Integral representations of shallow neural network with Rectified Power Unit activation function
This work provides a theoretical foundation for understanding the representation capabilities of shallow networks with RePU activations, which is incremental as it builds on existing integral representation frameworks.
The authors derived an integral representation formula for shallow neural networks using the Rectified Power Unit activation function, characterizing the set of representable functions with bounded norm and possibly unbounded width in both univariate and multidimensional cases.
In this effort, we derive a formula for the integral representation of a shallow neural network with the Rectified Power Unit activation function. Mainly, our first result deals with the univariate case of representation capability of RePU shallow networks. The multidimensional result in this paper characterizes the set of functions that can be represented with bounded norm and possibly unbounded width.