Matrix Function

Matrix functions, encompassing operations on matrices beyond basic linear algebra, are central to numerous scientific and engineering applications. Current research focuses on efficiently approximating these functions, particularly for high-dimensional data, leveraging techniques like low-rank approximations and novel neural network architectures such as Matrix Function Neural Networks (MFNs). These advancements are improving the performance of algorithms in diverse fields, including graph neural networks, fairness-aware machine learning, and distributed computation, by enabling the efficient handling of large-scale matrix operations and the discovery of underlying symmetries. The development of robust and scalable methods for computing and approximating matrix functions is thus crucial for progress in many areas.