Learning Minimalistic Tsetlin Machine Clauses with Markov Boundary-Guided Pruning

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.

TMComposites: Plug-and-Play Collaboration Between Specialized Tsetlin Machines

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.

An FPGA Architecture for Online Learning using the Tsetlin Machine

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-frugal and Interpretable AI Hardware Design using Learning Automata

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.

Verifying Properties of Tsetlin Machines

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.

Interpretable Tsetlin Machine-based Premature Ventricular Contraction Identification

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.

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.

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.

On the Equivalence of the Weighted Tsetlin Machine and the Perceptron

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.

Interpretable Option Discovery using Deep Q-Learning and Variational Autoencoders

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.