Related papers: What is a combinatorial interpretation?

When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…

Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…

In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called \textit{periodic…

This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…

Along with the great success of deep neural networks, there is also growing concern about their black-box nature. The interpretability issue affects people's trust on deep learning systems. It is also related to many ethical problems, e.g.,…

This paper presents a general framework for unifying functional interpretations. It is based on families of parameters allowing for different degrees of freedom on the design of the interpretation. In this way we are able to generalise…

We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…

The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…

We consider a problem of decomposition of a ternary function into a composition of binary ones from the viewpoint of communication complexity and algorithmic information theory as well as some applications to cellular automata.

This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…

We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two…

The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…

Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…

Machine-learning models have demonstrated great success in learning complex patterns that enable them to make predictions about unobserved data. In addition to using models for prediction, the ability to interpret what a model has learned…

We survey results on the hardness of approximating combinatorial optimization problems.

A combinatorial object representing schemas of, possibly skew, perspectives, called {\em a configuration of skew perspective} is defined. Some classifications of skew perspectives are presented.

Despite the growing body of work in interpretable machine learning, it remains unclear how to evaluate different explainability methods without resorting to qualitative assessment and user-studies. While interpretability is an inherently…

Recently, the presence in the literature (also recent) of voluminous discussions about the interpretation of quantum mechanics has been labelled as scandalous. We claim that a weak point of the debate which hosted such a conclusion is a…

In this note, we investigate a mixture of combinatorial spectra and stratified simplicial sets, which would be thought of as a model of the spectrum objects of $(\infty, \infty)$-categories.

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…