1. On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators
- Author
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Ole-Christoffer Granmo, Lei Jiao, Morten Goodwin, and Xuan Zhang
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Training set ,Learning automata ,Computer Science - Artificial Intelligence ,Computer science ,business.industry ,Applied Mathematics ,Time horizon ,Propositional calculus ,Logical connective ,Machine Learning (cs.LG) ,Artificial Intelligence (cs.AI) ,Operator (computer programming) ,Computational Theory and Mathematics ,Artificial Intelligence ,Pattern recognition (psychology) ,Convergence (routing) ,Identity (object-oriented programming) ,Computer Vision and Pattern Recognition ,Artificial intelligence ,business ,Software ,Interpretability - Abstract
The Tsetlin Machine (TM) is a recent machine learning algorithm with several distinct properties, such as interpretability, simplicity, and hardware-friendliness. Although numerous empirical evaluations report on its performance, the mathematical analysis of its convergence is still open. In this article, we analyze the convergence of the TM with only one clause involved for classification. More specifically, we examine two basic logical operators, namely, the "IDENTITY"- and "NOT" operators. Our analysis reveals that the TM, with just one clause, can converge correctly to the intended logical operator, learning from training data over an infinite time horizon. Besides, it can capture arbitrarily rare patterns and select the most accurate one when two candidate patterns are incompatible, by configuring a granularity parameter. The analysis of the convergence of the two basic operators lays the foundation for analyzing other logical operators. 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., Comment: 23 pages, 10 figures
- Published
- 2022
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