Implicit Neural Representations (INRs) have gained popularity for encoding signals as compact, differentiable entities. While commonly using techniques like Fourier positional encodings or non-traditional activation functions (e.g., Gaussian, sinusoid, or wavelets) to capture high-frequency content, their properties lack exploration within a unified theoretical framework. Addressing this gap, we conduct a comprehensive analysis of these activations from a sampling theory perspective. Our investigation reveals that sinc activations, previously unused in conjunction with INRs, are theoretically optimal for signal encoding. Additionally, we establish a connection between dynamical systems and INRs, leveraging sampling theory to bridge these two paradigms.
@article{arxiv.2402.05427,
title = {A Sampling Theory Perspective on Activations for Implicit Neural Representations},
author = {Hemanth Saratchandran and Sameera Ramasinghe and Violetta Shevchenko and Alexander Long and Simon Lucey},
journal= {arXiv preprint arXiv:2402.05427},
year = {2024}
}