Related papers: Mutual Interpretability of Weak Essentially Undeci…

Decision trees (DTs) epitomize the ideal of interpretability of machine learning (ML) models. The interpretability of decision trees motivates explainability approaches by so-called intrinsic interpretability, and it is at the core of…

We investigate the topological complexity of non Borel recognizable tree languages with regard to the difference hierarchy of analytic sets. We show that, for each integer $n \geq 1$, there is a $D_{\omega^n}({\bf \Sigma}^1_1)$-complete…

The minimum classical extension S$^{+g}$ of a classically sound theory S based on intuitionistic logic, defined by adding to S the Gentzen negative interpretations of its mathematical axioms, contains a faithful translation S$^g$ of the…

We focus on the persistence principle over weak interpretability logic. Our object of study is the logic obtained by adding the persistence principle to weak interpretability logic from several perspectives. Firstly, we prove that this…

In this paper, we give a simple combinatorial explanation of a formula of A. Postnikov relating bicolored rooted trees to bicolored binary trees. We also present generalized formulas for the number of labeled k-ary trees, rooted labeled…

Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…

The interpretation of the apparent unification of gauge couplings within supersymmetric theories depends on uncertainties induced through heavy particle thresholds. While in standard grand unified theories these effects can be estimated…

In this review, we examine the problem of designing interpretable and explainable machine learning models. Interpretability and explainability lie at the core of many machine learning and statistical applications in medicine, economics,…

The paper presents a solution to the long-standing question about the decidability of the two-variable fragment of the superintuitionistic predicate logic $\mathbf{QLC}$ defined by the class of linear Kripke frames, which is also the…

Characters of $E_8\otimes E_8$ and SO(32) heterotic strings involving the full internal symmetry Cartan subalgebra generators are defined after circle compactification so that they are T dual. The novel point, as compared with an earlier…

The Burrows-Wheeler transform (BWT) is a reversible transform that converts a string $w$ into another string $\mathsf{BWT}(w)$. The size of the run-length encoded BWT (RLBWT) can be interpreted as a measure of repetitiveness in the class of…

Frege's theorem says that second-order Peano arithmetic is interpretable in Hume's Principle and full impredicative comprehension. Hume's Principle is one example of an abstraction principle, while another paradigmatic example is Basic Law…

Automata admitting at most one accepting run per structure, known as unambiguous automata, find applications in verification of reactive systems as they extend the class of deterministic automata whilst maintaining some of their desirable…

Calabi--Yau manifolds are essential for string theory but require computing intractable metrics. Here we show that symbolic regression can distill neural approximations into simple, interpretable formulas. Our five-term expression matches…

Fundamental conjectures in modular representation theory of finite groups, more precisely, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture, can be expressed in terms of fusion systems. We use fusion systems to connect…

Life expectancy is a fundamental indicator of population health and socio-economic well-being, yet accurately forecasting it remains challenging due to the interplay of demographic, environmental, and healthcare factors. This study…

Let $\mathbb F$ denote an algebraically closed field and assume that $q\in \mathbb F$ is a primitive $d^{\rm \, th}$ root of unity with $d\not=1,2,4$. The universal Askey--Wilson algebra $\triangle_q$ is a unital associative $\mathbb…

We consider the decentralized binary hypothesis testing problem on trees of bounded degree and increasing depth. For a regular tree of depth t and branching factor k>=2, we assume that the leaves have access to independent and identically…

With the advent of highly predictive but opaque deep learning models, it has become more important than ever to understand and explain the predictions of such models. Existing approaches define interpretability as the inverse of complexity…

We show that if \kappa\ is a weakly compact cardinal then the embeddability relation on (generalized) trees of size \kappa\ is invariantly universal. This means that for every analytic quasi-order R on the generalized Cantor space 2^\kappa\…