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Representing Sounds as Neural Amplitude Fields: A Benchmark of Coordinate-MLPs and A Fourier Kolmogorov-Arnold Framework

Linfei Li, Lin Zhang, Zhong Wang, Fengyi Zhang, Zelin Li, Ying Shen

TL;DR

The paper addresses the gap in evaluating implicit neural representations for audio by benchmarking Coordinate-MLPs with three positional encodings and sixteen activations, uncovering sensitivity to hyperparameters and encoding choices. To overcome these limitations, it introduces Fourier-ASR, a Fourier-KAN-based framework that leverages the Kolmogorov-Arnold representation to decompose signals into locally periodic Fourier components, augmented by a Frequency-Adaptive Learning Strategy for stable convergence. The authors provide the first open-source audio INR benchmark, demonstrate that carefully designed encodings boost Coordinate-MLP performance while Fourier-ASR delivers robust, parameter-tuning-free representations, and show improved interpretability and efficiency via Fourier-KAN. Overall, the work suggests that continuous implicit audio representations hold promise for high-fidelity compression, synthesis, and generation, with Fourier-ASR offering a principled, scalable alternative to traditional Coordinate-MLP approaches. The theoretical and empirical findings pave the way for more robust, interpretable audio representations with broad applications in audio processing tasks.

Abstract

Although Coordinate-MLP-based implicit neural representations have excelled in representing radiance fields, 3D shapes, and images, their application to audio signals remains underexplored. To fill this gap, we investigate existing implicit neural representations, from which we extract 3 types of positional encoding and 16 commonly used activation functions. Through combinatorial design, we establish the first benchmark for Coordinate-MLPs in audio signal representations. Our benchmark reveals that Coordinate-MLPs require complex hyperparameter tuning and frequency-dependent initialization, limiting their robustness. To address these issues, we propose Fourier-ASR, a novel framework based on the Fourier series theorem and the Kolmogorov-Arnold representation theorem. Fourier-ASR introduces Fourier Kolmogorov-Arnold Networks (Fourier-KAN), which leverage periodicity and strong nonlinearity to represent audio signals, eliminating the need for additional positional encoding. Furthermore, a Frequency-adaptive Learning Strategy (FaLS) is proposed to enhance the convergence of Fourier-KAN by capturing high-frequency components and preventing overfitting of low-frequency signals. Extensive experiments conducted on natural speech and music datasets reveal that: (1) well-designed positional encoding and activation functions in Coordinate-MLPs can effectively improve audio representation quality; and (2) Fourier-ASR can robustly represent complex audio signals without extensive hyperparameter tuning. Looking ahead, the continuity and infinite resolution of implicit audio representations make our research highly promising for tasks such as audio compression, synthesis, and generation. The source code will be released publicly to ensure reproducibility. The code is available at https://github.com/lif314/Fourier-ASR.

Representing Sounds as Neural Amplitude Fields: A Benchmark of Coordinate-MLPs and A Fourier Kolmogorov-Arnold Framework

TL;DR

The paper addresses the gap in evaluating implicit neural representations for audio by benchmarking Coordinate-MLPs with three positional encodings and sixteen activations, uncovering sensitivity to hyperparameters and encoding choices. To overcome these limitations, it introduces Fourier-ASR, a Fourier-KAN-based framework that leverages the Kolmogorov-Arnold representation to decompose signals into locally periodic Fourier components, augmented by a Frequency-Adaptive Learning Strategy for stable convergence. The authors provide the first open-source audio INR benchmark, demonstrate that carefully designed encodings boost Coordinate-MLP performance while Fourier-ASR delivers robust, parameter-tuning-free representations, and show improved interpretability and efficiency via Fourier-KAN. Overall, the work suggests that continuous implicit audio representations hold promise for high-fidelity compression, synthesis, and generation, with Fourier-ASR offering a principled, scalable alternative to traditional Coordinate-MLP approaches. The theoretical and empirical findings pave the way for more robust, interpretable audio representations with broad applications in audio processing tasks.

Abstract

Although Coordinate-MLP-based implicit neural representations have excelled in representing radiance fields, 3D shapes, and images, their application to audio signals remains underexplored. To fill this gap, we investigate existing implicit neural representations, from which we extract 3 types of positional encoding and 16 commonly used activation functions. Through combinatorial design, we establish the first benchmark for Coordinate-MLPs in audio signal representations. Our benchmark reveals that Coordinate-MLPs require complex hyperparameter tuning and frequency-dependent initialization, limiting their robustness. To address these issues, we propose Fourier-ASR, a novel framework based on the Fourier series theorem and the Kolmogorov-Arnold representation theorem. Fourier-ASR introduces Fourier Kolmogorov-Arnold Networks (Fourier-KAN), which leverage periodicity and strong nonlinearity to represent audio signals, eliminating the need for additional positional encoding. Furthermore, a Frequency-adaptive Learning Strategy (FaLS) is proposed to enhance the convergence of Fourier-KAN by capturing high-frequency components and preventing overfitting of low-frequency signals. Extensive experiments conducted on natural speech and music datasets reveal that: (1) well-designed positional encoding and activation functions in Coordinate-MLPs can effectively improve audio representation quality; and (2) Fourier-ASR can robustly represent complex audio signals without extensive hyperparameter tuning. Looking ahead, the continuity and infinite resolution of implicit audio representations make our research highly promising for tasks such as audio compression, synthesis, and generation. The source code will be released publicly to ensure reproducibility. The code is available at https://github.com/lif314/Fourier-ASR.
Paper Structure (37 sections, 51 equations, 3 figures, 12 tables)

This paper contains 37 sections, 51 equations, 3 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Coordinate-MLPs.
  4. Positional Encoding.
  5. Activation Functions.
  6. Method
  7. Problem Formulation
  8. Benchmark of Coordinate-MLP-based NeAF
  9. Fourier-ASR
  10. Fourier Kolmogorov-Arnold Networks (Fourier-KAN).
  11. Frequency-adaptive Learning Strategy (FaLS).
  12. Experiments
  13. Experimental Setup
  14. Datasets.
  15. Networks.
  16. ...and 22 more sections

Figures (3)

  • Figure 1: Properties of Coordinate-MLPs and Fourier-ASR. Validations are in the appendix (Appendix A).
  • Figure 2: (a) The problem definition of implicit audio representations; (b) The audio representation framework based on Coordinate-MLPs; (c) Fourier-ASR, a novel audio signal representation framework based on Fourier-KAN.
  • Figure 3: Qualitative experiments on "Bach".