Robustifying Fourier Features Embeddings for Implicit Neural Representations

TL;DR

This paper addresses spectral bias in Implicit Neural Representations by proposing a robust method that combines MLPs with Fourier features, aiming to improve performance in representing complex scenes without noise degradation.

Contribution

The paper introduces a novel approach that enhances Fourier feature embeddings with MLPs, validated through a theoretical theorem, to mitigate spectral bias and noise issues in INRs.

Findings

Improved representation of varying frequency scenes.

Reduced noise in output compared to traditional Fourier features.

Enhanced performance in downstream tasks.

Abstract

Implicit Neural Representations (INRs) employ neural networks to represent continuous functions by mapping coordinates to the corresponding values of the target function, with applications e.g., inverse graphics. However, INRs face a challenge known as spectral bias when dealing with scenes containing varying frequencies. To overcome spectral bias, the most common approach is the Fourier features-based methods such as positional encoding. However, Fourier features-based methods will introduce noise to output, which degrades their performances when applied to downstream tasks. In response, this paper initially hypothesizes that combining multi-layer perceptrons (MLPs) with Fourier feature embeddings mutually enhances their strengths, yet simultaneously introduces limitations inherent in Fourier feature embeddings. By presenting a simple theorem, we validate our hypothesis, which serves as a foundation for the design of our solution. Leveraging these insights, we propose the use of multi-layer perceptrons (MLPs) without additive