# On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators

arXiv: https://arxiv.org/abs/2007.14268 · HTML: https://mlsanity.com/paper/2007.14268/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2020.

## Built on by (most cited first, 23 of 23)

- [Coalesced Multi-Output Tsetlin Machines with Clause Sharing](https://mlsanity.com/paper/2108.07594/) (2021)
- [On the Convergence of Tsetlin Machines for the XOR Operator](https://mlsanity.com/paper/2101.02547/) (2021)
- [Tsetlin Machine Embedding: Representing Words Using Logical Expressions](https://mlsanity.com/paper/2301.00709/) (2023)
- [Building Concise Logical Patterns by Constraining Tsetlin Machine Clause Size](https://mlsanity.com/paper/2301.08190/) (2023)
- [Word-level Human Interpretable Scoring Mechanism for Novel Text Detection Using Tsetlin Machines](https://mlsanity.com/paper/2105.04708/) (2021)
- [Tsetlin Machine for Solving Contextual Bandit Problems](https://mlsanity.com/paper/2202.01914/) (2022)
- [Drop Clause: Enhancing Performance, Interpretability and Robustness of the Tsetlin Machine](https://mlsanity.com/paper/2105.14506/) (2021)
- [Exploring Effects of Hyperdimensional Vectors for Tsetlin Machines](https://mlsanity.com/paper/2406.02648/) (2024)
- [On the Convergence of Tsetlin Machines for the AND and the OR Operators](https://mlsanity.com/paper/2109.09488/) (2021)
- [Interpretable Tsetlin Machine-based Premature Ventricular Contraction Identification](https://mlsanity.com/paper/2301.10181/) (2023)
- [Dynamic Tsetlin Machine Accelerators for On-Chip Training at the Edge using FPGAs](https://mlsanity.com/paper/2504.19797/) (2025)
- [Logic-based AI for Interpretable Board Game Winner Prediction with Tsetlin Machine](https://mlsanity.com/paper/2203.04378/) (2022)
- [On the Equivalence of the Weighted Tsetlin Machine and the Perceptron](https://mlsanity.com/paper/2212.13634/) (2022)
- [VDHLA: Variable Depth Hybrid Learning Automaton and Its Application to Defense Against the Selfish Mining Attack in Bitcoin](https://mlsanity.com/paper/2302.12096/) (2023)
- [TPFL: Tsetlin-Personalized Federated Learning with Confidence-Based Clustering](https://mlsanity.com/paper/2409.10392/) (2024)
- [Omni TM-AE: A Scalable and Interpretable Embedding Model Using the Full Tsetlin Machine State Space](https://mlsanity.com/paper/2505.16386/) (2025)
- [Uncertainty Quantification in the Tsetlin Machine](https://mlsanity.com/paper/2507.04175/) (2025)
- [Verifying Properties of Tsetlin Machines](https://mlsanity.com/paper/2303.14464/) (2023)
- [Learning Minimalistic Tsetlin Machine Clauses with Markov Boundary-Guided Pruning](https://mlsanity.com/paper/2309.06315/) (2023)
- [Generalized Convergence Analysis of Tsetlin Machines: A Probabilistic Approach to Concept Learning](https://mlsanity.com/paper/2310.02005/) (2023)
- [Pruning Literals for Highly Efficient Explainability at Word Level](https://mlsanity.com/paper/2411.04557/) (2024)
- [A Methodology for Transparent Logic-Based Classification Using a Multi-Task Convolutional Tsetlin Machine](https://mlsanity.com/paper/2510.01906/) (2025)
- [Compressed Recurrent Feedback in Tsetlin Machines: A Reproducible Boolean-FSM Study](https://mlsanity.com/paper/2609.06133/) (2026)

## Abstract (arXiv)

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.