Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks

• URL: http://arxiv.org/abs/2409.09323v2
• Date: Fri, 20 Sep 2024 04:49:18 GMT
• Title: Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks
• Authors: Ali Mehrabian, Parsa Mojarad Adi, Moein Heidari, Ilker Hacihaliloglu,
• Abstract summary: Implicit neural representations (INRs) use neural networks to provide continuous and resolution-independent representations of complex signals. 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. Experimental results show that our proposed FKAN model outperforms three state-of-the-art baseline schemes.
• Score: 4.499833362998488
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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