用傅里叶激活函数提升神经隐式表示的频率建模能力
Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks
- 用傅里叶级数建模可学习激活函数，捕捉任务特异性频率成分
- 在图像与3D体素重建中，PSNR、SSIM和IoU均优于现有方法
- 适合需要高分辨率和复杂细节建模的视觉信号表示任务
隐式神经表示（INRs）利用神经网络实现复杂信号的连续、分辨率无关表示，参数量小。但现有模型常无法捕捉特定任务的重要频率成分。本文提出傅里叶柯尔莫哥洛夫-阿诺德网络（FKAN）用于INRs。FKAN在第一层使用以傅里叶级数建模的可学习激活函数，有效控制并学习任务特异性频率成分。此外，具有可学习傅里叶系数的激活函数提升了网络捕捉复杂模式与细节的能力，有利于高维高分辨率数据。实验表明，所提FKAN模型在三个先进基线方案上表现更优，在图像表示任务中提升了峰值信噪比（PSNR）和结构相似性指数（SSIM），在3D占用体积表示任务中提升了交并比（IoU）。代码已公开于github.com/Ali-Meh619/FKAN。
原文摘要 · Abstract (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. The code is available at github.com/Ali-Meh619/FKAN.
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