Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks

TL;DR

Implicit neural representations often underfit high-frequency content due to spectral bias in standard MLP activations. This work introduces Fourier Kolmogorov-Arnold Network (FKAN), whose first-layer activation functions are learnable Fourier series that adaptively control task-specific frequency components. The FKAN architecture, with an initial Fourier-activated block followed by $L$ hidden layers, demonstrates improved image representation and 3D occupancy performance, achieving up to $8.91\%$ PSNR and $5.62\%$ SSIM gains on images and up to $0.96\%$ IoU on occupancy tasks, along with faster convergence. These results indicate enhanced fidelity for high-frequency reconstruction and broaden the applicability of INRs to high-dimensional signals such as images and occupancy volumes, with potential extensions to neural radiance fields.

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.

Figures (5)

• Figure 1: Illustration of the proposed FKAN model. The proposed architecture includes an FKAN block for capturing task-specific frequency components with learnable activation functions and includes $L$ hidden layers to learn non-linear patterns in the input signals.
• Figure 2: Comparison of the image representation between proposed FKAN and baselines.
• Figure 3: Illustration of the convergence rates of the models for the image representation task.
• Figure 4: Comparison of the occupancy volume representation between proposed FKAN and baselines.
• Figure 5: Illustration of the convergence rates of the models for the occupancy volume representation task.