Related papers: A topos for a nonstandard functional interpretatio…
We consider a philosophical question that is implicit in Selmer Bringsjord's paper, "The narrational case against Church's Thesis": If, as Mendelson argues, the classically accepted definitions of foundational concepts such as "partial…
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
Tuple interpretations are a class of algebraic interpretation that subsumes both polynomial and matrix interpretations as it does not impose simple termination and allows non-linear interpretations. It was developed in the context of…
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…
By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers.
Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…
In this paper we use the notion of slice monogenic functions \cite{slicecss} to define a new functional calculus for an $n$-tuple $T$ of not necessarily commuting operators. This calculus is different from the one discussed in…
Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more…
Neural networks often pack many unrelated concepts into a single neuron - a puzzling phenomenon known as 'polysemanticity' which makes interpretability much more challenging. This paper provides a toy model where polysemanticity can be…
In this paper, we consider the simultaneous approximation of real points by rational points with the error of approximation given by the functions of `non-standard' heights. We prove analogues of Khintchine and Jarn\'ik-Besicovitch theorems…
In this paper, we unify the study of classical and non-classical algebra-valued models of set theory, by studying variations of the interpretation functions for identity and set-membership. Although, these variations coincide with the…
We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear…
In this work we discuss an elementary self-contained presentation of the notion of a semiabelian category, introduced by Raikov and Palamodov. Fundamental examples of (non-abelian) semiabelian categories occuring in Functional Analysis and…
Network interpretation as an effort to reveal the features learned by a network remains largely visualization-based. In this paper, our goal is to tackle semantic network interpretation at both filter and decision level. For filter-level…
An important line of research attempts to explain CNN image classifier predictions and intermediate layer representations in terms of human-understandable concepts. Previous work supports that deep representations are linearly separable…
We argue that existing definitions of interpretability are not actionable in that they fail to inform users about general, sound, and robust interpretable model design. This makes current interpretability research fundamentally ill-posed.…
These notes are concerned with the existence and the basic properties of the set-theoretic universes for nonstandard analysis, compiled by a beginner in the subject. It assumes a basic background in first-order logic, though the necessary…
This text gives a rough, but linear summary covering some key definitions, notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the classical monograph by Barendregt. First, we define a theory of untyped extensional…
Interoperability is crucial for modern scientific advancement, yet its fragmented definitions across domains hinder researchers' ability to effectively reap the rewards. This paper proposes a new, universal definition by tracing the…
A few topics beyond the standard model are reviewed.