傅里叶-科尔莫戈洛夫-阿诺德网络中的隐式神经表示

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

隐式神经表示（INRs）利用神经网络提供连续且与分辨率无关的复杂信号表示，且参数数量较少。然而，现有的INR模型常常无法捕捉与每个任务特定的重要频率成分。为解决这一问题，本文提出了一种傅里叶科尔莫戈洛夫阿诺德网络（FKAN）用于INRs。所提出的FKAN利用可学习的激活函数，其在第一层中建模为傅里叶级数，以有效控制和学习任务特定的频率成分。此外，具有可学习傅里叶系数的激活函数提高了网络捕捉复杂模式和细节的能力，这对于高分辨率和高维数据是有益的。实验结果表明，我们提出的FKAN模型优于三种最先进的基准方案，并分别改善了图像表示任务的峰值信噪比（PSNR）和结构相似性指数测量（SSIM），以及3D占用体积表示任务的交并比（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.