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The Tsetlin Machine (TM) has gained significant attention in Machine Learning (ML). By employing logical fundamentals, it facilitates pattern learning and representation, offering an alternative approach for developing comprehensible Artificial Intelligence (AI) with a specific focus on pattern classification in the form of conjunctive clauses. In the domain of Natural Language Processing (NLP), TM is utilised to construct word embedding and describe target words using clauses. To enhance the descriptive capacity of these clauses, we study the concept of Reasoning by Elimination (RbE) in clauses' formulation, which involves incorporating feature negations to provide a more comprehensive representation. In more detail, this paper employs the Tsetlin Machine Auto-Encoder (TM-AE) architecture to generate dense word vectors, aiming at capturing contextual information by extracting feature-dense vectors for a given vocabulary. Thereafter, the principle of RbE is explored to improve descriptivity and optimise the performance of the TM. Specifically, the specificity parameter s and the voting margin parameter T are leveraged to regulate feature distribution in the state space, resulting in a dense representation of information for each clause. In addition, we investigate the state spaces of TM-AE, especially for the forgotten/excluded features. Empirical investigations on artificially generated data, the IMDB dataset, and the 20 Newsgroups dataset showcase the robustness of the TM, with accuracy reaching 90.62\% for the IMDB., Comment: 8 pages, 8 figures

Tsetlin machines (TMs) have been successful in several application domains, operating with high efficiency on Boolean representations of the input data. However, Booleanizing complex data structures such as sequences, graphs, images, signal spectra, chemical compounds, and natural language is not trivial. In this paper, we propose a hypervector (HV) based method for expressing arbitrarily large sets of concepts associated with any input data. Using a hyperdimensional space to build vectors drastically expands the capacity and flexibility of the TM. We demonstrate how images, chemical compounds, and natural language text are encoded according to the proposed method, and how the resulting HV-powered TM can achieve significantly higher accuracy and faster learning on well-known benchmarks. Our results open up a new research direction for TMs, namely how to expand and exploit the benefits of operating in hyperspace, including new booleanization strategies, optimization of TM inference and learning, as well as new TM applications., Comment: 9 pages, 17 figures

The Tsetlin Machine (TM) has achieved competitive results on several image classification benchmarks, including MNIST, K-MNIST, F-MNIST, and CIFAR-2. However, color image classification is arguably still in its infancy for TMs, with CIFAR-10 being a focal point for tracking progress. Over the past few years, TM's CIFAR-10 accuracy has increased from around 61% in 2020 to 75.1% in 2023 with the introduction of Drop Clause. In this paper, we leverage the recently proposed TM Composites architecture and introduce a range of TM Specialists that use various image processing techniques. These include Canny edge detection, Histogram of Oriented Gradients, adaptive mean thresholding, adaptive Gaussian thresholding, Otsu's thresholding, color thermometers, and adaptive color thermometers. In addition, we conduct a rigorous hyperparameter search, where we uncover optimal hyperparameters for several of the TM Specialists. The result is a toolbox that provides new state-of-the-art results on CIFAR-10 for TMs with an accuracy of 82.8%. In conclusion, our toolbox of TM Specialists forms a foundation for new TM applications and a landmark for further research on TM Composites in image analysis., Comment: 8 pages, 3 figures

We propose a novel way of assessing and fusing noisy dynamic data using a Tsetlin Machine. Our approach consists in monitoring how explanations in form of logical clauses that a TM learns changes with possible noise in dynamic data. This way TM can recognize the noise by lowering weights of previously learned clauses, or reflect it in the form of new clauses. We also perform a comprehensive experimental study using notably different datasets that demonstrated high performance of the proposed approach.

Many machine learning models use the manipulation of dimensions as a driving force to enable models to identify and learn important features in data. In the case of sequential data this manipulation usually happens on the token dimension level. Despite the fact that many tasks require a change in sequence length itself, the step of sequence length reduction usually happens out of necessity and in a single step. As far as we are aware, no model uses the sequence length reduction step as an additional opportunity to tune the models performance. In fact, sequence length manipulation as a whole seems to be an overlooked direction. In this study we introduce a novel attention-based method that allows for the direct manipulation of sequence lengths. To explore the method's capabilities, we employ it in an autoencoder model. The autoencoder reduces the input sequence to a smaller sequence in latent space. It then aims to reproduce the original sequence from this reduced form. In this setting, we explore the methods reduction performance for different input and latent sequence lengths. We are able to show that the autoencoder retains all the significant information when reducing the original sequence to half its original size. When reducing down to as low as a quarter of its original size, the autoencoder is still able to reproduce the original sequence with an accuracy of around 90%., Comment: 8 pages, 5 images, 1 table

In this paper, we introduce a sparse Tsetlin Machine (TM) with absorbing Tsetlin Automata (TA) states. In brief, the TA of each clause literal has both an absorbing Exclude- and an absorbing Include state, making the learning scheme absorbing instead of ergodic. When a TA reaches an absorbing state, it will never leave that state again. If the absorbing state is an Exclude state, both the automaton and the literal can be removed from further consideration. The literal will as a result never participates in that clause. If the absorbing state is an Include state, on the other hand, the literal is stored as a permanent part of the clause while the TA is discarded. A novel sparse data structure supports these updates by means of three action lists: Absorbed Include, Include, and Exclude. By updating these lists, the TM gets smaller and smaller as the literals and their TA withdraw. In this manner, the computation accelerates during learning, leading to faster learning and less energy consumption., Comment: Accepted to ISTM2023. 7 pages, 8 figures

