English

Intelligent Matrix Exponentiation

Machine Learning 2020-08-11 v1 Neural and Evolutionary Computing Representation Theory Machine Learning

Abstract

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.

Keywords

Cite

@article{arxiv.2008.03936,
  title  = {Intelligent Matrix Exponentiation},
  author = {Thomas Fischbacher and Iulia M. Comsa and Krzysztof Potempa and Moritz Firsching and Luca Versari and Jyrki Alakuijala},
  journal= {arXiv preprint arXiv:2008.03936},
  year   = {2020}
}

Comments

20 pages, 10 figures

R2 v1 2026-06-23T17:44:31.043Z