Related papers: Commensurability and bi-interpretability of groups

We entirely classify definable sets up to definable bijections in $\mathbb{Z}$-groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable…

The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatable groupoids are proved. Necessary and sufficient…

We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen-Lenstra…

Adding interpretability to multivariate methods creates a powerful synergy for exploring complex physical systems with higher order correlations while bringing about a degree of clarity in the underlying dynamics of the system.

There is a need of ensuring machine learning models that are interpretable. Higher interpretability of the model means easier comprehension and explanation of future predictions for end-users. Further, interpretable machine learning models…

This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit…

We prove the definability, and actually the finiteness of the commutator width, of many commutator subgroups in groups definable in o-minimal structures. It applies in particular to derived series and to lower central series of solvable…

We describe conditions that characterize amenability for groups in terms of positive definite functions valued in a von Neumann algebra.

Recent years have seen a boom in interest in machine learning systems that can provide a human-understandable rationale for their predictions or decisions. However, exactly what kinds of explanation are truly human-interpretable remains…

Graph clustering groups entities -- the vertices of a graph -- based on their similarity, typically using a complex distance function over a large number of features. Successful integration of clustering approaches in automated…

We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of…

The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…

We define the notion of computability of F{\o}lner sets for finitely generated amenable groups. We prove, by an explicit description, that the Kharlampovich group, a finitely presented solvable group with unsolvable word problem, has…

Interpretability provides a means for humans to verify aspects of machine learning (ML) models and empower human+ML teaming in situations where the task cannot be fully automated. Different contexts require explanations with different…

We study groups definable in existentially closed geometric fields with commuting derivations. Our main result is that such a group can be definably embedded in a group interpretable in the underlying geometric field. Compared to earlier…

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.

We investigate what it means for a (Hausdorff, second-countable) topological group to be computable. We compare several potential definitions in the literature. We relate these notions with the well-established definitions of effective…

Computations in the cohomology of finite groups.

This work can be thought as a contribution to the model theory of group extensions. We study the groups G which are interpretable in the disjoint union of two structures (seen as a two-sorted structure). We show that if one of the two…

We introduce the notion of a bicollapsible 2-complex. This allows us to generalize the hyperbolicity of one-relator groups with torsion to a broader class of groups with presentations whose relators are proper powers. We also prove that…