# Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2409.09323 · HTML: https://mlsanity.com/paper/2409.09323/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 23 references that are in the map.
- First posted on arXiv 14 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Understanding training and generalization in deep learning by Fourier analysis](https://mlsanity.com/paper/1808.04295/) (2018)
- [Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation](https://mlsanity.com/paper/2406.01034/) (2024)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddings](https://mlsanity.com/paper/2310.18846/) (2023)
- [DINER: Disorder-Invariant Implicit Neural Representation](https://mlsanity.com/paper/2211.07871/) (2022)
- [Analyzing the Internals of Neural Radiance Fields](https://mlsanity.com/paper/2306.00696/) (2023)

## Built on by (most cited first, 5 of 5)

- [Kolmogorov-Arnold Attention: Is Learnable Attention Better For Vision Transformers?](https://mlsanity.com/paper/2503.10632/) (2025)
- [Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2502.06153/) (2025)
- [Polynomial, trigonometric, and tropical activations](https://mlsanity.com/paper/2502.01247/) (2025)
- [Deformable Medical Image Registration with KAN-based Implicit Neural Representations](https://mlsanity.com/paper/2509.22874/) (2025)
- [Learnable Spectral Activations](https://mlsanity.com/paper/2610.07419/) (2026)

## Abstract (arXiv)

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.