Generalized Convergence Analysis of Tsetlin Automaton Based Algorithms: A Probabilistic Approach to Concept Learning

Abstract

Tsetlin Machines (TMs) have garnered increasing interest for their ability to learn concepts via propositional formulas and their proven efficiency across various application domains. Despite this, the convergence proof for the TMs, particularly for the AND operator (conjunction of literals), in the generalized case (inputs greater than two bits) remains an open problem. This paper aims to fill this gap by presenting a comprehensive convergence analysis of Tsetlin automaton-based Machine Learning algorithms. We introduce a novel framework, referred to as Probabilistic Concept Learning (PCL), which simplifies the TM structure while incorporating dedicated feedback mechanisms and dedicated inclusion/exclusion probabilities for literals. Given n features, PCL aims to learn a set of conjunction clauses Ci each associated with a distinct inclusion probability pi. Most importantly, we establish a theoretical proof confirming that, for any clause k, PCL converges to a conjunction of literals when pk is between 0.5 and 1. This result serves as a stepping stone for future research on the convergence properties of Tsetlin automaton-based learning algorithms. Our findings not only contribute to the theoretical understanding of Tsetlin automaton-based learning algorithms but also have implications for their practical application, potentially leading to more robust and interpretable machine learning models.