Robustifying Fourier Features Embeddings for Implicit Neural Representations

2025-02-08

AI Summary

Implicit Neural Representations (INRs) suffer from spectral bias and noise amplification introduced by Fourier feature embeddings. This work provides the first theoretical analysis demonstrating that the coupling of multi-layer perceptrons (MLPs) with Fourier encoding exacerbates their inherent limitations. To address this, we propose a decoupled robust embedding mechanism: instead of additive Fourier encoding, we redesign the feature mapping pathway to explicitly suppress noise propagation. Our approach preserves high-frequency modeling capability while eliminating sensitivity to input perturbations. Evaluated on NeRF rendering and signed distance function (SDF) reconstruction, it achieves an average PSNR improvement of 2.3 dB, significantly enhances high-frequency detail fidelity, improves downstream task robustness, and reduces noise sensitivity by 42%.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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

Problem

• Address spectral bias in INRs
• Reduce noise in Fourier features
• Enhance MLPs with Fourier embeddings

Innovation

• MLPs combined with Fourier features
• Overcomes spectral bias in INRs
• Reduces noise in Fourier embeddings