Lei Jiao

Bimal Bhattarai, Ole-Christoffer Granmo, Lei Jiao et al.

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.

Ole-Christoffer Granmo, Per-Arne Andersen, Lei Jiao et al.

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.

Mohamed-Bachir Belaid, Jivitesh Sharma, Lei Jiao et al.

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 $0.5<p_k<1$. This result serves as a stepping stone for future research on the convergence properties of Tsetlin automaton-based learning algorithms. Our findings not only contribute to the theoretical understanding of Tsetlin Machines but also have implications for their practical application, potentially leading to more robust and interpretable machine learning models.

Runar Helin, Ole-Christoffer Granmo, Mayur Kishor Shende et al.

Data modeling using Tsetlin machines (TMs) is all about building logical rules from the data features. The decisions of the model are based on a combination of these logical rules. Hence, the model is fully transparent and it is possible to get explanations of its predictions. In this paper, we present a probability score for TM predictions and develop new techniques for uncertainty quantification to increase the explainability further. The probability score is an inherent property of any TM variant and is derived through an analysis of the TM learning dynamics. Simulated data is used to show a clear connection between the learned TM probability scores and the underlying probabilities of the data. A visualization of the probability scores also reveals that the TM is less confident in its predictions outside the training data domain, which contrasts the typical extrapolation phenomenon found in Artificial Neural Networks. The paper concludes with an application of the uncertainty quantification techniques on an image classification task using the CIFAR-10 dataset, where they provide new insights and suggest possible improvements to current TM image classification models.

Vojtech Halenka, Ole-Christoffer Granmo, Lei Jiao et al.

Feature Selection (FS) is crucial for improving model interpretability, reducing complexity, and sometimes for enhancing accuracy. The recently introduced Tsetlin machine (TM) offers interpretable clause-based learning, but lacks established tools for estimating feature importance. In this paper, we adapt and evaluate a range of FS techniques for TMs, including classical filter and embedded methods as well as post-hoc explanation methods originally developed for neural networks (e.g., SHAP and LIME) and a novel family of embedded scorers derived from TM clause weights and Tsetlin automaton (TA) states. We benchmark all methods across 12 datasets, using evaluation protocols, like Remove and Retrain (ROAR) strategy and Remove and Debias (ROAD), to assess causal impact. Our results show that TM-internal scorers not only perform competitively but also exploit the interpretability of clauses to reveal interacting feature patterns. Simpler TM-specific scorers achieve similar accuracy retention at a fraction of the computational cost. This study establishes the first comprehensive baseline for FS in TM and paves the way for developing specialized TM-specific interpretability techniques.

Ahmed K. Kadhim, Lei Jiao, Rishad Shafik et al.

The increasing complexity of large-scale language models has amplified concerns regarding their interpretability and reusability. While traditional embedding models like Word2Vec and GloVe offer scalability, they lack transparency and often behave as black boxes. Conversely, interpretable models such as the Tsetlin Machine (TM) have shown promise in constructing explainable learning systems, though they previously faced limitations in scalability and reusability. In this paper, we introduce Omni Tsetlin Machine AutoEncoder (Omni TM-AE), a novel embedding model that fully exploits the information contained in the TM's state matrix, including literals previously excluded from clause formation. This method enables the construction of reusable, interpretable embeddings through a single training phase. Extensive experiments across semantic similarity, sentiment classification, and document clustering tasks show that Omni TM-AE performs competitively with and often surpasses mainstream embedding models. These results demonstrate that it is possible to balance performance, scalability, and interpretability in modern Natural Language Processing (NLP) systems without resorting to opaque architectures.

Lei Jiao, Xuan Zhang, Ole-Christoffer Granmo

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.

Bimal Bhattarai, Ole-Christoffer Granmo, Lei Jiao

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.

Rohan Kumar Yadav, Lei Jiao, Ole-Christoffer Granmo et al.

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.

Bimal Bhattarai, Ole-Christoffer Granmo, Lei Jiao

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.

K. Darshana Abeyrathna, Bimal Bhattarai, Morten Goodwin et al.

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.

Xuan Zhang, Lei Jiao, Ole-Christoffer Granmo et al.

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.

Ole-Christoffer Granmo, Sondre Glimsdal, Lei Jiao et al.

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

Erlend Olsvik, Christian M. D. Trinh, Kristian Muri Knausgård et al.

Our understanding and ability to effectively monitor and manage coastal ecosystems are severely limited by observation methods. Automatic recognition of species in natural environment is a promising tool which would revolutionize video and image analysis for a wide range of applications in marine ecology. However, classifying fish from images captured by underwater cameras is in general very challenging due to noise and illumination variations in water. Previous classification methods in the literature relies on filtering the images to separate the fish from the background or sharpening the images by removing background noise. This pre-filtering process may negatively impact the classification accuracy. In this work, we propose a Convolutional Neural Network (CNN) using the Squeeze-and-Excitation (SE) architecture for classifying images of fish without pre-filtering. Different from conventional schemes, this scheme is divided into two steps. The first step is to train the fish classifier via a public data set, i.e., Fish4Knowledge, without using image augmentation, named as pre-training. The second step is to train the classifier based on a new data set consisting of species that we are interested in for classification, named as post-training. The weights obtained from pre-training are applied to post-training as a priori. This is also known as transfer learning. Our solution achieves the state-of-the-art accuracy of 99.27% accuracy on the pre-training. The accuracy on the post-training is 83.68%. Experiments on the post-training with image augmentation yields an accuracy of 87.74%, indicating that the solution is viable with a larger data set.