Intelligent Matrix Exponentiation
This work addresses the need for interpretable and efficient deep learning models, offering a foundational approach with broad applicability in machine learning.
The authors tackled the challenge of designing a simple yet powerful neural network architecture by using a single matrix exponential as the only nonlinearity, achieving universal approximation and outperforming other architectures on benchmarks like CIFAR-10 with fewer parameters.
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.