Related papers: A topos for a nonstandard functional interpretatio…
Explainable AI (XAI) is frequently positioned as a technical problem of revealing the inner workings of an AI model. This position is affected by unexamined onto-epistemological assumptions: meaning is treated as immanent to the model, the…
The question in the title is ambiguous. At least the understanding of words essentially different and function theory should be clarified. We discuss approaches to do that. We also present a new framework for analytic function theories…
This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in…
Epistemic logic with non-standard knowledge operators, especially the "knowing-value" operator, has recently gathered much attention. With the "knowing-value" operator, we can express knowledge of individual variables, but not of the…
Word embeddings are substantially successful in capturing semantic relations among words. However, these lexical semantics are difficult to be interpreted. Definition modeling provides a more intuitive way to evaluate embeddings by…
We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (resp. connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple…
To tackle interpretability in deep learning, we present a novel framework to jointly learn a predictive model and its associated interpretation model. The interpreter provides both local and global interpretability about the predictive…
We discuss a new approach to functional interpretations based on uniform quantification and relativization. The uniform quantification in the background permits a more penetrating analysis of principles related to collection and…
We investigate the interpretability ordering $\trianglelefteq^*$ using generalized Ehrenfeucht-Mostowski models. This gives a new approach to proving inequalities and investigating the structure of types.
Social scientists are increasingly turning to unstructured datasets to unlock new empirical insights, e.g., estimating descriptive statistics of or causal effects on quantitative measures derived from text, audio, or video data. In many…
In this article we utilise abstract convexity theory in order to unify and generalize many different concepts from nonsmooth analysis. We introduce the concepts of abstract codifferentiability, abstract quasidifferentiability and abstract…
We present a new variant of the V\"axj\"o interpretation: contextualistic statistical realistic. Basic ideas of the V\"axj\"o interpretation-2001 are essentially clarified. We also discuss applications to biology, psychology, sociology,…
The article examines Nikolskii and Besov spaces with norms defined using $L_p$-averaged mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative…
This article presents a survey of recent developments on pseudodifferential operators on noncommutative tori. We describe currently available constructions of those operators: by means of a $C^*$--dynamical system, by using an analogue of…
Traditional mathematical notation can lead to confusion. Expressions that appear to define composite functions sometimes do not. A particular example with engineering applications is studied in detail.
Approaching new data can be quite deterrent; you do not know how your categories of interest are realized in it, commonly, there is no labeled data at hand, and the performance of domain adaptation methods is unsatisfactory. Aiming to…
Although sloppy interpretation is usually accounted for by theories of ellipsis, it often arises in non-elliptical contexts. In this paper, a theory of sloppy interpretation is provided which captures this fact. The underlying idea is that…
We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…
We introduce the space of grid functions, a space of generalized functions of nonstandard analysis that provides a coherent generalization both of the space of distributions and of the space of Young measures. We will show that in the space…
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…