Tsetlin machine

A Tsetlin Machine is an Artificial Intelligence algorithm based on propositional logic.

A simple block diagram of the Tsetlin Machine

Background

A Tsetlin machine is a form of learning automaton based upon algorithms from reinforcement learning to learn expressions from propositional logic. Ole-Christoffer Granmo gave the method its name after Michael Lvovitch Tsetlin and his Tsetlin automata. The method uses computationally simpler and more efficient primitives compared to more ordinary artificial neural networks.^[1]

As of April 2018 it has shown promising results on a number of test sets.^[2][3]

Types

• Original Tsetlin Machine^[1]
• Convolutional Tsetlin Machine^[4]
• Regression Tsetlin Machine^[5]
• Relational Tsetlin Machine^[6]
• Weighted Tsetlin Machine^[7][8]
• Arbitrarily Deterministic Tsetlin Machine^[9]
• Parallel Asynchronous Tsetlin Machine^[10]
• Coalesced Multi-Output Tsetlin Machine^[11]
• Tsetlin Machine for Contextual Bandit Problems^[12]
• Tsetlin Machine Autoencoder^[13]

Applications

• Keyword spotting^[14]
• Aspect-based sentiment analysis^[15]
• Word-sense disambiguation^[16]
• Novelty detection^[17]
• Intrusion detection^[18]
• Semantic relation analysis^[19]
• Image analysis^[4]
• Text categorization^[20]
• Fake news detection^[21]
• Game playing^[22]
• Batteryless sensing^[23]
• Recommendation systems^[24]
• Word embedding^[13]
• ECG analysis^[25]

Original Tsetlin Machine

 

A detailed block diagram of the original Tsetlin Machine

List of Hyperparameters^[26]

Description	Symbol
Number of binary inputs	${\displaystyle N_{\text{Inputs}}}$
Number of classes	${\displaystyle N_{\text{Classes}}}$
Number of clauses per class	${\displaystyle N_{\text{Clauses}}}$
Number of automaton states	${\displaystyle 2n}$
Automaton decision boundary	n
Automaton initialization state	${\displaystyle \varnothing _{\text{Init}}}$
Feedback threshold	T
Learning Sensitivity	s

Tsetlin Automaton

 

The Tsetlin Automaton is the fundamental 'learning unit' of the Tsetlin machine. It tackles the multi-armed bandit problem, learning the optimal action in an environment from penalties and rewards. Computationally, it can be seen as an FSM that changes its states based on the inputs. The FSM will generate its outputs based on the current states.

• A quintuple describes a two-action Tsetlin Automaton:

$${\displaystyle \{{\underline {\Phi }},{\underline {\alpha }},{\underline {\beta }},F(\cdot ,\cdot ),G(\cdot )\}.}$$

 

• A Tsetlin Automaton has ${\displaystyle 2n}$  states, here 6:

$${\displaystyle {\underline {\Phi }}=\{\phi _{1},\phi _{2},\phi _{3},\phi _{4},\phi _{5},\phi _{6}\}}$$

 

• The FSM can be triggered by two input events

$${\displaystyle {\underline {\beta }}=\{\beta _{\mathrm {Penalty} },\beta _{\mathrm {Reward} }\}}$$

 

• The rules of state migration of the FSM are stated as

$${\displaystyle F(\phi _{u},\beta _{v})={\begin{cases}\phi _{u+1},&{\text{if}}~1\leq u\leq 3~{\text{and}}~v={\text{Penalty}}\\\phi _{u-1},&{\text{if}}~4\leq u\leq 6~{\text{and}}~v={\text{Penalty}}\\\phi _{u-1},&{\text{if}}~1<u\leq 3~{\text{and}}~v={\text{Reward}}\\\phi _{u+1},&{\text{if}}~4\leq u<6~{\text{and}}~v={\text{Reward}}\\\phi _{u},&{\text{otherwise}}.\end{cases}}}$$

 

• It includes two output actions

$${\displaystyle {\underline {\alpha }}=\{\alpha _{1},\alpha _{2}\}}$$

 

• Which can be generated by the algorithm

$${\displaystyle G(\phi _{u})={\begin{cases}\alpha _{1},&{\text{if}}~1\leq u\leq 3\\\alpha _{2},&{\text{if}}~4\leq u\leq 6.\end{cases}}}$$

 

Boolean Input

A basic Tsetlin Machine takes a vector ${\displaystyle X=[x_{1},\ldots ,x_{o}]}$  of o Boolean features as input, to be classified into one of two classes, ${\displaystyle y=0}$  or ${\displaystyle y=1}$ . Together with their negated counterparts, ${\displaystyle {\bar {x}}_{k}={\lnot }{x}_{k}=1-x_{k}}$ , the features form a literal set ${\displaystyle L=\{x_{1},\ldots ,x_{o},{\bar {x}}_{1},\ldots ,{\bar {x}}_{o}\}}$ .

