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Theoretical computer science has found fertile ground in many areas of mathematics. The approach has been to consider classical problems through the prism of computational complexity, where the number of basic computational steps taken to…

Neural Architecture Search (NAS) has emerged as a powerful framework for automatically discovering neural architectures that balance accuracy and efficiency. However, as AI transitions from static benchmarks to real-world deployment, the…

Neural architecture search (NAS) has been extensively studied in the past few years. A popular approach is to represent each neural architecture in the search space as a directed acyclic graph (DAG), and then search over all DAGs by…

This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…

We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…

Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…

In recent years, ideas from statistics and scientific computing have begun to interact in increasingly sophisticated and fruitful ways with ideas from computer science and the theory of algorithms to aid in the development of improved…

Despite the significant advances achieved in Artificial Neural Networks (ANNs), their design process remains notoriously tedious, depending primarily on intuition, experience and trial-and-error. This human-dependent process is often…

The vision of Organic Computing addresses challenges that arise in the design of future information systems that are comprised of numerous, heterogeneous, resource-constrained and error-prone components or devices. Here, the notion organic…

Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging…

All but a few digital computers used for scientific computations have supported floating-point and digital arithmetic of rather limited numerical precision. The underlying assumptions were that the systems being studied were basically…

Neural architecture search (NAS) has become increasingly popular in the deep learning community recently, mainly because it can provide an opportunity to allow interested users without rich expertise to benefit from the success of deep…

Neural Architecture Search (NAS) is a promising and rapidly evolving research area. Training a large number of neural networks requires an exceptional amount of computational power, which makes NAS unreachable for those researchers who have…

Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…

This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…

This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.

Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…

Neural algorithmic reasoning (NAR) is a growing field that aims to embed algorithmic logic into neural networks by imitating classical algorithms. In this extended abstract, we detail our attempt to build a neural algorithmic reasoner that…

Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…

We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…