Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks
This work addresses a specific bottleneck in INR models for tasks like image and 3D occupancy representation, offering incremental improvements in accuracy.
The paper tackles the problem of implicit neural representations (INRs) failing to capture task-specific frequency components by proposing a Fourier Kolmogorov Arnold network (FKAN) that uses learnable Fourier series activations to control and learn these components, resulting in improved performance metrics such as PSNR, SSIM, and IoU over state-of-the-art baselines.
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.