mlsanityData to 7 Oct 2026

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

arXiv 2109.09488 ↗First posted 17 Sep 2021cs.LG cs.AIcited by 4

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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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 10 of its 22 references that are in the map. First posted on arXiv 17 Sep 2021.

Builds on

10 of 22 references.

References · 10

  1. 2016"Why Should I Trust You?": Explaining the Predictions of Any Classifiercited by 5,040
  2. 2019Attention is not Explanationcited by 916
  3. 2018The Tsetlin Machine -- A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition with Propositional Logiccited by 71
  4. 2019The Convolutional Tsetlin Machinecited by 37
  5. 2020On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operatorscited by 23
  6. 2020Massively Parallel and Asynchronous Tsetlin Machine Architecture Supporting Almost Constant-Time Scalingcited by 20
  7. 2021On the Convergence of Tsetlin Machines for the XOR Operatorcited by 16
  8. 2020Measuring the Novelty of Natural Language Text Using the Conjunctive Clauses of a Tsetlin Machine Text Classifiercited by 15
  9. 2021Enhancing Interpretable Clauses Semantically using Pretrained Word Representationcited by 10
  10. 2020A Regression Tsetlin Machine with Integer Weighted Clauses for Compact Pattern Representationcited by 2

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Cited by year

Citing papers per year: 2022: 1; 2023: 3.

4 papers.

  1. 2023Building Concise Logical Patterns by Constraining Tsetlin Machine Clause Sizecited by 14
  2. 2023Interpretable Tsetlin Machine-based Premature Ventricular Contraction Identificationcited by 3
  3. 2022On the Equivalence of the Weighted Tsetlin Machine and the Perceptroncited by 1
  4. 2023Generalized Convergence Analysis of Tsetlin Machines: A Probabilistic Approach to Concept Learningcited by 0