# Intelligent Matrix Exponentiation

arXiv: https://arxiv.org/abs/2008.03936 · HTML: https://mlsanity.com/paper/2008.03936/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2020.

## Built on by (most cited first, 2 of 2)

- [Analytical Solution of a Three-layer Network with a Matrix Exponential Activation Function](https://mlsanity.com/paper/2407.02540/) (2024)
- [Neural Fields Encode Adaptation Geometry](https://mlsanity.com/paper/2610.07253/) (2026)

## Abstract (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.