The Tsetlin Machine

The code and datasets for the Tsetlin Machine. Implements the Tsetlin Machine from https://arxiv.org/abs/1804.01508, including the multiclass version. The Tsetlin Machine solves complex pattern recognition problems with easy-to-interpret propositional formulas, composed by a collective of Tsetlin Automata.

Basics

Classification

A basic Tsetlin Machine takes a vector of Boolean features as input, to be classified into one of two classes, or . Together with their negated counterparts, , the features form a literal set .

A Tsetlin Machine pattern is formulated as a conjunctive clause , formed by ANDing a subset of the literal set:

.

For example, the clause consists of the literals and outputs iff .

The number of clauses employed is a user set parameter . Half of the clauses are assigned positive polarity. The other half is assigned negative polarity. The clause outputs, in turn, are combined into a classification decision through summation and thresholding using the unit step function :

.

In other words, classification is based on a majority vote, with the positive clauses voting for and the negative for . The classifier

,

Learning

A clause is composed by a team of Tsetlin Automata, each Tsetlin Automaton deciding to Include or Exclude a specific literal in the clause (see figure above). Learning which literals to include is based on reinforcement: Type I feedback produces frequent patterns, while Type II feedback increases the discrimination power of the patterns.

A Tsetlin Machine learns on-line, processing one training example at a time.

Type I feedback is given stochastically to clauses with positive polarity when and to clauses with negative polarity when . An afflicted clause, in turn, reinforces each of its Tsetlin Automata based on: (i) the clause output ; (ii) the action of the targeted Tsetlin Automaton - Include or Exclude; and (iii) the value of the literal assigned to the automaton. Two rules govern Type I feedback:

• Include is rewarded and Exclude is penalized with probability if and . This reinforcement is strong (triggers with high probability) and makes the clause remember and refine the pattern it recognizes in .
• Include is penalized and Exclude is rewarded with probability if or . This reinforcement is weak (triggers with low probability) and coarsens infrequent patterns, making them frequent.

Above, is a hyperparameter that controls the frequency of the patterns produced.

Type II feedback is given stochastically to clauses with positive polarity when and to clauses with negative polarity when . It penalizes Exclude with probability 1 if and . This feedback is strong and produces candidate literals for discriminating between and .

Resource allocation dynamics ensure that clauses distribute themselves across the frequent patterns, rather than missing some and overconcentrating on others. That is, for any input , the probability of reinforcing a clause gradually drops to zero as the clause output sum

approaches a user-set target for ( for ). To exemplify, the below plot shows the probability of reinforcing a clause when and for different clause output sums :

If a clause is not reinforced, it does not give feedback to its Tsetlin Automata, and these are thus left unchanged. In the extreme, when the voting sum equals or exceeds the target (the Tsetlin Machine has successfully recognized the input ), no clauses are reinforced. Accordingly, they are free to learn new patterns, naturally balancing the pattern representation resources.

See https://arxiv.org/abs/1804.01508 for details.

Learning Behaviour

The below figure depicts average learning progress (over 50 runs) of the Tsetlin Machine on a binarized, but otherwise unenhanced version of the MNIST dataset (https://en.wikipedia.org/wiki/MNIST_database). See also https://github.com/cair/fast-tsetlin-machine-with-mnist-demo.

As seen in the figure, both test and training accuracy increase almost monotonically across the epochs. Even while accuracy on the training data approaches 99.9%, accuracy on the test data continues to increase as well, hitting 98.2% after 400 epochs. This is quite different from what occurs with backpropagation on a neural network, where accuracy on test data starts to drop at some point due to overfitting, without proper regularization mechanisms.

