Intelligent Matrix Exponentiation

Authors: Thomas Fischbacher, Iulia M. Comșa, Krzysztof Potempa, Moritz Firsching, Luca Versari and Jyrki Alakuijala
Preprint: 2008.03936, 2020
Full text: arXiv

We present a novel machine learning architecture that uses the exponential of a single input-dependent matrix as its only nonlinearity. The mathematical simplicity of this architecture allows a detailed analysis of its behaviour, providing robustness guarantees via Lipschitz bounds. Despite its simplicity, a single matrix exponential layer already provides universal approximation properties and can learn fundamental functions of the input, such as periodic functions or multivariate polynomials. This architecture outperforms other general-purpose architectures on benchmark problems, including CIFAR-10, using substantially fewer parameters.