Clause Computing Module

A Tsetlin Machine pattern is formulated as a conjunctive clause ${\displaystyle C_{j}}$ , formed by ANDing a subset ${\displaystyle L_{j}{\subseteq }L}$  of the literal set:

     ${\displaystyle C_{j}(X)=\bigwedge _{{l}{\in }L_{j}}l=\prod _{{l}{\in }L_{j}}l}$ .

For example, the clause ${\displaystyle C_{j}(X)=x_{1}\land {\lnot }x_{2}=x_{1}{\bar {x}}_{2}}$  consists of the literals ${\displaystyle L_{j}=\{x_{1},{\bar {x}}_{2}\}}$  and outputs 1 iff ${\displaystyle x_{1}=1}$  and ${\displaystyle x_{2}=0}$ .

Summation and Thresholding Module

The number of clauses employed is a user-configurable parameter n. 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 ${\displaystyle u(v)=1~{\text{if}}~v\geq 0~{\text{else}}~0}$ :

$${\displaystyle {\hat {y}}=u\left(\sum _{j=1}^{n/2}C_{j}^{+}(X)-\sum _{j=1}^{n/2}C_{j}^{-}(X)\right).}$$

 

In other words, classification is based on a majority vote, with the positive clauses voting for ${\displaystyle y=1}$  and the negative for ${\displaystyle y=0}$ . The classifier

     ${\displaystyle {\hat {y}}=u\left(x_{1}{\bar {x}}_{2}+{\bar {x}}_{1}x_{2}-x_{1}x_{2}-{\bar {x}}_{1}{\bar {x}}_{2}\right)}$ ,

for instance, captures the XOR-relation.

Feedback Module

Type I Feedback

Type I Feedback

Action	Clause	1		0
	Literal	1	0	1	0
Include Literal	P(Reward)	${\displaystyle {\frac {s-1}{s}}}$	—	0	0
	P(Inaction)	${\displaystyle {\frac {1}{s}}}$	—	${\displaystyle {\frac {s-1}{s}}}$	${\displaystyle {\frac {s-1}{s}}}$
	P(Penalty)	0	—	${\displaystyle {\frac {1}{s}}}$	${\displaystyle {\frac {1}{s}}}$
Exclude Literal	P(Reward)	0	${\displaystyle {\frac {1}{s}}}$	${\displaystyle {\frac {1}{s}}}$	${\displaystyle {\frac {1}{s}}}$
	P(Inaction)	${\displaystyle {\frac {1}{s}}}$	${\displaystyle {\frac {s-1}{s}}}$	${\displaystyle {\frac {s-1}{s}}}$	${\displaystyle {\frac {s-1}{s}}}$
	P(Penalty)	${\displaystyle {\frac {s-1}{s}}}$	0	0	0

Type II Feedback

Type II Feedback

Action	Clause	1		0
	Literal	1	0	1	0
Include Literal	P(Reward)	0	—	0	0
	P(Inaction)	1.0	—	1.0	1.0
	P(Penalty)	0	—	0	0
Exclude Literal	P(Reward)	0	0	0	0
	P(Inaction)	1.0	0	1.0	1.0
	P(Penalty)	0	1.0	0	0

Resource Allocation

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 X, the probability of reinforcing a clause gradually drops to zero as the clause output sum

$${\displaystyle v=\sum _{j=1}^{n/2}C_{j}^{+}(X)-\sum _{j=1}^{n/2}C_{j}^{-}(X)}$$

 

approaches a user-set target T for ${\displaystyle y=1}$  (${\displaystyle -T}$  for ${\displaystyle y=0}$ ).

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 v equals or exceeds the target T (the Tsetlin Machine has successfully recognized the input X), no clauses are reinforced. Accordingly, they are free to learn new patterns, naturally balancing the pattern representation resources.

