  Motivated by the growing theoretical understanding of neural networks that
employ the Rectified Linear Unit (ReLU) as their activation function, we
revisit the use of ReLU activation functions for learning implicit neural
representations (INRs). Inspired by second order B-spline wavelets, we
incorporate a set of simple constraints to the ReLU neurons in each layer of a
deep neural network (DNN) to remedy the spectral bias. This in turn enables its
use for various INR tasks. Empirically, we demonstrate that, contrary to
popular belief, one can learn state-of-the-art INRs based on a DNN composed of
only ReLU neurons. Next, by leveraging recent theoretical works which
characterize the kinds of functions ReLU neural networks learn, we provide a
way to quantify the regularity of the learned function. This offers a
principled approach to selecting the hyperparameters in INR architectures. We
substantiate our claims through experiments in signal representation, super
resolution, and computed tomography, demonstrating the versatility and
effectiveness of our method. The code for all experiments can be found at
https://github.com/joeshenouda/relu-inrs.
