Related papers: A General Framework for Relational Parametricity
We establish a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. At the center of this framework lies the concept of a $\leqslant$-parametric graph:…
This report is an extension of 'A Model of Parametric Dependent Type Theory in Bridge/Path Cubical Sets' (Nuyts, arXiv:1706.04383). The purpose of this text is to prove all technical aspects of our model for dependent type theory with…
Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original…
The objective of this manuscript is to introduce and develop the concept of a generalized $\theta$-parametric metric space-a novel extension that enriches the modern metric fixed point theory. We study of its fundamental properties,…
Denotational models of type theory, such as set-theoretic, domain-theoretic, or category-theoretic models use (actual) infinite sets of objects in one way or another. The potential infinite, seen as an extensible finite, requires a dynamic…
Deep learning, despite its remarkable achievements, is still a young field. Like the early stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad-hoc design decisions, and the lack of a uniform and…
Linear properties are ubiquitous in the representations of language models; however, testing them experimentally remains a challenging task. This work focuses on relational linearity: the hypothesis that, for a fixed relation (e.g.,…
Parse graphs have been widely used in Human Pose Estimation (HPE) to model the hierarchical structure and context relations of the human body. However, such methods often suffer from parameter redundancy. More importantly, they rely on…
Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…
Free theorems are a popular tool in reasoning about parametrically polymorphic code. They are also of instructive use in teaching. Their derivation, though, can be tedious, as it involves unfolding a lot of definitions, then hoping to be…
We introduce an equivalence relation on the global class of morphisms of a category that extends several classical notions of equivalence in mathematics. We show that the standard group-action equivalence is a special case of our framework.…
The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…
Context-aware recommendation algorithms focus on refining recommendations by considering additional information, available to the system. This topic has gained a lot of attention recently. Among others, several factorization methods were…
One introduces a class of projective parameterizations that resemble generalized de Jonqui\`eres maps. Any such parametrization defines a birational map $\mathfrak{F}$ of $\pp^n$ onto a hypersurface $V(F)\subset \pp^{n+1}$ with a strong…
\textit{Graph neural networks} (GNNs) are effective models for many dynamical systems consisting of entities and relations. Although most GNN applications assume a single type of entity and relation, many situations involve multiple types…
In this work we comment in more detail on what happens to the parametrized framework first presented by Cardoso et al. when there are departures from the Schwarzschild background metric, as well as possible deviations in the "dynamics". We…
Classical Ramsey theory has successfully extended to relational structures, yielding a wealth of results that have profoundly influenced other areas of mathematics. Interestingly, the same development has not occurred in the case of dual…
We give an algebraic characterization of the syntax and operational semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed syntax with variable binding and equipped with reduction rules via a…
Marginal models involve restrictions on the conditional and marginal association structure of a set of categorical variables. They generalize log-linear models for contingency tables, which are the fundamental tools for modelling the…
Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…