Implementations

Software

• Tsetlin Machine in C,^[27][28] Python,^[29][30] multithreaded Python,^[31] CUDA^[32]
• Convolutional Tsetlin Machine ^[33][4]
• Weighted Tsetlin Machine in C++^[34]

Hardware

• One of the first FPGA-based hardware implementation^[35][36] of the Tsetlin Machine on the Iris dataset was developed by the µSystems (microSystems) Research Group at Newcastle University.
• They also presented the first ASIC^[37][38] implementation of the Tsetlin Machine focusing on energy frugality, claiming it could deliver 10 trillion operation per Joule.^[39] The ASIC design had demoed on DATA2020.^[40]

Additional Read

Books

• An Introduction to Tsetlin Machines ^[41]

Conferences

• International Symposium on the Tsetlin Machine (ISTM) ^[42][43]

Videos

• Tsetlin Machine—A new paradigm for pervasive AI^[40]
• Keyword Spotting Using Tsetlin Machines ^[44]
• IOLTS Presentation: Explainability and Dependability Analysis of Learning Automata based AI hardware ^[45]
• FPGA and uC co-design: Tsetlin Machine on Iris demo ^[35][36]
• The-Ruler-of-Tsetlin-Automaton ^[46]
• Interpretable clustering and dimension reduction with Tsetlin automata machine learning.^[47]
• Predicting and explaining economic growth using real-time interpretable learning ^[48]
• Early detection of breast cancer from a simple blood test^[49]
• Recent advances in Tsetlin Machines ^[50]

Papers

• On the Convergence of Tsetlin Machines for the XOR Operator ^[51]
• Learning Automata based Energy-efficient AI Hardware Design for IoT Applications ^[26]
• On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators ^[52]
• The Tsetlin Machine - A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition with Propositional Logic ^[1]

Publications/News/Articles

• A low-power AI alternative to neural networks ^[39]

