Title: Convergence Analysis of Tsetlin Machines for Basic Boolean Operators under Noise-Free and Noisy Training Conditions
Primary area: other topics in machine learning (i.e., none of the above)
Keywords: Tsetlin Automata, Propositional Logic, Tsetlin Machine, Convergence Analysis, Basic Boolean Operators

Abstract: The Tsetlin Machine (TM) is an innovative machine learning algorithm grounded in propositional logic, achieving state-of-the-art performance in a variety of pattern recognition tasks. While previous studies have analyzed its convergence properties for the 1-bit operator under both noisy and noise-free training conditions, as well as for the XOR operator under noise-free conditions, this work extends the theoretical analysis to the AND and OR operators, thereby providing a more comprehensive analysis of fundamental Boolean operations. We show that the TM almost surely converges to correctly represent the AND and OR operators when trained on noise-free data over an infinite time horizon. Notably, our analysis of the OR operator reveals a distinct characteristic: the TM is capable of representing two sub-patterns jointly within a single clause, which contrasts with its behavior in the XOR case. Furthermore, we investigate the TM’s behavior when learning AND, OR, and XOR operators under noisy training conditions, including the presence of mislabeled samples and irrelevant input variables. In the presence of incorrect labels, the TM does not converge to the exact target operators but remains capable of learning efficiently. In contrast, when irrelevant variables are present, the TM still converges almost surely to the correct operators. Together, these results offer a comprehensive theoretical foundation for understanding the convergence behavior of TMs across basic Boolean operators.