# Kolmogorov-Arnold Fourier Networks

arXiv: https://arxiv.org/abs/2502.06018 · HTML: https://mlsanity.com/paper/2502.06018/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 60 references that are in the map.
- First posted on arXiv 9 Feb 2025.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [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)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Breaking the Curse of Dimensionality with Convex Neural Networks](https://mlsanity.com/paper/1412.8690/) (2014)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [FLOPs as a Direct Optimization Objective for Learning Sparse Neural Networks](https://mlsanity.com/paper/1811.03060/) (2018)
- [Training Neural Networks Using Reproducing Kernel Space Interpolation and Model Reduction](https://mlsanity.com/paper/2308.16754/) (2023)

## Built on by (most cited first, 18 of 18)

- [STORM: Search-Guided Generative World Models for Robotic Manipulation](https://mlsanity.com/paper/2512.18477/) (2025)
- [Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate](https://mlsanity.com/paper/2604.21174/) (2026)
- [Adaptive-VoCo: Complexity-Aware Visual Token Compression for Vision-Language Models](https://mlsanity.com/paper/2512.18496/) (2025)
- [Rational ANOVA Networks](https://mlsanity.com/paper/2602.04006/) (2026)
- [A Graph Meta-Network for Learning on Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.16316/) (2026)
- [Reflective Confidence: Correcting Reasoning Flaws via Online Self-Correction](https://mlsanity.com/paper/2512.18605/) (2025)
- [A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2601.18672/) (2026)
- [Partition-of-Unity Gaussian Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.23599/) (2026)
- [GTMA: Dynamic Representation Optimization for OOD Vision-Language Models](https://mlsanity.com/paper/2512.18504/) (2025)
- [PTTA: A Pure Text-to-Animation Framework for High-Quality Creation](https://mlsanity.com/paper/2512.18614/) (2025)
- [RevFFN: Memory-Efficient Full-Parameter Fine-Tuning of Mixture-of-Experts LLMs with Reversible Blocks](https://mlsanity.com/paper/2512.20920/) (2025)
- [A Three-Level Alignment Framework for Large-Scale 3D Retrieval and Controlled 4D Generation](https://mlsanity.com/paper/2512.22294/) (2025)
- [Learning Dynamic Scene Reconstruction with Sinusoidal Geometric Priors](https://mlsanity.com/paper/2512.22295/) (2025)
- [Self-Rewarded Multimodal Coherent Reasoning Across Diverse Visual Domains](https://mlsanity.com/paper/2512.22545/) (2025)
- [Forgetting as a Feature: Cognitive Alignment of Large Language Models](https://mlsanity.com/paper/2601.09726/) (2025)
- [Multi-Agent Cooperative Learning for Robust Vision-Language Alignment under OOD Concepts](https://mlsanity.com/paper/2601.09746/) (2026)
- [LogicGaze: Benchmarking Causal Consistency in Visual Narratives via Counterfactual Verification](https://mlsanity.com/paper/2602.00292/) (2026)
- [Adaptive RBF-KAN: A Comparative Evaluation of Dynamic Shape Parameters in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2605.21534/) (2026)

## Abstract (arXiv)

Although Kolmogorov-Arnold-based interpretable networks (KANs) possess strong theoretical expressiveness, they suffer from severe parameter explosion and limited ability to capture high-frequency features in high-dimensional tasks. To address these issues, we propose the Kolmogorov-Arnold Fourier Network (KAF), which fundamentally redefines the KAN paradigm through spectral reparameterization. Our key contributions include: (1) proposing a fundamental basis transformation from the local, grid-based B-spline representation to a global, adaptive spectral representation. This shift changes the network's inductive bias, reducing parameter complexity from O(G) to O(1) while preserving expressiveness; (2) introducing trainable Random Fourier Features (RFF) initialized via a spectral alignment strategy, which allows the model to break the smoothness limitation of fixed kernels and accurately capture high-frequency components; and (3) implementing an adaptive hybrid GELU-Fourier activation mechanism that progressively enhances frequency representation during training. Comprehensive experiments demonstrate the superiority of KAF across computer vision (CV), natural language processing (NLP), audio, and partial differential equation (PDE) solving tasks, achieving state-of-the-art performance with improved efficiency. The code is available at https://github.com/kolmogorovArnoldFourierNetwork/KAF.