Related papers: A 2-adjunction between representations and preorde…

Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…

Within this research, two combinatorial bijections using Young diagrams were studied. The first is a special case of a bijective correspondence between two classes of combinatorial objects. Its proof, based on Young diagrams, establishes…

We want to replace categories, functors and natural transformations by categories, open functors and open natural transformations. In analogy with open dynamical systems, the adjective open is added here to mean that some external…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

We consider two problems that appear at first sight to be unrelated. The first problem is to count certain diagrams consisting of noncrossing arcs in the plane. The second problem concerns the weak order on the symmetric group. Each…

In the philosophical literature, symmetries of physical theories are most often interpreted within the general doctrine called 'Sophistication'. Roughly speaking, it says that models related by symmetries can peacefully co-exist while…

We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…

We apply the notion of relative adjoint functor to generalise closed monoidal categories. We define representations in such categories and give their relation with left actions of monoids. The translation of these representations under lax…

In many real-world applications, modeling both the internal structure of sets and their temporal relationships is essential for capturing complex underlying patterns. Sequential multiple-instance learning aims to address this challenge by…

We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of…

Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to…

It is evidence that representation learning can improve model's performance over multiple downstream tasks in many real-world scenarios, such as image classification and recommender systems. Existing learning approaches rely on establishing…

We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.

For a smooth map between noetherian schemes, Verdier relates the top relative differentials of the map with the twisted inverse image functor `upper shriek'. We show that the associated traces for smooth proper maps can be rendered concrete…

This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we…

This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…

Effective task representations should facilitate compositionality, such that after learning a variety of basic tasks, an agent can perform compound tasks consisting of multiple steps simply by composing the representations of the…

We first introduce the notion of meta-rank for a 2-parameter persistence module, an invariant that captures the information behind images of morphisms between 1D slices of the module. We then define the meta-diagram of a 2-parameter…