Noisy XOR Demo

./NoisyXORDemo.py

Accuracy on test data (no noise): 1.0
Accuracy on training data (40% noise): 0.603

Prediction: x1 = 1, x2 = 0, ... -> y =  1
Prediction: x1 = 0, x2 = 1, ... -> y =  1
Prediction: x1 = 0, x2 = 0, ... -> y =  0
Prediction: x1 = 1, x2 = 1, ... -> y =  0

Requirements

• Python 2.7.x https://www.python.org/downloads/
• Numpy http://www.numpy.org/
• Cython http://cython.org/

Other Implementations

• High-level Tsetlin Machine Python API with fast C-extensions. Implements the Tsetlin Machine, Convolutional Tsetlin Machine, Regression Tsetlin Machine, Weighted Tsetlin Machine, and Embedding Tsetlin Machine, with support for continuous features, multi-granular clauses, and clause indexing, https://github.com/cair/pyTsetlinMachine, https://pypi.org/project/pyTsetlinMachine/
• Multi-threaded implementation of the Tsetlin Machine, Convolutional Tsetlin Machine, Regression Tsetlin Machine, and Weighted Tsetlin Machine, with support for continuous features and multi-granular clauses, https://github.com/cair/pyTsetlinMachineParallel, https://pypi.org/project/pyTsetlinMachineParallel/
• Fast C++ implementation of the Weighted Tsetlin Machine with MNIST-, IMDb-, and Connect-4 demos, https://github.com/adrianphoulady/weighted-tsetlin-machine-cpp
• Fast bit-operation based implementation in C with MNIST demo, https://github.com/cair/fast-tsetlin-machine-with-mnist-demo
• CUDA implementation with IMDB text classification demo, https://github.com/cair/fast-tsetlin-machine-in-cuda-with-imdb-demo
• Hardware implementations, https://github.com/JieGH/Hardware_TM_Demo
• Kivy implementation, https://github.com/DarshanaAbeyrathna/Tsetlin-Machine-Based-AI-Enabled-Mobile-App-for-Forecasting-the-Number-of-Corona-Patients
• C implementation, https://github.com/cair/TsetlinMachineC
• Parallelized C++ implementation of Multi-class and Regression Tsetlin Machine with scikit-learn-compatible Python wrapper, https://github.com/WojciechMigda/Tsetlini, https://github.com/WojciechMigda/PyTsetlini
• Rust implementation, https://github.com/KhaledSharif/TsetlinMachine
• Rust implementation with fast bit-operations, including MNIST demo, https://github.com/jcriddle4/tsetlin_rust_mnist
• C++ implementation, https://github.com/222464/TsetlinMachine
• Node.js implementation, https://github.com/anon767/TsetlinMachine
• C# implementation, https://github.com/cokobware/TsetlinMachineCSharp

Other Architectures

• The Convolutional Tsetlin Machine, https://github.com/cair/convolutional-tsetlin-machine
• The Regression Tsetlin Machine, https://github.com/cair/regression-tsetlin-machine

Videos

• Explainability and Dependability Analysis of Learning Automata based AI Hardware. IOLTS presentation by Rishad Shafik, Microsystems Research Group, Newcastle University. https://youtu.be/IjzZY0fDYiA
• Tsetlin Machine - A new paradigm for pervasive AI. DATE SCONA Workshop presentation by Adrian Wheeldon, Microsystems Research Group, Newcastle University. https://youtu.be/TaspuovmSR8
• Tsetlin Machine on Iris Data Set Demo with Handheld MignonAI (http://www.mignon.ai). Presentation by Jie Lei, Microsystems Research Group, Newcastle University. https://youtu.be/BzaPGByX-hg
• Interpretable clustering and dimension reduction with Tsetlin automata machine learning. Presentation by Christian D. Blakely, PwC Switzerland. https://youtu.be/5-09LOGLcV8
• Predicting and explaining economic growth using real-time interpretable learning. Presentation by Christian D. Blakely, PwC Switzerland. https://youtu.be/J6K7V7V7ayo
• Early detection of breast cancer from a simple blood test. Presentation by Christian D. Blakely, PwC Switzerland. https://youtu.be/FrHN_aRLRug
• Recent advances in Tsetlin Machines. NORA.ai Webinar presentation by Ole-Christoffer Granmo, CAIR, University of Agder. https://youtu.be/GHelDh3bN00

Tutorials

Convolutional Tsetlin Machine tutorial, https://github.com/cair/convolutional-tsetlin-machine-tutorial

