Interpretability of ReLU for Inversion

Interpretability continues to be a focus of much research in deep neural network. In this work, we focus on the mathematical interpretability of fully-connected neural networks, especially those that use a rectified linear unit (ReLU) activation function. Our analysis elucidates the difficulty of approximating the reciprocal function. Notwithstanding, using the ReLU activation function halves the error compared with a linear model. In addition, one might have expected the errors to increase only towards the singular point x = 0, but both the linear and ReLU errors are fairly oscillatory and increase near both edge points.