Related papers: Randomized Numerical Linear Algebra : A Perspectiv…

Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial…

Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the…

Recent advancements in neural network quantisation have yielded remarkable outcomes, with three-bit networks reaching state-of-the-art full-precision accuracy in complex tasks. These achievements present valuable opportunities for…

Algorithm portfolio and selection approaches have achieved remarkable improvements over single solvers. However, the implementation of such systems is often highly customised and specific to the problem domain. This makes it difficult for…

Training deep neural networks (DNNs) in large-cluster computing environments is increasingly necessary, as networks grow in size and complexity. Local memory and processing limitations require robust data and model parallelism for crossing…

Reinforcement learning (RL) algorithms involve the deep nesting of highly irregular computation patterns, each of which typically exhibits opportunities for distributed computation. We argue for distributing RL components in a composable…

While there exist a plethora of deep learning tools and frameworks, the fast-growing complexity of the field brings new demands and challenges, such as more flexible network design, speedy computation on distributed setting, and…

We develop a randomized Newton method capable of solving learning problems with huge dimensional feature spaces, which is a common setting in applications such as medical imaging, genomics and seismology. Our method leverages randomized…

Dijkstra observed that verifying correctness of a program is difficult and conjectured that derivation of a program hand-in-hand with its proof of correctness was the answer. We illustrate this goal-oriented approach by applying it to the…

We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive…

Large Language Models (LLMs) demonstrate human-level capabilities in dialogue, reasoning, and knowledge retention. However, even the most advanced LLMs face challenges such as hallucinations and real-time updating of their knowledge.…

Embeddings play a pivotal role across various disciplines, offering compact representations of complex data structures. Randomized methods like Johnson-Lindenstrauss (JL) provide state-of-the-art and essentially unimprovable theoretical…

Deep Learning (DL) has the potential to optimize machine learning in both the scientific and clinical communities. However, greater expertise is required to develop DL algorithms, and the variability of implementations hinders their…

Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…

Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…

Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…

Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…

This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential…

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…

A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…