Tsetlin Machines (TMs) have garnered increasing interest for their ability to learn concepts via propositional formulas and their proven efficiency across various application domains. Despite this, the convergence proof for the TMs, particularly for the AND operator (\emph{conjunction} of literals), in the generalized case (inputs greater than two bits) remains an open problem. This paper aims to fill this gap by presenting a comprehensive convergence analysis of Tsetlin automaton-based Machine Learning algorithms. We introduce a novel framework, referred to as Probabilistic Concept Learning (PCL), which simplifies the TM structure while incorporating dedicated feedback mechanisms and dedicated inclusion/exclusion probabilities for literals. Given $n$ features, PCL aims to learn a set of conjunction clauses $C_i$ each associated with a distinct inclusion probability $p_i$. Most importantly, we establish a theoretical proof confirming that, for any clause $C_k$, PCL converges to a conjunction of literals when $0.5

A set of variables is the Markov blanket of a random variable if it contains all the information needed for predicting the variable. If the blanket cannot be reduced without losing useful information, it is called a Markov boundary. Identifying the Markov boundary of a random variable is advantageous because all variables outside the boundary are superfluous. Hence, the Markov boundary provides an optimal feature set. However, learning the Markov boundary from data is challenging for two reasons. If one or more variables are removed from the Markov boundary, variables outside the boundary may start providing information. Conversely, variables within the boundary may stop providing information. The true role of each candidate variable is only manifesting when the Markov boundary has been identified. In this paper, we propose a new Tsetlin Machine (TM) feedback scheme that supplements Type I and Type II feedback. The scheme introduces a novel Finite State Automaton - a Context-Specific Independence Automaton. The automaton learns which features are outside the Markov boundary of the target, allowing them to be pruned from the TM during learning. We investigate the new scheme empirically, showing how it is capable of exploiting context-specific independence to find Markov boundaries. Further, we provide a theoretical analysis of convergence. Our approach thus connects the field of Bayesian networks (BN) with TMs, potentially opening up for synergies when it comes to inference and learning, including TM-produced Bayesian knowledge bases and TM-based Bayesian inference., Comment: Accepted to ISTM2023, 8 pages, 6 figures

Tsetlin Machines (TMs) provide a fundamental shift from arithmetic-based to logic-based machine learning. Supporting convolution, they deal successfully with image classification datasets like MNIST, Fashion-MNIST, and CIFAR-2. However, the TM struggles with getting state-of-the-art performance on CIFAR-10 and CIFAR-100, representing more complex tasks. This paper introduces plug-and-play collaboration between specialized TMs, referred to as TM Composites. The collaboration relies on a TM's ability to specialize during learning and to assess its competence during inference. When teaming up, the most confident TMs make the decisions, relieving the uncertain ones. In this manner, a TM Composite becomes more competent than its members, benefiting from their specializations. The collaboration is plug-and-play in that members can be combined in any way, at any time, without fine-tuning. We implement three TM specializations in our empirical evaluation: Histogram of Gradients, Adaptive Gaussian Thresholding, and Color Thermometers. The resulting TM Composite increases accuracy on Fashion-MNIST by two percentage points, CIFAR-10 by twelve points, and CIFAR-100 by nine points, yielding new state-of-the-art results for TMs. Overall, we envision that TM Composites will enable an ultra-low energy and transparent alternative to state-of-the-art deep learning on more tasks and datasets., Comment: 8 pages, 6 figures

There is a need for machine learning models to evolve in unsupervised circumstances. New classifications may be introduced, unexpected faults may occur, or the initial dataset may be small compared to the data-points presented to the system during normal operation. Implementing such a system using neural networks involves significant mathematical complexity, which is a major issue in power-critical edge applications. This paper proposes a novel field-programmable gate-array infrastructure for online learning, implementing a low-complexity machine learning algorithm called the Tsetlin Machine. This infrastructure features a custom-designed architecture for run-time learning management, providing on-chip offline and online learning. Using this architecture, training can be carried out on-demand on the \ac{FPGA} with pre-classified data before inference takes place. Additionally, our architecture provisions online learning, where training can be interleaved with inference during operation. Tsetlin Machine (TM) training naturally descends to an optimum, with training also linked to a threshold hyper-parameter which is used to reduce the probability of issuing feedback as the TM becomes trained further. The proposed architecture is modular, allowing the data input source to be easily changed, whilst inbuilt cross-validation infrastructure allows for reliable and representative results during system testing. We present use cases for online learning using the proposed infrastructure and demonstrate the energy/performance/accuracy trade-offs.

