# On the Convergence of Tsetlin Machines for the AND and the OR Operators

arXiv: https://arxiv.org/abs/2109.09488 · HTML: https://mlsanity.com/paper/2109.09488/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 17 Sep 2021.

## Builds on (most cited first, 10 of 10)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [The Tsetlin Machine -- A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition with Propositional Logic](https://mlsanity.com/paper/1804.01508/) (2018)
- [The Convolutional Tsetlin Machine](https://mlsanity.com/paper/1905.09688/) (2019)
- [On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators](https://mlsanity.com/paper/2007.14268/) (2020)
- [Massively Parallel and Asynchronous Tsetlin Machine Architecture Supporting Almost Constant-Time Scaling](https://mlsanity.com/paper/2009.04861/) (2020)
- [On the Convergence of Tsetlin Machines for the XOR Operator](https://mlsanity.com/paper/2101.02547/) (2021)
- [Measuring the Novelty of Natural Language Text Using the Conjunctive Clauses of a Tsetlin Machine Text Classifier](https://mlsanity.com/paper/2011.08755/) (2020)
- [Enhancing Interpretable Clauses Semantically using Pretrained Word Representation](https://mlsanity.com/paper/2104.06901/) (2021)
- [A Regression Tsetlin Machine with Integer Weighted Clauses for Compact Pattern Representation](https://mlsanity.com/paper/2002.01245/) (2020)

## Built on by (most cited first, 4 of 4)

- [Building Concise Logical Patterns by Constraining Tsetlin Machine Clause Size](https://mlsanity.com/paper/2301.08190/) (2023)
- [Interpretable Tsetlin Machine-based Premature Ventricular Contraction Identification](https://mlsanity.com/paper/2301.10181/) (2023)
- [On the Equivalence of the Weighted Tsetlin Machine and the Perceptron](https://mlsanity.com/paper/2212.13634/) (2022)
- [Generalized Convergence Analysis of Tsetlin Machines: A Probabilistic Approach to Concept Learning](https://mlsanity.com/paper/2310.02005/) (2023)

## Abstract (arXiv)

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.