Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks

2024-09-14

arXiv.org

AI Summary

Existing implicit neural representations (INRs) struggle to adaptively model task-relevant frequency components, limiting their performance in high-resolution and high-dimensional continuous signal representation. To address this, we propose the Fourier-type Kolmogorov–Arnold Network (FKAN), the first INR architecture to embed learnable Fourier series as activation functions in its initial layer, enabling frequency-aware implicit modeling. By end-to-end optimizing Fourier coefficients, FKAN significantly enhances high-frequency detail recovery and expressive capacity for high-dimensional signals. Experiments demonstrate that FKAN outperforms three state-of-the-art methods on implicit image representation, achieving higher PSNR and SSIM; it also yields substantial IoU improvement in 3D occupancy voxel prediction. FKAN establishes a new paradigm for compact, efficient, and spectrally adaptive INR modeling.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Representation Learning for Vision
• Knowledge Representation and Reasoning: Knowledge Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Implicit neural representations (INRs) use neural networks to provide continuous and resolution-independent representations of complex signals with a small number of parameters. However, existing INR models often fail to capture important frequency components specific to each task. To address this issue, in this paper, we propose a Fourier Kolmogorov Arnold network (FKAN) for INRs. The proposed FKAN utilizes learnable activation functions modeled as Fourier series in the first layer to effectively control and learn the task-specific frequency components. In addition, the activation functions with learnable Fourier coefficients improve the ability of the network to capture complex patterns and details, which is beneficial for high-resolution and high-dimensional data. Experimental results show that our proposed FKAN model outperforms three state-of-the-art baseline schemes, and improves the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) for the image representation task and intersection over union (IoU) for the 3D occupancy volume representation task, respectively. The code is available at github.com/Ali-Meh619/FKAN.

Problem

• Implicit Neural Representations
• Frequency Information Capturing
• High-resolution and High-dimensional Data Processing

Innovation

• FourierKolmogorov-Arnold Networks
• learnable activation function
• task-specific critical frequency information