Energy efficiency is a crucial requirement for enabling powerful artificial intelligence applications at the microedge. Hardware acceleration with frugal architectural allocation is an effective method for reducing energy. Many emerging applications also require the systems design to incorporate interpretable decision models to establish responsibility and transparency. The design needs to provision for additional resources to provide reachable states in real-world data scenarios, defining conflicting design tradeoffs between energy efficiency. is challenging. Recently a new machine learning algorithm, called the Tsetlin machine, has been proposed. The algorithm is fundamentally based on the principles of finite-state automata and benefits from natural logic underpinning rather than arithmetic. In this paper, we investigate methods of energy-frugal artificial intelligence hardware design by suitably tuning the hyperparameters, while maintaining high learning efficacy. To demonstrate interpretability, we use reachability and game-theoretic analysis in two simulation environments: a SystemC model to study the bounded state transitions in the presence of hardware faults and Nash equilibrium between states to analyze the learning convergence. Our analyses provides the first insights into conflicting design tradeoffs involved in energy-efficient and interpretable decision models for this new artificial intelligence hardware architecture. We show that frugal resource allocation coupled with systematic prodigality between randomized reinforcements can provide decisive energy reduction while also achieving robust and interpretable learning.

Tsetlin Machines (TsMs) are a promising and interpretable machine learning method which can be applied for various classification tasks. We present an exact encoding of TsMs into propositional logic and formally verify properties of TsMs using a SAT solver. In particular, we introduce in this work a notion of similarity of machine learning models and apply our notion to check for similarity of TsMs. We also consider notions of robustness and equivalence from the literature and adapt them for TsMs. Then, we show the correctness of our encoding and provide results for the properties: adversarial robustness, equivalence, and similarity of TsMs. In our experiments, we employ the MNIST and IMDB datasets for (respectively) image and sentiment classification. We discuss the results for verifying robustness obtained with TsMs with those in the literature obtained with Binarized Neural Networks on MNIST., Comment: 12 pages, accepted at ISTM (https://istm.no/)

Neural network-based models have found wide use in automatic long-term electrocardiogram (ECG) analysis. However, such black box models are inadequate for analysing physiological signals where credibility and interpretability are crucial. Indeed, how to make ECG analysis transparent is still an open problem. In this study, we develop a Tsetlin machine (TM) based architecture for premature ventricular contraction (PVC) identification by analysing long-term ECG signals. The architecture is transparent by describing patterns directly with logical AND rules. To validate the accuracy of our approach, we compare the TM performance with those of convolutional neural networks (CNNs). Our numerical results demonstrate that TM provides comparable performance with CNNs on the MIT-BIH database. To validate interpretability, we provide explanatory diagrams that show how TM makes the PVC identification from confirming and invalidating patterns. We argue that these are compatible with medical knowledge so that they can be readily understood and verified by a medical doctor. Accordingly, we believe this study paves the way for machine learning (ML) for ECG analysis in clinical practice.

Tsetlin machine (TM) is a logic-based machine learning approach with the crucial advantages of being transparent and hardware-friendly. While TMs match or surpass deep learning accuracy for an increasing number of applications, large clause pools tend to produce clauses with many literals (long clauses). As such, they become less interpretable. Further, longer clauses increase the switching activity of the clause logic in hardware, consuming more power. This paper introduces a novel variant of TM learning - Clause Size Constrained TMs (CSC-TMs) - where one can set a soft constraint on the clause size. As soon as a clause includes more literals than the constraint allows, it starts expelling literals. Accordingly, oversized clauses only appear transiently. To evaluate CSC-TM, we conduct classification, clustering, and regression experiments on tabular data, natural language text, images, and board games. Our results show that CSC-TM maintains accuracy with up to 80 times fewer literals. Indeed, the accuracy increases with shorter clauses for TREC, IMDb, and BBC Sports. After the accuracy peaks, it drops gracefully as the clause size approaches a single literal. We finally analyze CSC-TM power consumption and derive new convergence properties., Comment: 17 pages, 4 figures

Embedding words in vector space is a fundamental first step in state-of-the-art natural language processing (NLP). Typical NLP solutions employ pre-defined vector representations to improve generalization by co-locating similar words in vector space. For instance, Word2Vec is a self-supervised predictive model that captures the context of words using a neural network. Similarly, GLoVe is a popular unsupervised model incorporating corpus-wide word co-occurrence statistics. Such word embedding has significantly boosted important NLP tasks, including sentiment analysis, document classification, and machine translation. However, the embeddings are dense floating-point vectors, making them expensive to compute and difficult to interpret. In this paper, we instead propose to represent the semantics of words with a few defining words that are related using propositional logic. To produce such logical embeddings, we introduce a Tsetlin Machine-based autoencoder that learns logical clauses self-supervised. The clauses consist of contextual words like "black," "cup," and "hot" to define other words like "coffee," thus being human-understandable. We evaluate our embedding approach on several intrinsic and extrinsic benchmarks, outperforming GLoVe on six classification tasks. Furthermore, we investigate the interpretability of our embedding using the logical representations acquired during training. We also visualize word clusters in vector space, demonstrating how our logical embedding co-locate similar words., Comment: 9 pages, 7 figures

Tsetlin Machine (TM) has been gaining popularity as an inherently interpretable machine leaning method that is able to achieve promising performance with low computational complexity on a variety of applications. The interpretability and the low computational complexity of the TM are inherited from the Boolean expressions for representing various sub-patterns. Although possessing favorable properties, TM has not been the go-to method for AI applications, mainly due to its conceptual and theoretical differences compared with perceptrons and neural networks, which are more widely known and well understood. In this paper, we provide detailed insights for the operational concept of the TM, and try to bridge the gap in the theoretical understanding between the perceptron and the TM. More specifically, we study the operational concept of the TM following the analytical structure of perceptrons, showing the resemblance between the perceptrons and the TM. Through the analysis, we indicated that the TM's weight update can be considered as a special case of the gradient weight update. We also perform an empirical analysis of TM by showing the flexibility in determining the clause length, visualization of decision boundaries and obtaining interpretable boolean expressions from TM. In addition, we also discuss the advantages of TM in terms of its structure and its ability to solve more complex problems.