References

1. Granmo, Ole-Christoffer (2018-04-04). "The Tsetlin Machine - A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition with Propositional Logic". arXiv:1804.01508 [cs.AI].
2. Christiansen, Atle. "The Tsetlin Machine outperforms neural networks - Center for Artificial Intelligence Research". cair.uia.no. Retrieved 2018-05-03.
3. Øyvann, Stig (23 March 2018). "AI-gjennombrudd i Agder | Computerworld". Computerworld (in Norwegian). Retrieved 2018-05-04.
4. Granmo, Ole-Christoffer; Glimsdal, Sondre; Jiao, Lei; Goodwin, Morten; Omlin, Christian W.; Berge, Geir Thore (2019-12-27). "The Convolutional Tsetlin Machine". arXiv:1905.09688 [cs.LG].
5. Abeyrathna, K. Darshana; Granmo, Ole-Christoffer; Zhang, Xuan; Jiao, Lei; Goodwin, Morten (2020). "The regression Tsetlin machine: a novel approach to interpretable nonlinear regression". Philosophical Transactions of the Royal Society A. 378 (2164). Bibcode:2020RSPTA.37890165D. doi:10.1098/rsta.2019.0165. hdl:11250/2651754. PMID 31865880. S2CID 209439954."
6. Saha, Rupsa; Granmo, Ole-Christoffer; Zadorozhny, Vladimir; Goodwin, Morten (2022). "A relational Tsetlin machine with applications to natural language understanding". Journal of Intelligent Information Systems. Springer. 59: 121–148. doi:10.1007/s10844-021-00682-5. S2CID 231986401.
7. Phoulady, Adrian; Granmo, Ole-Christoffer; Gorji, Saeed Rahimi; Phoulady, Hady Ahmady (2019-11-28). "The Weighted Tsetlin Machine: Compressed Representations with Weighted Clauses". arXiv:1911.12607 [cs.LG].
8. Abeyrathna, K. Darshana; Granmo, Ole-Christoffer; Goodwin, Morten (2021). "Extending the Tsetlin Machine With Integer-Weighted Clauses for Increased Interpretability". IEEE Access. 9: 8233–8248. doi:10.1109/ACCESS.2021.3049569. S2CID 218581474."
9. Abeyrathna, K. Darshana; Granmo, Ole-Christoffer; Shafik, Rishad; Yakovlev, Alex; Wheeldon, Adrian; Lei, Jie; Goodwin, Morten (2021). "A multi-step finite-state automaton for arbitrarily deterministic Tsetlin Machine learning". Expert Systems. Wiley: exsy.12836. doi:10.1111/exsy.12836. S2CID 242770808.
10. Abeyrathna, K. Darshana; Bhattarai, Bimal; Goodwin, Morten; Gorji, Saeed; Granmo, Ole-Christoffer; Jiao, Lei; Saha, Rupsa; Yadav, Rohan K. (2021). Massively Parallel and Asynchronous Tsetlin Machine Architecture Supporting Almost Constant-Time Scaling (PDF). Thirty-eighth International Conference on Machine Learning (ICML 2021).
11. Glimsdal, Sondre; Granmo, Ole-Christoffer (2021-08-17). "Coalesced Multi-Output Tsetlin Machines with Clause Sharing". arXiv:2108.07594 [cs.AI].
12. Seraj, Raihan; Sharma, Jivitesh; Granmo, Ole-Christoffer (2022). Tsetlin Machine for Solving Contextual Bandit Problems. Thirty-sixth Conference on Neural Information Processing Systems (NeurIPS 2022).
13. Bhattarai, Bimal; Granmo, Ole-Christoffer; Jiao, Lei; Yadav, Rohan; Sharma, Jivitesh (2023-01-03). "Tsetlin Machine Embedding: Representing Words Using Logical Expressions". arXiv:2301.00709 [cs.CL].
14. Lei, Jie; Shafik, Rishad; Wheeldon, Adrian; Yakovlev, Alex; Granmo, Ole-Christoffer; Kawsar, Fahim; Akhil, Mathur (2021-04-09). "Low-Power Audio Keyword Spotting using Tsetlin Machines". Journal of Low Power Electronics and Applications. 11 (2): 18. doi:10.3390/jlpea11020018.
15. Yadav, Rohan Kumar; Jiao, Lei; Granmo, Ole-Christoffer; Goodwin, Morten (2021). Human-Level Interpretable Learning for Aspect-Based Sentiment Analysis. The Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI-21). AAAI.
16. Yadav, Rohan Kumar; Jiao, Lei; Granmo, Ole-Christoffer; Goodwin, Morten (2021). Interpretability in Word Sense Disambiguation using Tsetlin Machine. 13th International Conference on Agents and Artificial Intelligence (ICAART 2021). INSTICC.
17. Bhattarai, Bimal; Granmo, Ole-Christoffer; Jiao, Lei (2022). "Word-level human interpretable scoring mechanism for novel text detection using Tsetlin Machines". Applied Intelligence. Springer. doi:10.1007/s10489-022-03281-1.
18. Abeyrathna, K. Darshana; Pussewalage, Harsha S. Gardiyawasam; Ranasinghea, Sasanka N.; Oleshchuk, Vladimir A.; Granmo, Ole-Christoffer (2020). Intrusion Detection with Interpretable Rules Generated Using the Tsetlin Machine. 2020 IEEE Symposium Series on Computational Intelligence (SSCI). IEEE.
19. Saha, Rupsa; Granmo, Ole-Christoffer; Goodwin, Morten (2021). "Using Tsetlin Machine to discover interpretable rules in natural language processing applications". Expert Systems. Wiley. doi:10.1111/exsy.12873. S2CID 244096520.
