…
A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally…
Modern database systems face a significant challenge in effectively handling the Variety of data. The primary objective of this paper is to establish a unified data model and theoretical framework for multi-model data management. To achieve…