This paper addresses the dire need for a platform that efficiently provides a framework for running reinforcement learning (RL) experiments. We propose the CaiRL Environment Toolkit as an efficient, compatible, and more sustainable alternative for training learning agents and propose methods to develop more efficient environment simulations. There is an increasing focus on developing sustainable artificial intelligence. However, little effort has been made to improve the efficiency of running environment simulations. The most popular development toolkit for reinforcement learning, OpenAI Gym, is built using Python, a powerful but slow programming language. We propose a toolkit written in C++ with the same flexibility level but works orders of magnitude faster to make up for Python's inefficiency. This would drastically cut climate emissions. CaiRL also presents the first reinforcement learning toolkit with a built-in JVM and Flash support for running legacy flash games for reinforcement learning research. We demonstrate the effectiveness of CaiRL in the classic control benchmark, comparing the execution speed to OpenAI Gym. Furthermore, we illustrate that CaiRL can act as a drop-in replacement for OpenAI Gym to leverage significantly faster training speeds because of the reduced environment computation time., Comment: Published in 2022 IEEE Conference on Games (CoG)

Deep Reinforcement Learning (RL) is unquestionably a robust framework to train autonomous agents in a wide variety of disciplines. However, traditional deep and shallow model-free RL algorithms suffer from low sample efficiency and inadequate generalization for sparse state spaces. The options framework with temporal abstractions is perhaps the most promising method to solve these problems, but it still has noticeable shortcomings. It only guarantees local convergence, and it is challenging to automate initiation and termination conditions, which in practice are commonly hand-crafted. Our proposal, the Deep Variational Q-Network (DVQN), combines deep generative- and reinforcement learning. The algorithm finds good policies from a Gaussian distributed latent-space, which is especially useful for defining options. The DVQN algorithm uses MSE with KL-divergence as regularization, combined with traditional Q-Learning updates. The algorithm learns a latent-space that represents good policies with state clusters for options. We show that the DVQN algorithm is a promising approach for identifying initiation and termination conditions for option-based reinforcement learning. Experiments show that the DVQN algorithm, with automatic initiation and termination, has comparable performance to Rainbow and can maintain stability when trained for extended periods after convergence., Comment: 12 pages, 5 figures, Proceedings of the 3rd International Conference on Intelligent Technologies and Applications

Reinforcement Learning (RL) is a general framework concerned with an agent that seeks to maximize rewards in an environment. The learning typically happens through trial and error using explorative methods, such as epsilon-greedy. There are two approaches, model-based and model-free reinforcement learning, that show concrete results in several disciplines. Model-based RL learns a model of the environment for learning the policy while model-free approaches are fully explorative and exploitative without considering the underlying environment dynamics. Model-free RL works conceptually well in simulated environments, and empirical evidence suggests that trial and error lead to a near-optimal behavior with enough training. On the other hand, model-based RL aims to be sample efficient, and studies show that it requires far less training in the real environment for learning a good policy. A significant challenge with RL is that it relies on a well-defined reward function to work well for complex environments and such a reward function is challenging to define. Goal-Directed RL is an alternative method that learns an intrinsic reward function with emphasis on a few explored trajectories that reveals the path to the goal state. This paper introduces a novel reinforcement learning algorithm for predicting the distance between two states in a Markov Decision Process. The learned distance function works as an intrinsic reward that fuels the agent's learning. Using the distance-metric as a reward, we show that the algorithm performs comparably to model-free RL while having significantly better sample-efficiently in several test environments., Comment: 14 pages, 5 figures, In Proceedings of the International Conference on Innovative Techniques and Applications of Artificial Intelligence, SGAI2020

Machine ethics has received increasing attention over the past few years because of the need to ensure safe and reliable artificial intelligence (AI). The two dominantly used theories in machine ethics are deontological and utilitarian ethics. Virtue ethics, on the other hand, has often been mentioned as an alternative ethical theory. While this interesting approach has certain advantages over popular ethical theories, little effort has been put into engineering artificial virtuous agents due to challenges in their formalization, codifiability, and the resolution of ethical dilemmas to train virtuous agents. We propose to bridge this gap by using role-playing games riddled with moral dilemmas. There are several such games in existence, such as Papers, Please and Life is Strange, where the main character encounters situations where they must choose the right course of action by giving up something else dear to them. We draw inspiration from such games to show how a systemic role-playing game can be designed to develop virtues within an artificial agent. Using modern day AI techniques, such as affinity-based reinforcement learning and explainable AI, we motivate the implementation of virtuous agents that play such role-playing games, and the examination of their decisions through a virtue ethical lens. The development of such agents and environments is a first step towards practically formalizing and demonstrating the value of virtue ethics in the development of ethical agents., Comment: Premature submission of revised revision