Acknowledgements

I thank my colleagues from the Centre for Artificial Intelligence Research (CAIR), Lei Jiao, Xuan Zhang, Geir Thore Berge, Darshana Abeyrathna, Saeed Rahimi Gorji, Sondre Glimsdal, Rupsa Saha, Bimal Bhattarai, Rohan K. Yadev, Bernt Viggo Matheussen, Morten Goodwin, Christian Omlin, Vladimir Zadorozhny (University of Pittsburgh), Jivitesh Sharma, and Ahmed Abouzeid, for their contributions to the development of the Tsetlin machine family of techniques. I would also like to thank our House of CAIR partners, Alex Yakovlev, Rishad Shafik, Adrian Wheeldon, Jie Lei, Tousif Rahman (Newcastle University), Jonny Edwards (Temporal Computing), Marco Wiering (University of Groningen), Christian D. Blakely (PwC Switzerland), Adrian Phoulady, Anders Refsdal Olsen, Halvor Smørvik, and Erik Mathisen for their many contributions.

Tsetlin Machine Papers

@article{zhang2020convergence,
  title="{On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators}",
  author={Xuan Zhang and Lei Jiao and Ole-Christoffer Granmo and Morten Goodwin},
  journal = {arXiv preprint arXiv:2007.14268}, year = {2020},
  url = {https://arxiv.org/abs/2007.14268}
}

@article{blakely2020closedform,
  title="{Closed-Form Expressions for Global and Local Interpretation of Tsetlin Machines with Applications to Explaining High-Dimensional Data}",
  author={Christian D. Blakely and Ole-Christoffer Granmo},
  journal = {arXiv preprint arXiv:2007.13885}, year = {2020},
  url = {https://arxiv.org/abs/2007.13885}
}

@article{abeyrathna2020deterministic,
  title="{A Novel Multi-Step Finite-State Automaton for Arbitrarily Deterministic Tsetlin Machine Learning}",
  author={K. Darshana Abeyrathna and Ole-Christoffer Granmo and Rishad Shafik and Alex Yakovlev and Adrian Wheeldon and Jie Lei and Morten Goodwin},
  journal = {arXiv preprint arXiv:2007.02114}, year = {2020}
}

@article{wheeldon2020learning, 
  author={Adrian {Wheeldon} and Rishad {Shafik} and Tousif {Rahman} and Jie {Lei} and Alex {Yakovlev} and Ole-Christoffer {Granmo}}, 
  journal={Philosophical Transactions of the Royal Society A},
  title="{Learning Automata based Energy-efficient AI Hardware Design for IoT}",
  year={2020}
}

@InProceedings{shafik2020explainability,
  title="{Explainability and Dependability Analysis of Learning Automata based AI Hardware}",
  author={Rishad {Shafik} and Adrian {Wheeldon} and Alex {Yakovlev}},
  booktitle={IEEE 26th International Symposium on On-Line Testing and Robust System Design (IOLTS)},
  year={2020},
  organization={IEEE}
}

@article{lavrova2020,
  author = {D. S. {Lavrova} and N. N. {Eliseev}},
  title = "{Network Attacks Detection based on Tsetlin Machine}",
  pages = {17-23},
  journal = {Information Security Problems. Computer Systems.}, year = {2020}
}

@article{abeyrathna2020integer,
  author = {Abeyrathna, Kuruge Darshana and Granmo, Ole-Christoffer and Goodwin, Morten},
  title = "{Extending the Tsetlin Machine With Integer-Weighted Clauses for Increased Interpretability}",
  journal = {arXiv preprint arXiv:2005.05131}, year = {2020}
}

@InProceedings{gorji2020indexing,
  title="{Increasing the Inference and Learning Speed of Tsetlin Machines with Clause Indexing}",
  author={Saeed {Gorji} and Ole Christoffer {Granmo} and Sondre {Glimsdal} and Jonathan {Edwards} and Morten {Goodwin}},
  booktitle={International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems},
  year={2020},
  organization={Springer}
}

@InProceedings{abeyrathna2020integerregression,
  title="{A Regression Tsetlin Machine with Integer Weighted Clauses for Compact Pattern Representation,}",
  author={Abeyrathna, Kuruge Darshana and Granmo, Ole-Christoffer and Goodwin, Morten},
  booktitle={International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems},
  year={2020},
  organization={Springer}
}

@InProceedings{phoulady2020weighted, 
  author={Adrian {Phoulady} and Ole-Christoffer {Granmo} and Saeed Rahimi {Gorji} and Hady Ahmady {Phoulady}}, 
  booktitle={Proceedings of the Ninth International Workshop on Statistical Relational AI (StarAI 2020)}, 
  title="{The Weighted Tsetlin Machine: Compressed Representations with Clause Weighting}",
  year={2020}
}

