Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations

A team of researchers has developed a novel method called Adaptive Local Frequency Filtering to enhance Fourier-encoded Implicit Neural Representations (INRs). Traditional Fourier feature mappings use a fixed set of frequencies across an entire spatial domain, which struggles with signals that have locally varying frequency spectra, often resulting in slow convergence for high-frequency details. The new approach introduces a spatially varying parameter, α(x), that dynamically modulates the encoded Fourier components. This allows the model to smoothly transition between low-pass, band-pass, and high-pass filtering behaviors at different locations, adapting to the local characteristics of the signal.

From a theoretical perspective, the team analyzed the method's effect through the lens of the Neural Tangent Kernel (NTK), providing an interpretation of how the adaptive filter reshapes the effective kernel spectrum. Practically, experiments across 2D image fitting, 3D shape representation, and sparse data reconstruction tasks demonstrated consistent improvements. The method not only achieves higher reconstruction quality but also leads to faster optimization compared to standard fixed-frequency baselines. Furthermore, the learned α(x) map offers an intuitive visualization of the model's spatially varying frequency preferences, aiding in the interpretability of how the INR handles complex, non-stationary signals.