Related papers: There are no minimal effectively inseparable theor…

Existing approaches for the design of interpretable agent behavior consider different measures of interpretability in isolation. In this paper we posit that, in the design and deployment of human-aware agents in the real world, notions of…

The irreducible integrable representations with finite-dimensional weight spaces of toroidal Lie algebras on which the center acts non-trivially were classified by S.Eswara Rao. In this paper we give a compact proof of the results that lead…

Interpretability aims to explain the behavior of deep neural networks. Despite rapid growth, there is mounting concern that much of this work has not translated into practical impact, raising questions about its relevance and utility. This…

Two salient notions of sameness of theories are synonymy, also known as definitional equivalence, and bi-interpretability. Of these two definitional equivalence is the strictest notion. In which cases can we infer synonymy from…

Interpretable representations are the backbone of many explainers that target black-box predictive systems based on artificial intelligence and machine learning algorithms. They translate the low-level data representation necessary for good…

We establish a framework for the study of the effective theory of weak convergence of measures. We define two effective notions of weak convergence of measures on $\mathbb{R}$: one uniform and one non-uniform. We show that these notions are…

Recently, interpretable models called self-explaining models (SEMs) have been proposed with the goal of providing interpretability robustness. We evaluate the interpretability robustness of SEMs and show that explanations provided by SEMs…

Given a subshift over an arbitrary alphabet, we construct a representation of the associated unital algebra. We describe a criteria for the faithfulness of this representation in terms of the existence of cycles with no exits. Subsequently,…

We prove, for stably computably enumerable formal systems, direct analogues of the first and second incompleteness theorems of G\"odel. A typical stably computably enumerable set is the set of Diophantine equations with no integer…

This late-breaking work presents a large-scale analysis of explainable AI (XAI) literature to evaluate claims of human explainability. We collaborated with a professional librarian to identify 18,254 papers containing keywords related to…

We prove that every finite distributive lattice is isomorphic to a final segment of the d.c.e. Turing degrees (i.e., the degrees of differences of computably enumerable sets). As a corollary, we are able to infer the undecidability of the…

The current literature on AI-advised decision making -- involving explainable AI systems advising human decision makers -- presents a series of inconclusive and confounding results. To synthesize these findings, we propose a simple theory…

Integrated information theory is a mathematical, quantifiable theory of conscious experience. The linchpin of this theory, the $\phi$ measure, quantifies a system's irreducibility to disjoint parts. Purely as a measure of irreducibility, we…

We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…

There exist applications of reinforcement learning like medicine where policies need to be ''interpretable'' by humans. User studies have shown that some policy classes might be more interpretable than others. However, it is costly to…

A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…

We present a method for constructing countable models of small theories and apply it to prove theorems on the maximal number of countable non-isomorphic models of linearly ordered theories.

We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…

Some of the most obviously correct physical theories - namely string theory and the multiverse - make no testable predictions, leading many to question whether we should accept something as scientific even if it makes no testable…