使用傅立葉科爾莫哥洛夫-阿諾德網絡的隱式神經表示

Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks

September 14, 2024

作者: Ali Mehrabian, Parsa Mojarad Adi, Moein Heidari, Ilker Hacihaliloglu

cs.AI

摘要

隱式神經表示法（INRs）使用神經網絡提供連續且與解析度無關的複雜信號表示，並僅使用少量參數。然而，現有的INR模型常常無法捕捉與每個任務特定的重要頻率成分。為解決此問題，在本文中，我們提出了一種傅立葉科爾莫哥洛夫阿諾德網絡（FKAN）用於INRs。所提出的FKAN利用可學習的激活函數，模擬為傅立葉級數在第一層，以有效控制並學習任務特定的頻率成分。此外，具有可學習傅立葉係數的激活函數提高了網絡捕捉複雜模式和細節的能力，這對於高解析度和高維數據是有益的。實驗結果表明，我們提出的FKAN模型優於三種最先進的基線方案，並分別改善了圖像表示任務的峰值信噪比（PSNR）和結構相似性指數測量（SSIM），以及3D佔用體積表示任務的交集超聯合（IoU）。

English

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.