Recent social networks' misinformation mitigation approaches tend to investigate how to reduce misinformation by considering a whole-network statistical scale. However, unbalanced misinformation exposures among individuals urge to study fair allocation of mitigation resources. Moreover, the network has random dynamics which change over time. Therefore, we introduce a stochastic and non-stationary knapsack problem, and we apply its resolution to mitigate misinformation in social network campaigns. We further propose a generic misinformation mitigation algorithm that is robust to different social networks' misinformation statistics, allowing a promising impact in real-world scenarios. A novel loss function ensures fair mitigation among users. We achieve fairness by intelligently allocating a mitigation incentivization budget to the knapsack, and optimizing the loss function. To this end, a team of Learning Automata (LA) drives the budget allocation. Each LA is associated with a user and learns to minimize its exposure to misinformation by performing a non-stationary and stochastic walk over its state space. Our results show how our LA-based method is robust and outperforms similar misinformation mitigation methods in how the mitigation is fairly influencing the network users., Comment: These 14-pages paper is a version with appendices so that I can cite appendices in the original version of the paper which was accepted and submitted to AAAI22

Hex is a turn-based two-player connection game with a high branching factor, making the game arbitrarily complex with increasing board sizes. As such, top-performing algorithms for playing Hex rely on accurate evaluation of board positions using neural networks. However, the limited interpretability of neural networks is problematic when the user wants to understand the reasoning behind the predictions made. In this paper, we propose to use propositional logic expressions to describe winning and losing board game positions, facilitating precise visual interpretation. We employ a Tsetlin Machine (TM) to learn these expressions from previously played games, describing where pieces must be located or not located for a board position to be strong. Extensive experiments on $6\times6$ boards compare our TM-based solution with popular machine learning algorithms like XGBoost, InterpretML, decision trees, and neural networks, considering various board configurations with $2$ to $22$ moves played. On average, the TM testing accuracy is $92.1\%$, outperforming all the other evaluated algorithms. We further demonstrate the global interpretation of the logical expressions and map them down to particular board game configurations to investigate local interpretability. We believe the resulting interpretability establishes building blocks for accurate assistive AI and human-AI collaboration, also for more complex prediction tasks.

This paper introduces an interpretable contextual bandit algorithm using Tsetlin Machines, which solves complex pattern recognition tasks using propositional logic. The proposed bandit learning algorithm relies on straightforward bit manipulation, thus simplifying computation and interpretation. We then present a mechanism for performing Thompson sampling with Tsetlin Machine, given its non-parametric nature. Our empirical analysis shows that Tsetlin Machine as a base contextual bandit learner outperforms other popular base learners on eight out of nine datasets. We further analyze the interpretability of our learner, investigating how arms are selected based on propositional expressions that model the context.

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., Comment: arXiv admin note: text overlap with arXiv:2101.02547

Using finite-state machines to learn patterns, Tsetlin machines (TMs) have obtained competitive accuracy and learning speed across several benchmarks, with frugal memory- and energy footprint. A TM represents patterns as conjunctive clauses in propositional logic (AND-rules), each clause voting for or against a particular output. While efficient for single-output problems, one needs a separate TM per output for multi-output problems. Employing multiple TMs hinders pattern reuse because each TM then operates in a silo. In this paper, we introduce clause sharing, merging multiple TMs into a single one. Each clause is related to each output by using a weight. A positive weight makes the clause vote for output $1$, while a negative weight makes the clause vote for output $0$. The clauses thus coalesce to produce multiple outputs. The resulting coalesced Tsetlin Machine (CoTM) simultaneously learns both the weights and the composition of each clause by employing interacting Stochastic Searching on the Line (SSL) and Tsetlin Automata (TA) teams. Our empirical results on MNIST, Fashion-MNIST, and Kuzushiji-MNIST show that CoTM obtains significantly higher accuracy than TM on $50$- to $1$K-clause configurations, indicating an ability to repurpose clauses. E.g., accuracy goes from $71.99$% to $89.66$% on Fashion-MNIST when employing $50$ clauses per class (22 Kb memory). While TM and CoTM accuracy is similar when using more than $1$K clauses per class, CoTM reaches peak accuracy $3\times$ faster on MNIST with $8$K clauses. We further investigate robustness towards imbalanced training data. Our evaluations on imbalanced versions of IMDb- and CIFAR10 data show that CoTM is robust towards high degrees of class imbalance. Being able to share clauses, we believe CoTM will enable new TM application domains that involve multiple outputs, such as learning language models and auto-encoding., Comment: 23 pages, 9 figures

