title: Intelligent Matrix Exponentiation
abstract: We present a novel machine learning architecture that uses a single high-dimensional nonlinearity consisting of the exponential of a single input-dependent matrix. 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 and extrapolate fundamental functions of the input, such as periodic structure or geometric invariants. This architecture outperforms other general-purpose architectures on benchmark problems, including CIFAR-10, using fewer parameters.
authors: Thomas Fischbacher Iulia Maria Comsa Krzysztof Potempa Moritz Firsching Luca Versari Jyrki Alakuijala
hIndex: Thomas Fischbacher 18