Related papers: Nest-representable tolerances
We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of some compatible relation with its converse. The second way is independent from the variety…
We give examples and counterexamples concerning varieties in which every tolerance is representable as $R \circ R^-$, for some reflexive and admissible relation $R$.
An identity s=t is linear if each variable occurs at most once in each of the terms s and t. Let T be a tolerance relation of an algebra A in a variety defined by a set of linear identities. We prove that there exist an algebra B in the…
We present some identities dealing with reflexive and admissible relations and which, through a variety, are equivalent to congruence modularity.
It has recently been argued that AI models' representations are becoming aligned as their scale and performance increase. Empirical analyses have been designed to support this idea and conjecture the possible alignment of different…
This chapter is divided into two parts. The first part is a survey of some recent results on nests and the orderability problem. The second part consists of results, partial results and open questions, all viewed in the light of nests. From…
Numerous fundamental database and reasoning problems are known to be NP-hard in general but tractable on instances where the underlying hypergraph structure is $\beta$-acyclic. Despite the importance of many of these problems, there has…
Many assumptions that underpin human concepts of identity do not hold for machine minds that can be copied, edited, or simulated. We argue that there exist many different coherent identity boundaries (e.g.\ instance, model, persona), and…
We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility…
In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…
This communication records some observations made in the course of studying one-relator groups from the point of view of residual solvability. As a contribution to clas- sification efforts we single out some relator types that render the…
A cornerstone of the classical view of tolerance is the elimination of self-reactive T cells during negative selection in the thymus. However, high-throughput T-cell receptor sequencing data has so far failed to detect substantial…
The paper introduces an extension of the proposal according to which conceptual representations in cognitive agents should be intended as heterogeneous proxytypes. The main contribution of this paper is in that it details how to reconcile,…
Recent advancements in machine learning and deep learning have brought algorithmic fairness into sharp focus, illuminating concerns over discriminatory decision making that negatively impacts certain individuals or groups. These concerns…
The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventieth of the twentieth century by B. Zelinka and the first author. Since tolerances need not be transitive, their blocks may…
We define a property sub-representability and we give a complete characterisation of sub-representability of posets.
We formalize the notion of nesting probabilistic programming queries and investigate the resulting statistical implications. We demonstrate that while query nesting allows the definition of models which could not otherwise be expressed,…
A representation of heterogeneous stochastic populations that are composed of sub-populations with different levels of distinguishability is introduced together with an analysis of its properties. It is demonstrated that any instance of…
We argue that representations in AI models, particularly deep networks, are converging. First, we survey many examples of convergence in the literature: over time and across multiple domains, the ways by which different neural networks…
In this paper, we define locally matchable subsets of a group which is extracted from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…