Intelligent Matrix Exponentiation
Fischbacher, Thomas, Comsa, Iulia M., Potempa, Krzysztof, Firsching, Moritz, Versari, Luca, Alakuijala, Jyrki
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.
Aug-10-2020