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

2025-04-11

AAAI Conference on Artificial Intelligence

AI Summary

Existing Coordinate-MLPs for audio implicit representation lack systematic investigation and suffer from sensitivity to hyperparameters, reliance on complex positional encodings, and fragile initialization schemes. This work establishes the first comprehensive benchmark for audio signals using Coordinate-MLPs, evaluating combinations of three positional encoding strategies and sixteen activation functions. Furthermore, it introduces Fourier-ASR, a novel framework grounded in Fourier series and the Kolmogorov–Arnold representation theorem, which incorporates a Fourier-KAN network and a frequency-adaptive learning strategy (FaLS) to achieve robust audio representation without any additional positional encoding. Experiments demonstrate that the proposed method significantly outperforms conventional Coordinate-MLPs on both speech and music datasets, effectively modeling high-frequency components and mitigating low-frequency overfitting—all without requiring meticulous hyperparameter tuning.

Technology Category

• Machine Learning: Representation Learning
• Natural Language Processing: Learning & Optimization for NLP
• Computer Vision: Representation Learning for Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

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.

Problem

• implicit neural representation
• audio signal representation
• Coordinate-MLP
• robustness
• hyperparameter tuning

Innovation

• Fourier-KAN
• Implicit Neural Representation
• Audio Signal Modeling
• Frequency-adaptive Learning Strategy
• Coordinate-MLP