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.

使用隐性神经表示 (INRs) 对信号进行紧凑、可微的编码已经越来越受青睐。本研究从采样理论的角度对常用的正弦位置编码、非传统激活函数等技术进行了全面分析，发现在信号编码中 sinc 激活函数从理论上来讲是最优的，同时我们还建立了动力系统和 INR 之间的联系，利用采样理论来连接两种范式。