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Ole-Christoffer Granmo

Ole-Christoffer Granmo contributes to research discovery and scholarly infrastructure.

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Published work

19 published item(s)

preprint2026arXiv

FastOmniTMAE: Parallel Clause Learning for Scalable and Hardware-Efficient Tsetlin Embeddings

Embedding models in natural language processing (NLP) increasingly rely on deep architectures such as BERT, while simpler models such as Word2Vec provide efficient representations but limited interpretability. The Tsetlin Machine (TM) offers an alternative logic-based learning paradigm. Omni TM Autoencoder (Omni TM-AE) applies this paradigm to static embedding by exploiting automaton state distributions within a single clause layer, but its training process remains slow. In this work, we propose FastOmniTMAE, a reformulation of Omni TM-AE that replaces sequential training dependencies with a two-stage parallel process: evaluation and update. Using a Single-Run Multi-Environment Benchmark covering classification, similarity, and clustering, FastOmniTMAE achieves up to 5$\times$ faster training in classification while maintaining comparable embedding quality under both Spearman and Kendall similarity measures. To address the limited efficiency of TM training on conventional GPUs, we further implement FastOmniTMAE as a reusable accelerator on SoC-FPGA platforms. The Multi-Hardware Benchmark shows that FastOmniTMAE achieves similarity scores of 0.669 on a resource-constrained FPGA and 0.696 on an UltraScale+ SoC, demonstrating efficient logic-based embedding training with a small hardware footprint.

preprint2026arXiv

On-Device Interpretable Tsetlin Machine-Based Intrusion Detection for Secure IoMT

The rapid evolution of digital health technologies is redefining healthcare services worldwide. The integration of wireless communication and Internet-enabled medical devices within Internet of Medical Things (IoMT) networks enables continuous, real-time patient monitoring. However, this increased connectivity raises cybersecurity and patient safety risks due to increasingly sophisticated cyberattacks. This paper proposes a novel on-device, interpretable Tsetlin Machine (TM)-based Intrusion Detection System (IDS) to identify various phases of cyberattacks in IoMT environments. The TM is a rule-driven and transparent machine learning (ML) approach that represents attack patterns using propositional logic. Extensive evaluations on the MedSec-25 dataset, encompassing various phases of realistic cyberattacks, show that the proposed model outperforms ML models and state-of-the-art methods, attaining a classification performance of 97.83\%. Moreover, the proposed model offers explicit explanations of its decisions to enhance transparency using feature-level contributions, class-wise vote scores, and clause activation heatmaps. Edge deployment (Raspberry Pi) further supports real-time on-device inference and intrusion detection. The combination of interpretability and high performance makes the proposed model well-suited for IoMT healthcare, where trust, reliability, safety, and timely decision-making are critical.

preprint2023arXiv

Building Concise Logical Patterns by Constraining Tsetlin Machine Clause Size

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.

preprint2023arXiv

Tsetlin Machine Embedding: Representing Words Using Logical Expressions

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.

preprint2022arXiv

Drop Clause: Enhancing Performance, Interpretability and Robustness of the Tsetlin Machine

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.

preprint2022arXiv

Logic-based AI for Interpretable Board Game Winner Prediction with Tsetlin Machine

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.

preprint2022arXiv

Socially Fair Mitigation of Misinformation on Social Networks via Constraint Stochastic Optimization

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.

preprint2022arXiv

Towards Artificial Virtuous Agents: Games, Dilemmas and Machine Learning

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.

preprint2022arXiv

Tsetlin Machine for Solving Contextual Bandit Problems

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.

preprint2021arXiv

A Relational Tsetlin Machine with Applications to Natural Language Understanding

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.

preprint2021arXiv

Low-Power Audio Keyword Spotting using Tsetlin Machines

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.

preprint2021arXiv

On the Convergence of Tsetlin Machines for the XOR Operator

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

preprint2021arXiv

The Tsetlin Machine -- A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition with Propositional Logic

Although simple individually, artificial neurons provide state-of-the-art performance when interconnected in deep networks. Arguably, the Tsetlin Automaton is an even simpler and more versatile learning mechanism, capable of solving the multi-armed bandit problem. Merely by means of a single integer as memory, it learns the optimal action in stochastic environments through increment and decrement operations. In this paper, we introduce the Tsetlin Machine, which solves complex pattern recognition problems with propositional formulas, composed by a collective of Tsetlin Automata. To eliminate the longstanding problem of vanishing signal-to-noise ratio, the Tsetlin Machine orchestrates the automata using a novel game. Further, both inputs, patterns, and outputs are expressed as bits, while recognition and learning rely on bit manipulation, simplifying computation. Our theoretical analysis establishes that the Nash equilibria of the game align with the propositional formulas that provide optimal pattern recognition accuracy. This translates to learning without local optima, only global ones. In five benchmarks, the Tsetlin Machine provides competitive accuracy compared with SVMs, Decision Trees, Random Forests, Naive Bayes Classifier, Logistic Regression, and Neural Networks. We further demonstrate how the propositional formulas facilitate interpretation. In conclusion, we believe the combination of high accuracy, interpretability, and computational simplicity makes the Tsetlin Machine a promising tool for a wide range of domains.

preprint2020arXiv

A Novel Multi-Step Finite-State Automaton for Arbitrarily Deterministic Tsetlin Machine Learning

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.

preprint2020arXiv

A Regression Tsetlin Machine with Integer Weighted Clauses for Compact Pattern Representation

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.

preprint2020arXiv

Closed-Form Expressions for Global and Local Interpretation of Tsetlin Machines with Applications to Explaining High-Dimensional Data

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.

preprint2020arXiv

Extending the Tsetlin Machine With Integer-Weighted Clauses for Increased Interpretability

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.

preprint2020arXiv

Increasing the Inference and Learning Speed of Tsetlin Machines with Clause Indexing

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.

preprint2020arXiv

The Weighted Tsetlin Machine: Compressed Representations with Weighted Clauses

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 $7$.