@InProceedings{wheeldon2020pervasive, 
  author={Adrian {Wheeldon} and Rishad {Shafik} and Alex {Yakovlev} and Jonathan {Edwards} and Ibrahim {Haddadi} and Ole-Christoffer {Granmo}}, 
  booktitle={SCONA Workshop at Design, Automation and Test in Europe (DATE 2020)}, 
  title="{Tsetlin Machine: A New Paradigm for Pervasive AI}",
  year={2020}
}

@article{abeyrathna2019nonlinear, 
  author={K. Darshana {Abeyrathna} and Ole-Christoffer {Granmo} and Xuan {Zhang} and Lei {Jiao} and Morten {Goodwin}}, 
  journal={Philosophical Transactions of the Royal Society A},
  title="{The Regression Tsetlin Machine - A Novel Approach to Interpretable Non-Linear Regression}",
  volume={378}, issue={2164},
  year={2019}
}

@InProceedings{gorji2019multigranular,
  author = {Saeed Rahimi {Gorji} and Ole-Christoffer {Granmo} and Adrian {Phoulady} and Morten {Goodwin}},
  title = "{A Tsetlin Machine with Multigranular Clauses}",
  booktitle="Lecture Notes in Computer Science: Proceedings of the Thirty-ninth International Conference on Innovative Techniques and Applications of Artificial Intelligence (SGAI-2019)", year="2019",
  volume = {11927},
  publisher="Springer International Publishing"
}

@article{berge2019text, 
  author={Geir Thore {Berge} and Ole-Christoffer {Granmo} and Tor Oddbjørn {Tveit} and Morten {Goodwin} and Lei {Jiao} and Bernt Viggo {Matheussen}}, 
  journal={IEEE Access}, 
  title="{Using the Tsetlin Machine to Learn Human-Interpretable Rules for High-Accuracy Text Categorization with Medical Applications}",
  volume={7},
  pages={115134-115146}, 
  year={2019}, 
  doi={10.1109/ACCESS.2019.2935416}, 
  ISSN={2169-3536}
}

@article{granmo2019convtsetlin,
  author = {{Granmo}, Ole-Christoffer and {Glimsdal}, Sondre and {Jiao}, Lei and {Goodwin}, Morten and {Omlin}, Christian W. and {Berge}, Geir Thore},
  title = "{The Convolutional Tsetlin Machine}",
  journal = {arXiv preprint arXiv:1905.09688}, year = {2019}
}

@InProceedings{abeyrathna2019regressiontsetlin,
  author = {{Abeyrathna}, Kuruge Darshana and {Granmo}, Ole-Christoffer and {Jiao}, Lei and {Goodwin}, Morten},
  title = "{The Regression Tsetlin Machine: A Tsetlin Machine for Continuous Output Problems}",
  editor="Moura Oliveira, Paulo and Novais, Paulo and Reis, Lu{\'i}s Paulo ",
  booktitle="Progress in Artificial Intelligence", year="2019",
  publisher="Springer International Publishing",
  pages="268--280"
}

@InProceedings{abeyrathna2019continuousinput,
  author = {{Abeyrathna}, Kuruge Darshana and {Granmo}, Ole-Christoffer and {Zhang}, Xuan and {Goodwin}, Morten},
  title = "{A Scheme for Continuous Input to the Tsetlin Machine with Applications to Forecasting Disease Outbreaks}",
  booktitle = "{Advances and Trends in Artificial Intelligence. From Theory to Practice}", year = "2019",
  editor = "Wotawa, Franz and Friedrich, Gerhard and Pill, Ingo and Koitz-Hristov, Roxane and Ali, Moonis",
  publisher = "Springer International Publishing",
  pages = "564--578"
}

@article{granmo2018tsetlin,
  author = {{Granmo}, Ole-Christoffer},
  title = "{The Tsetlin Machine - A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition with Propositional Logic}",
  journal = {arXiv preprint arXiv:1804.01508}, year = {2018}
}

Licence

Copyright (c) 2020 Ole-Christoffer Granmo

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.