In this article, we introduce a novel variant of the Tsetlin machine (TM) that randomly drops clauses, the key learning elements of a TM. In effect, TM with drop clause ignores a random selection of the clauses in each epoch, selected according to a predefined probability. In this way, additional stochasticity is introduced in the learning phase of TM. To explore the effects drop clause has on accuracy, training time, interpretability and robustness, we conduct extensive experiments on nine benchmark datasets in natural language processing~(NLP) (IMDb, R8, R52, MR and TREC) and image classification (MNIST, Fashion MNIST, CIFAR-10 and CIFAR-100). Our proposed model outperforms baseline machine learning algorithms by a wide margin and achieves competitive performance in comparison with recent deep learning model such as BERT and AlexNET-DFA. In brief, we observe up to +10% increase in accuracy and 2x to 4x faster learning compared with standard TM. We further employ the Convolutional TM to document interpretable results on the CIFAR datasets, visualizing how the heatmaps produced by the TM become more interpretable with drop clause. We also evaluate how drop clause affects learning robustness by introducing corruptions and alterations in the image/language test data. Our results show that drop clause makes TM more robust towards such changes., Comment: 8 pages + references and appendix

The proliferation of fake news, i.e., news intentionally spread for misinformation, poses a threat to individuals and society. Despite various fact-checking websites such as PolitiFact, robust detection techniques are required to deal with the increase in fake news. Several deep learning models show promising results for fake news classification, however, their black-box nature makes it difficult to explain their classification decisions and quality-assure the models. We here address this problem by proposing a novel interpretable fake news detection framework based on the recently introduced Tsetlin Machine (TM). In brief, we utilize the conjunctive clauses of the TM to capture lexical and semantic properties of both true and fake news text. Further, we use the clause ensembles to calculate the credibility of fake news. For evaluation, we conduct experiments on two publicly available datasets, PolitiFact and GossipCop, and demonstrate that the TM framework significantly outperforms previously published baselines by at least $5\%$ in terms of accuracy, with the added benefit of an interpretable logic-based representation. Further, our approach provides higher F1-score than BERT and XLNet, however, we obtain slightly lower accuracy. We finally present a case study on our model's explainability, demonstrating how it decomposes into meaningful words and their negations., Comment: 11 pages, 4 figures, 4 tables

Recent research in novelty detection focuses mainly on document-level classification, employing deep neural networks (DNN). However, the black-box nature of DNNs makes it difficult to extract an exact explanation of why a document is considered novel. In addition, dealing with novelty at the word-level is crucial to provide a more fine-grained analysis than what is available at the document level. In this work, we propose a Tsetlin machine (TM)-based architecture for scoring individual words according to their contribution to novelty. Our approach encodes a description of the novel documents using the linguistic patterns captured by TM clauses. We then adopt this description to measure how much a word contributes to making documents novel. Our experimental results demonstrate how our approach breaks down novelty into interpretable phrases, successfully measuring novelty., Comment: 18 pages, 11 figures, 8 tables

Tsetlin Machine (TM) is an interpretable pattern recognition algorithm based on propositional logic, which has demonstrated competitive performance in many Natural Language Processing (NLP) tasks, including sentiment analysis, text classification, and Word Sense Disambiguation. To obtain human-level interpretability, legacy TM employs Boolean input features such as bag-of-words (BOW). However, the BOW representation makes it difficult to use any pre-trained information, for instance, word2vec and GloVe word representations. This restriction has constrained the performance of TM compared to deep neural networks (DNNs) in NLP. To reduce the performance gap, in this paper, we propose a novel way of using pre-trained word representations for TM. The approach significantly enhances the performance and interpretability of TM. We achieve this by extracting semantically related words from pre-trained word representations as input features to the TM. Our experiments show that the accuracy of the proposed approach is significantly higher than the previous BOW-based TM, reaching the level of DNN-based models., Comment: BlackboxNLP 2021

TMs are a pattern recognition approach that uses finite state machines for learning and propositional logic to represent patterns. In addition to being natively interpretable, they have provided competitive accuracy for various tasks. In this paper, we increase the computing power of TMs by proposing a first-order logic-based framework with Herbrand semantics. The resulting TM is relational and can take advantage of logical structures appearing in natural language, to learn rules that represent how actions and consequences are related in the real world. The outcome is a logic program of Horn clauses, bringing in a structured view of unstructured data. In closed-domain question-answering, the first-order representation produces 10x more compact KBs, along with an increase in answering accuracy from 94.83% to 99.48%. The approach is further robust towards erroneous, missing, and superfluous information, distilling the aspects of a text that are important for real-world understanding., Comment: 14 pages, 3 figures, 7 tables, relational approach to TM in NLP

The emergence of Artificial Intelligence (AI) driven Keyword Spotting (KWS) technologies has revolutionized human to machine interaction. Yet, the challenge of end-to-end energy efficiency, memory footprint and system complexity of current Neural Network (NN) powered AI-KWS pipelines has remained ever present. This paper evaluates KWS utilizing a learning automata powered machine learning algorithm called the Tsetlin Machine (TM). Through significant reduction in parameter requirements and choosing logic over arithmetic based processing, the TM offers new opportunities for low-power KWS while maintaining high learning efficacy. In this paper we explore a TM based keyword spotting (KWS) pipeline to demonstrate low complexity with faster rate of convergence compared to NNs. Further, we investigate the scalability with increasing keywords and explore the potential for enabling low-power on-chip KWS., Comment: 20 pp

