# The Convolutional Tsetlin Machine

arXiv: https://arxiv.org/abs/1905.09688 · HTML: https://mlsanity.com/paper/1905.09688/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2019.

## Built on by (most cited first, 30 of 37)

- [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)
- [Building Concise Logical Patterns by Constraining Tsetlin Machine Clause Size](https://mlsanity.com/paper/2301.08190/) (2023)
- [Enhancing Interpretable Clauses Semantically using Pretrained Word Representation](https://mlsanity.com/paper/2104.06901/) (2021)
- [Word-level Human Interpretable Scoring Mechanism for Novel Text Detection Using Tsetlin Machines](https://mlsanity.com/paper/2105.04708/) (2021)
- [A Relational Tsetlin Machine with Applications to Natural Language Understanding](https://mlsanity.com/paper/2102.10952/) (2021)
- [Drop Clause: Enhancing Performance, Interpretability and Robustness of the Tsetlin Machine](https://mlsanity.com/paper/2105.14506/) (2021)
- [An Optimized Toolbox for Advanced Image Processing with Tsetlin Machine Composites](https://mlsanity.com/paper/2406.00704/) (2024)
- [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)
- [TMComposites: Plug-and-Play Collaboration Between Specialized Tsetlin Machines](https://mlsanity.com/paper/2309.04801/) (2023)
- [MATADOR: Automated System-on-Chip Tsetlin Machine Design Generation for Edge Applications](https://mlsanity.com/paper/2403.10538/) (2024)
- [An All-digital 8.6-nJ/Frame 65-nm Tsetlin Machine Image Classification Accelerator](https://mlsanity.com/paper/2501.19347/) (2025)
- [A Comparison Between Tsetlin Machines and Deep Neural Networks in the Context of Recommendation Systems](https://mlsanity.com/paper/2212.10136/) (2022)
- [A Voting Approach for Explainable Classification with Rule Learning](https://mlsanity.com/paper/2311.07323/) (2023)
- [The Probabilistic Tsetlin Machine: A Novel Approach to Uncertainty Quantification](https://mlsanity.com/paper/2410.17851/) (2024)
- [Dynamic Tsetlin Machine Accelerators for On-Chip Training at the Edge using FPGAs](https://mlsanity.com/paper/2504.19797/) (2025)
- [The Tsetlin Machine Goes Deep: Logical Learning and Reasoning With Graphs](https://mlsanity.com/paper/2507.14874/) (2025)
- [Rule Learning by Modularity](https://mlsanity.com/paper/2212.12335/) (2022)
- [On the Equivalence of the Weighted Tsetlin Machine and the Perceptron](https://mlsanity.com/paper/2212.13634/) (2022)
- [Contracting Tsetlin Machine with Absorbing Automata](https://mlsanity.com/paper/2310.11481/) (2023)
- [Parametric Matrix Models](https://mlsanity.com/paper/2401.11694/) (2024)
- [The Sparse Tsetlin Machine: Sparse Representation with Active Literals](https://mlsanity.com/paper/2405.02375/) (2024)
- [TPFL: Tsetlin-Personalized Federated Learning with Confidence-Based Clustering](https://mlsanity.com/paper/2409.10392/) (2024)
- [Runtime Tunable Tsetlin Machines for Edge Inference on eFPGAs](https://mlsanity.com/paper/2502.07823/) (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)
- [Generalized Convergence Analysis of Tsetlin Machines: A Probabilistic Approach to Concept Learning](https://mlsanity.com/paper/2310.02005/) (2023)
- [An Approach for Efficient Neural Architecture Search Space Definition](https://mlsanity.com/paper/2310.17669/) (2023)
- [Pre-Sorted Tsetlin Machine (The Genetic K-Medoid Method)](https://mlsanity.com/paper/2403.09680/) (2024)

## Abstract (arXiv)

Convolutional neural networks (CNNs) have obtained astounding successes for important pattern recognition tasks, but they suffer from high computational complexity and the lack of interpretability. The recent Tsetlin Machine (TM) attempts to address this lack by using easy-to-interpret conjunctive clauses in propositional logic to solve complex pattern recognition problems. The TM provides competitive accuracy in several benchmarks, while keeping the important property of interpretability. It further facilitates hardware-near implementation since inputs, patterns, and outputs are expressed as bits, while recognition and learning rely on straightforward bit manipulation. In this paper, we exploit the TM paradigm by introducing the Convolutional Tsetlin Machine (CTM), as an interpretable alternative to CNNs. Whereas the TM categorizes an image by employing each clause once to the whole image, the CTM uses each clause as a convolution filter. That is, a clause is evaluated multiple times, once per image patch taking part in the convolution. To make the clauses location-aware, each patch is further augmented with its coordinates within the image. The output of a convolution clause is obtained simply by ORing the outcome of evaluating the clause on each patch. In the learning phase of the TM, clauses that evaluate to 1 are contrasted against the input. For the CTM, we instead contrast against one of the patches, randomly selected among the patches that made the clause evaluate to 1. Accordingly, the standard Type I and Type II feedback of the classic TM can be employed directly, without further modification. The CTM obtains a peak test accuracy of 99.4% on MNIST, 96.31% on Kuzushiji-MNIST, 91.5% on Fashion-MNIST, and 100.0% on the 2D Noisy XOR Problem, which is competitive with results reported for simple 4-layer CNNs, BinaryConnect, Logistic Circuits and an FPGA-accelerated Binary CNN.