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In recent years, deep learning has become prevalent to solve applications from multiple domains. Convolutional Neural Networks (CNNs) particularly have demonstrated state of the art performance for the task of image classification. However,…

Recent advances in machine learning have led to a surge in adoption of neural networks for various tasks, but lack of interpretability remains an issue for many others in which an understanding of the features influencing the prediction is…

Explainable AI (XAI) methods focus on explaining what a neural network has learned - in other words, identifying the features that are the most influential to the prediction. In this paper, we call them "distinguishing features". However,…

Deep learning continues to play as a powerful state-of-art technique that has achieved extraordinary accuracy levels in various domains of regression and classification tasks, including images, video, signal, and natural language data. The…

Shannon's seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding…

This dissertation explores applications of discrete geometry in mathematical neuroscience. We begin with convex neural codes, which model the activity of hippocampal place cells and other neurons with convex receptive fields. In Chapter 4,…

Motif counting plays a crucial role in understanding the structural properties of networks. By computing motif frequencies, researchers can draw key insights into the structural properties of the underlying network. As networks become…

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that…

Deep convolutional neural networks (CNNs) have achieved breakthrough performance in many pattern recognition tasks such as image classification. However, the development of high-quality deep models typically relies on a substantial amount…

This paper proposes a new paradigm for learning a set of independent logical rules in disjunctive normal form as an interpretable model for classification. We consider the problem of learning an interpretable decision rule set as training a…

Combining neural networks with continuous logic and multicriteria decision making tools can reduce the black box nature of neural models. In this study, we show that nilpotent logical systems offer an appropriate mathematical framework for…

Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…

Interpretability provides a toolset for understanding how and why neural networks behave in certain ways. However, there is little unity in the field: most studies employ ad-hoc evaluations and do not share theoretical foundations, making…

In order for machine learning to be deployed and trusted in many applications, it is crucial to be able to reliably explain why the machine learning algorithm makes certain predictions. For example, if an algorithm classifies a given…

Interpretability has become a necessary feature for machine learning models deployed in critical scenarios, e.g. legal system, healthcare. In these situations, algorithmic decisions may have (potentially negative) long-lasting effects on…

Semantic communication, leveraging advanced deep learning techniques, emerges as a new paradigm that meets the requirements of next-generation wireless networks. However, current semantic communication systems, which employ neural coding…

Hyperdimensional Computing affords simple, yet powerful operations to create long Hyperdimensional Vectors (hypervectors) that can efficiently encode information, be used for learning, and are dynamic enough to be modified on the fly. In…

The thesis explores the role machine learning methods play in creating intuitive computational models of neural processing. Combined with interpretability techniques, machine learning could replace human modeler and shift the focus of human…

Neural IR architectures, particularly cross-encoders, are highly effective models whose internal mechanisms are mostly unknown. Most works trying to explain their behavior focused on high-level processes (e.g., what in the input influences…

Adopting Convolutional Neural Networks (CNNs) in the daily routine of primary diagnosis requires not only near-perfect precision, but also a sufficient degree of generalization to data acquisition shifts and transparency. Existing CNN…