20. Berge, Geir Thore; Granmo, Ole-Christoffer; Tveit, Tor O.; Goodwin, Morten; Jiao, Lei; Matheussen, Bernt Viggo (2019). "Using the Tsetlin Machine to Learn Human-Interpretable Rules for High-Accuracy Text Categorization with Medical Applications". IEEE Access. 7: 115134–115146. doi:10.1109/ACCESS.2019.2935416. S2CID 52195410."
21. Bhattarai, Bimal; Granmo, Ole-Christoffer; Jiao, Lei (2022). Explainable Tsetlin Machine framework for fake news detection with credibility score assessment (PDF). 13th Conference on Language Resources and Evaluation (LREC 2022).
22. Giri, Charul; Granmo, Ole-Christoffer; Hoof, Herke van; Blakely, Christian D. (2022-03-10). Logic-based AI for Interpretable Board Game Winner Prediction with Tsetlin Machine. The 2022 International Joint Conference on Neural Networks (IJCNN 2022). arXiv:2203.04378.
23. Bakar, Abu; Rahman, Tousif; Shafik, Rishad; Kawsar, Fahim; Montanari, Alessandro (2023-01-24). Adaptive Intelligence for Batteryless Sensors Using Software-Accelerated Tsetlin Machines. ACM SenSys 2022. pp. 236–249.
24. Borgersen, Karl Audun; Goodwin, Morten; Sharma, Jivitesh (2022-12-20). "A Comparison Between Tsetlin Machines and Deep Neural Networks in the Context of Recommendation Systems". arXiv:2212.10136 [cs.AI].
25. Zhang, Jinbao; Zhang, Xuan; Jiao, Lei (2023-01-25). "Interpretable Tsetlin Machine-based Premature Ventricular Contraction Identification". arXiv:2301.10181 [eess.SP)].
26. Wheeldon, A.; Shafik, R.; Rahman, T.; Lei, J.; Yakovlev, A.; Granmo, O. C. (2020). "Learning Automata based Energy-efficient AI Hardware Design for IoT Applications". Philosophical Transactions of the Royal Society A. 378 (2182). Bibcode:2020RSPTA.37890593W. doi:10.1098/rsta.2019.0593. PMC 7536019. PMID 32921236.
27. cair/TsetlinMachineC, Centre for Artificial Intelligence Research (CAIR), 2019-04-18, retrieved 2020-07-27
28. cair/FastTsetlinMachineC, Centre for Artificial Intelligence Research (CAIR), 2019-02-15, retrieved 2021-02-15
29. cair/pyTsetlinMachine, Centre for Artificial Intelligence Research (CAIR), 2020-07-07, retrieved 2020-07-27
30. cair/TsetlinMachine, Centre for Artificial Intelligence Research (CAIR), 2020-07-27, retrieved 2020-07-27
31. cair/pyTsetlinMachineParallel, Centre for Artificial Intelligence Research (CAIR), 2020-07-07, retrieved 2020-07-27
32. cair/PyTsetlinMachineCUDA, Centre for Artificial Intelligence Research (CAIR), 2020-07-27, retrieved 2020-07-27
33. "cair/convolutional-tsetlin-machine-tutorial". GitHub. Retrieved 2020-07-27.
34. Phoulady, Adrian (2020-04-13), adrianphoulady/weighted-tsetlin-machine-cpp, retrieved 2020-07-27
35. JieGH (2020-03-22), JieGH/Hardware_TM_Demo, retrieved 2020-07-22
36. JieGH. "Tsetlin Machine on Iris Data Set Demo, Handheld #MignonAI". Youtube.
37. "Logic-based AI Everywhere: Tsetlin Machines in Hardware". Twitter. Retrieved 2020-07-27.
38. "mignon". www.mignon.ai. Retrieved 2020-07-27.
39. Bush, Steve (2020-07-27). "A low-power AI alternative to neural networks". Electronics Weekly. Retrieved 2020-07-27.
40. "Tsetlin Machine -- A new paradigm for pervasive AI". YouTube.
41. Granmo, Ole-Christoffer (2021). An Introduction to Tsetlin Machines.
42. "International Symposium on the Tsetlin Machine (ISTM)".
43. "Proceedings of the 2022 International Symposium on the Tsetlin Machine (ISTM)".
44. "Keyword Spotting Using Tsetlin Machines". YouTube.
45. "IOLTS Presentation: Explainability and Dependability Analysis of Learning Automata based AI hardware". YouTube.
46. "The-Ruler-of-Tsetlin-Automaton". YouTube.
47. "Interpretable Clustering & Dimension Reduction with Tsetlin Automata machine learning". YouTube.
48. "Predicting and explaining economic growth using real-time interpretable learning". YouTube.
49. "Early detection of breast cancer from a simple blood test". YouTube.
50. "Recent advances in Tsetlin Machines". YouTube.
51. Jiao, Lei; Zhang, Xuan; Granmo, Ole-Christoffer; Abeyrathna, K. Darshana (2022). "On the Convergence of Tsetlin Machines for the XOR Operator". IEEE Transactions on Pattern Analysis and Machine Intelligence. PP: 1. arXiv:2101.02547. doi:10.1109/TPAMI.2022.3203150. PMID 36070276. S2CID 230799244.
52. Zhang, Xuan; Jiao, Lei; Granmo, Ole-Christoffer; Goodwin, Morten (2021). "On the Convergence of Tsetlin Machines for the IDENTITY- and NOT Operators". IEEE Transactions on Pattern Analysis and Machine Intelligence. PP (10): 6345–6359. arXiv:2007.14268. doi:10.1109/TPAMI.2021.3085591. PMID 34077353. S2CID 220831619.