论文标题
智能矩阵指示
Intelligent Matrix Exponentiation
论文作者
论文摘要
我们提出了一种新颖的机器学习体系结构，该体系结构使用单个输入依赖性矩阵的指数作为其唯一的非线性。这种体系结构的数学简单性允许对其行为进行详细的分析，从而通过Lipschitz界限提供了稳健性。尽管具有简单性，但单个矩阵指数层已经提供了通用近似属性，并且可以学习输入的基本功能，例如周期函数或多元多项式。该体系结构的表现优于基准问题（包括CIFAR-10）的其他通用体系结构，使用较少的参数。
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.