The Tsetlin Machine (TM) is a novel machine learning algorithm with several distinct properties, including transparent inference and learning using hardware-near building blocks. Although numerous papers explore the TM empirically, many of its properties have not yet been analyzed mathematically. In this article, we analyze the convergence of the TM when input is non-linearly related to output by the XOR-operator. Our analysis reveals that the TM, with just two conjunctive clauses, can converge almost surely to reproducing XOR, learning from training data over an infinite time horizon. Furthermore, the analysis shows how the hyper-parameter T guides clause construction so that the clauses capture the distinct sub-patterns in the data. Our analysis of convergence for XOR thus lays the foundation for analyzing other more complex logical expressions. 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, Comment: 31 pages, 3 figures

Most supervised text classification approaches assume a closed world, counting on all classes being present in the data at training time. This assumption can lead to unpredictable behaviour during operation, whenever novel, previously unseen, classes appear. Although deep learning-based methods have recently been used for novelty detection, they are challenging to interpret due to their black-box nature. This paper addresses \emph{interpretable} open-world text classification, where the trained classifier must deal with novel classes during operation. To this end, we extend the recently introduced Tsetlin machine (TM) with a novelty scoring mechanism. The mechanism uses the conjunctive clauses of the TM to measure to what degree a text matches the classes covered by the training data. We demonstrate that the clauses provide a succinct interpretable description of known topics, and that our scoring mechanism makes it possible to discern novel topics from the known ones. Empirically, our TM-based approach outperforms seven other novelty detection schemes on three out of five datasets, and performs second and third best on the remaining, with the added benefit of an interpretable propositional logic-based representation., Comment: 10 pages, 5 figures, 3 tables

Using logical clauses to represent patterns, Tsetlin Machines (TMs) have recently obtained competitive performance in terms of accuracy, memory footprint, energy, and learning speed on several benchmarks. Each TM clause votes for or against a particular class, with classification resolved using a majority vote. While the evaluation of clauses is fast, being based on binary operators, the voting makes it necessary to synchronize the clause evaluation, impeding parallelization. In this paper, we propose a novel scheme for desynchronizing the evaluation of clauses, eliminating the voting bottleneck. In brief, every clause runs in its own thread for massive native parallelism. For each training example, we keep track of the class votes obtained from the clauses in local voting tallies. The local voting tallies allow us to detach the processing of each clause from the rest of the clauses, supporting decentralized learning. This means that the TM most of the time will operate on outdated voting tallies. We evaluated the proposed parallelization across diverse learning tasks and it turns out that our decentralized TM learning algorithm copes well with working on outdated data, resulting in no significant loss in learning accuracy. Furthermore, we show that the proposed approach provides up to 50 times faster learning. Finally, learning time is almost constant for reasonable clause amounts (employing from 20 to 7,000 clauses on a Tesla V100 GPU). For sufficiently large clause numbers, computation time increases approximately proportionally. Our parallel and asynchronous architecture thus allows processing of massive datasets and operating with more clauses for higher accuracy., Comment: Accepted to ICML 2021

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., Comment: 23 pages, 10 figures

Tsetlin Machines (TMs) capture patterns using conjunctive clauses in propositional logic, thus facilitating interpretation. However, recent TM-based approaches mainly rely on inspecting the full range of clauses individually. Such inspection does not necessarily scale to complex prediction problems that require a large number of clauses. In this paper, we propose closed-form expressions for understanding why a TM model makes a specific prediction (local interpretability). Additionally, the expressions capture the most important features of the model overall (global interpretability). We further introduce expressions for measuring the importance of feature value ranges for continuous features. The expressions are formulated directly from the conjunctive clauses of the TM, making it possible to capture the role of features in real-time, also during the learning process as the model evolves. Additionally, from the closed-form expressions, we derive a novel data clustering algorithm for visualizing high-dimensional data in three dimensions. Finally, we compare our proposed approach against SHAP and state-of-the-art interpretable machine learning techniques. For both classification and regression, our evaluation show correspondence with SHAP as well as competitive prediction accuracy in comparison with XGBoost, Explainable Boosting Machines, and Neural Additive Models.

Due to the high energy consumption and scalability challenges of deep learning, there is a critical need to shift research focus towards dealing with energy consumption constraints. Tsetlin Machines (TMs) are a recent approach to machine learning that has demonstrated significantly reduced energy usage compared to neural networks alike, while performing competitively accuracy-wise on several benchmarks. However, TMs rely heavily on energy-costly random number generation to stochastically guide a team of Tsetlin Automata to a Nash Equilibrium of the TM game. In this paper, we propose a novel finite-state learning automaton that can replace the Tsetlin Automata in TM learning, for increased determinism. The new automaton uses multi-step deterministic state jumps to reinforce sub-patterns. Simultaneously, flipping a coin to skip every $d$'th state update ensures diversification by randomization. The $d$-parameter thus allows the degree of randomization to be finely controlled. E.g., $d=1$ makes every update random and $d=\infty$ makes the automaton completely deterministic. Our empirical results show that, overall, only substantial degrees of determinism reduces accuracy. Energy-wise, random number generation constitutes switching energy consumption of the TM, saving up to 11 mW power for larger datasets with high $d$ values. We can thus use the new $d$-parameter to trade off accuracy against energy consumption, to facilitate low-energy machine learning., Comment: 10 pages, 8 figures, 7 tables

