On the Convergence of Tsetlin Machines for the AND and the OR Operators
This work provides incremental theoretical validation for a novel machine-learning algorithm, addressing foundational aspects for researchers in logic-based AI.
The paper analyzes the convergence of Tsetlin Machines for AND and OR operators, revealing that the algorithm can almost surely reproduce these operators from training data over an infinite time horizon, completing convergence analyses for basic Boolean algebra operators.
The Tsetlin Machine (TM) is a novel machine-learning algorithm based on propositional logic, which has obtained state-of-the-art performance on several pattern recognition problems. In previous studies, the convergence properties of TM for 1-bit operation and XOR operation have been analyzed. To make the analyses for the basic digital operations complete, in this article, we analyze the convergence when input training samples follow AND and OR operators respectively. Our analyses reveal that the TM can converge almost surely to reproduce AND and OR operators, which are learnt from training data over an infinite time horizon. The analyses on AND and OR operators, together with the previously analysed 1-bit and XOR operations, complete the convergence analyses on basic operators in Boolean algebra.