Related papers: What is a combinatorial interpretation?
Relation extraction aims to identify the target relations of entities in texts. Relation extraction is very important for knowledge base construction and text understanding. Traditional binary relation extraction, including supervised,…
A combinatorial characterization of measurable filters on a countable set is found. We apply it to the problem of measurability of the intersection of nonmeasurable filters.
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the…
A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane…
The lack of interpretability has hindered the large-scale adoption of AI technologies. However, the fundamental idea of interpretability, as well as how to put it into practice, remains unclear. We provide notions of interpretability based…
Causal inference plays an important role in explanatory analysis and decision making across various fields like statistics, marketing, health care, and education. Its main task is to estimate treatment effects and make intervention…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…
Artificial Intelligence models are becoming increasingly more powerful and accurate, supporting or even replacing humans' decision making. But with increased power and accuracy also comes higher complexity, making it hard for users to…
In a series of papers published in this Journal (J. Math. Phys.), a discussion was started on the significance of a new definition of projective representations in quaternionic Hilbert spaces. The present paper gives what we believe is a…
Interpretability of machine learning models has gained more and more attention among researchers in the artificial intelligence (AI) and human-computer interaction (HCI) communities. Most existing work focuses on decision making, whereas we…
In this note we present examples of cumulative connection constants included new fibonomial ones. All examples posses combinatorial interpretation.
This article is an introduction to combinatorics under the axiom of determinacy with a focus on partition properties and infinity Borel codes.
The symmetric interaction combinators are an equally expressive variant of Lafont's interaction combinators. They are a graph-rewriting model of deterministic computation. We define two notions of observational equivalence for them,…
In recent years, machine learning researchers have focused on methods to construct flexible and interpretable prediction models. However, an interpretability evaluation, a relationship between generalization performance and an…
In this paper, we will investigate a harmonic cycle (discrete harmonic form). With a CW-complex, we can construct the combinatorial Laplacian operator. The kernel of the operator is the harmonic space, the set of harmonic cycles, and is…
Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to…
During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning…
This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new…
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…