H-SIREN: Improving implicit neural representations with hyperbolic periodic functions

Abstract: Implicit neural representations (INR) have been recently adopted in various applications ranging from computer vision tasks to physics simulations by solving partial differential equations. Among existing INR-based works, multi-layer perceptrons with sinusoidal activation functions find widespread applications and are also frequently treated as a baseline for the development of better activation functions for INR applications. Recent investigations claim that the use of sinusoidal activation functions could be sub-optimal due to their limited supported frequency set as well as their tendency to generate over-smoothed solutions. We provide a simple solution to mitigate such an issue by changing the activation function at the first layer from $\sin(x)$ to $\sin(\sinh(2x))$. We demonstrate H-SIREN in various computer vision and fluid flow problems, where it surpasses the performance of several state-of-the-art INRs.