On the Convergence of Tsetlin Machines for the XOR Operator

TL;DR

This paper mathematically analyzes the convergence of Tsetlin Machines for learning the XOR operator, demonstrating that with minimal clauses, they can reliably learn XOR patterns, providing insights into their pattern recognition capabilities.

Contribution

The paper offers the first mathematical convergence analysis of Tsetlin Machines on XOR, revealing how hyper-parameters influence clause learning and laying groundwork for more complex logical expressions.

Findings

TM with two clauses converges to XOR almost surely

Hyper-parameter T guides clause construction effectively

Analysis explains TM's success in pattern recognition

Abstract

The Tsetlin Machine (TM) is a novel machine learning algorithm with several distinct properties, including transparent inference and learning using hardware-near building blocks. Although numerous papers explore the TM empirically, many of its properties have not yet been analyzed mathematically. In this article, we analyze the convergence of the TM when input is non-linearly related to output by the XOR-operator. Our analysis reveals that the TM, with just two conjunctive clauses, can converge almost surely to reproducing XOR, learning from training data over an infinite time horizon. Furthermore, the analysis shows how the hyper-parameter T guides clause construction so that the clauses capture the distinct sub-patterns in the data. Our analysis of convergence for XOR thus lays the foundation for analyzing other more complex logical expressions. These analyses altogether, from a mathematical perspective, provide new insights on why TMs have obtained state-of-the-art performance on several pattern recognition problems