Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations

2026-04-03

AI Summary

This work addresses the limitation of conventional Fourier-encoded implicit neural representations (INRs), which employ globally fixed frequencies and struggle to effectively capture spatially varying local spectra, leading to slow convergence of high-frequency details. To overcome this, the authors propose an adaptive local frequency filtering approach that introduces a spatially varying parameter α(x) to dynamically modulate Fourier components, enabling smooth, position-dependent transitions among low-pass, band-pass, and high-pass responses. This method establishes the first spatially adaptive frequency modulation mechanism within Fourier-encoded INRs and leverages neural tangent kernel (NTK) theory to reveal its spectral reshaping effect on the effective kernel, facilitating interpretable visualization of frequency preferences. Experiments demonstrate that the proposed approach significantly improves reconstruction quality and accelerates optimization across 2D image fitting, 3D shape representation, and sparse data reconstruction tasks, outperforming fixed-frequency baselines.

Abstract

Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial domain, making them poorly suited to signals with spatially varying local spectra and often leading to slow convergence of high-frequency details. To address this issue, we propose an adaptive local frequency filtering method for Fourier-encoded INRs. The proposed method introduces a spatially varying parameter $α(\mathbf{x})$ to modulate encoded Fourier components, enabling a smooth transition among low-pass, band-pass, and high-pass behaviors at different spatial locations. We further analyze the effect of the proposed filter from the neural tangent kernel (NTK) perspective and provide an NTK-inspired interpretation of how it reshapes the effective kernel spectrum. Experiments on 2D image fitting, 3D shape representation, and sparse data reconstruction demonstrate that the proposed method consistently improves reconstruction quality and leads to faster optimization compared with fixed-frequency baselines. In addition, the learned $α(\mathbf{x})$ provides an intuitive visualization of spatially varying frequency preferences, which helps explain the behavior of the model on non-stationary signals. These results indicate that adaptive local frequency modulation is a practical enhancement for Fourier-encoded INRs.

Problem

• Fourier-encoded implicit neural representations
• spatially varying local spectra
• fixed frequency mapping
• high-frequency convergence
• non-stationary signals

Innovation

• adaptive frequency filtering
• Fourier-encoded INRs
• spatially varying spectra
• neural tangent kernel
• implicit neural representations