A conditional, a fuzzy and a probabilistic interpretation of self-organising maps

TL;DR

This paper explores the connections between Self-Organising Maps, fuzzy logic, and preferential semantics, providing new interpretative frameworks and probabilistic insights into their behavior and properties.

Contribution

It introduces fuzzy and preferential semantics to interpret Self-Organising Maps, linking neural network behavior with description logics and probabilistic models.

Findings

Network behavior described by fuzzy and preferential interpretations

Properties verified through model checking

Probabilistic account derived from fuzzy interpretation

Abstract

In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category generalisation. In particular, we show that the input/output behavior of a Self-Organising Map after training can be described by a fuzzy description logic interpretation as well as by a preferential interpretation, based on a concept-wise multipreference semantics, which takes into account preferences with respect to different concepts and has been recently proposed for ranked and for weighted defeasible description logics. Properties of the network can be proven by model checking on the fuzzy or on the preferential interpretation. Starting from the fuzzy interpretation, we also provide a probabilistic account for this neural network model.