Despite significant effort, building models that are both interpretable and accurate is an unresolved challenge for many pattern recognition problems. In general, rule-based and linear models lack accuracy, while deep learning interpretability is based on rough approximations of the underlying inference. Using a linear combination of conjunctive clauses in propositional logic, Tsetlin Machines (TMs) have shown competitive performance on diverse benchmarks. However, to do so, many clauses are needed, which impacts interpretability. Here, we address the accuracy-interpretability challenge in machine learning by equipping the TM clauses with integer weights. The resulting Integer Weighted TM (IWTM) deals with the problem of learning which clauses are inaccurate and thus must team up to obtain high accuracy as a team (low weight clauses), and which clauses are sufficiently accurate to operate more independently (high weight clauses). Since each TM clause is formed adaptively by a team of Tsetlin Automata, identifying effective weights becomes a challenging online learning problem. We address this problem by extending each team of Tsetlin Automata with a stochastic searching on the line (SSL) automaton. In our novel scheme, the SSL automaton learns the weight of its clause in interaction with the corresponding Tsetlin Automata team, which, in turn, adapts the composition of the clause by the adjusting weight. We evaluate IWTM empirically using five datasets, including a study of interpetability. On average, IWTM uses 6.5 times fewer literals than the vanilla TM and 120 times fewer literals than a TM with real-valued weights. Furthermore, in terms of average F1-Score, IWTM outperforms simple Multi-Layered Artificial Neural Networks, Decision Trees, Support Vector Machines, K-Nearest Neighbor, Random Forest, XGBoost, Explainable Boosting Machines, and standard and real-value weighted TMs., Comment: 20 pages, 10 figures

The Tsetlin Machine (TM) is a machine learning algorithm founded on the classical Tsetlin Automaton (TA) and game theory. It further leverages frequent pattern mining and resource allocation principles to extract common patterns in the data, rather than relying on minimizing output error, which is prone to overfitting. Unlike the intertwined nature of pattern representation in neural networks, a TM decomposes problems into self-contained patterns, represented as conjunctive clauses. The clause outputs, in turn, are combined into a classification decision through summation and thresholding, akin to a logistic regression function, however, with binary weights and a unit step output function. In this paper, we exploit this hierarchical structure by introducing a novel algorithm that avoids evaluating the clauses exhaustively. Instead we use a simple look-up table that indexes the clauses on the features that falsify them. In this manner, we can quickly evaluate a large number of clauses through falsification, simply by iterating through the features and using the look-up table to eliminate those clauses that are falsified. The look-up table is further structured so that it facilitates constant time updating, thus supporting use also during learning. We report up to 15 times faster classification and three times faster learning on MNIST and Fashion-MNIST image classification, and IMDb sentiment analysis., Comment: 14 pages, 8 figures

The Regression Tsetlin Machine (RTM) addresses the lack of interpretability impeding state-of-the-art nonlinear regression models. It does this by using conjunctive clauses in propositional logic to capture the underlying non-linear frequent patterns in the data. These, in turn, are combined into a continuous output through summation, akin to a linear regression function, however, with non-linear components and unity weights. Although the RTM has solved non-linear regression problems with competitive accuracy, the resolution of the output is proportional to the number of clauses employed. This means that computation cost increases with resolution. To reduce this problem, we here introduce integer weighted RTM clauses. Our integer weighted clause is a compact representation of multiple clauses that capture the same sub-pattern-N repeating clauses are turned into one, with an integer weight N. This reduces computation cost N times, and increases interpretability through a sparser representation. We further introduce a novel learning scheme that allows us to simultaneously learn both the clauses and their weights, taking advantage of so-called stochastic searching on the line. We evaluate the potential of the integer weighted RTM empirically using six artificial datasets. The results show that the integer weighted RTM is able to acquire on par or better accuracy using significantly less computational resources compared to regular RTMs. We further show that integer weights yield improved accuracy over real-valued ones., Comment: 12 pages, 4 figures, 2 tables

The Tsetlin Machine (TM) is an interpretable mechanism for pattern recognition that constructs conjunctive clauses from data. The clauses capture frequent patterns with high discriminating power, providing increasing expression power with each additional clause. However, the resulting accuracy gain comes at the cost of linear growth in computation time and memory usage. In this paper, we present the Weighted Tsetlin Machine (WTM), which reduces computation time and memory usage by weighting the clauses. Real-valued weighting allows one clause to replace multiple, and supports fine-tuning the impact of each clause. Our novel scheme simultaneously learns both the composition of the clauses and their weights. Furthermore, we increase training efficiency by replacing $k$ Bernoulli trials of success probability $p$ with a uniform sample of average size $p k$, the size drawn from a binomial distribution. In our empirical evaluation, the WTM achieved the same accuracy as the TM on MNIST, IMDb, and Connect-4, requiring only $1/4$, $1/3$, and $1/50$ of the clauses, respectively. With the same number of clauses, the WTM outperformed the TM, obtaining peak test accuracies of respectively $98.63\%$, $90.37\%$, and $87.91\%$. Finally, our novel sampling scheme reduced sample generation time by a factor of $7$., Comment: Accepted at the Ninth International Workshop on Statistical Relational AI