Universal Approximators

Universal approximators are models capable of representing any continuous function to a desired accuracy, a fundamental property driving the success of many machine learning methods. Current research focuses on establishing the universal approximation capabilities of various architectures, including neural networks (e.g., multilayer perceptrons, transformers, neural integral operators), and analyzing their efficiency and generalization properties, often within specific function spaces or under constraints like limited width or depth. This research is crucial for understanding the theoretical foundations of deep learning and for developing more efficient and reliable machine learning algorithms across diverse applications, from solving differential equations to analyzing complex datasets.