mlsanityData to 14 Oct 2026

Kolmogorov-Arnold Fourier Networks

arXiv 2502.06018 ↗First posted 9 Feb 2025cs.LG cs.AIcited by 18

Not on the map. Why?

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.

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

25 of 60 references.

References · 25

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020Language Models are Few-Shot Learnerscited by 32,419
  3. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 30,186
  4. 2019EfficientNet: Rethinking Model Scaling for Convolutional Neural Networkscited by 6,442
  5. 2020Training data-efficient image transformers & distillation through attentioncited by 4,586
  6. 2017MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applicationscited by 3,845
  7. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,611
  8. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
  9. 2015Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Codingcited by 2,329
  10. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,238
  11. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
  12. 2021MLP-Mixer: An all-MLP Architecture for Visioncited by 1,446
13 more
  1. 2018On the Spectral Bias of Neural Networkscited by 1,341
  2. 2021EfficientNetV2: Smaller Models and Faster Trainingcited by 1,135
  3. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 950
  4. 2015Automatic differentiation in machine learning: a surveycited by 855
  5. 2017Solving high-dimensional partial differential equations using deep learningcited by 556
  6. 2018Deep Learning for Classical Japanese Literaturecited by 422
  7. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
  8. 2014Breaking the Curse of Dimensionality with Convex Neural Networkscited by 331
  9. 2018Stronger generalization bounds for deep nets via a compression approachcited by 307
  10. 2019Universal Approximation with Deep Narrow Networkscited by 200
  11. 2020The Kolmogorov-Arnold representation theorem revisitedcited by 89
  12. 2018FLOPs as a Direct Optimization Objective for Learning Sparse Neural Networkscited by 7
  13. 2023Training Neural Networks Using Reproducing Kernel Space Interpolation and Model Reductioncited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 10; 2026: 8.

18 papers.

Sort:

By area:

  1. 2025STORM: Search-Guided Generative World Models for Robotic Manipulationcited by 7
  2. 2026Making Gaussian Kolmogorov-Arnold Networks Reliable and Accuratecited by 3
  3. 2025Adaptive-VoCo: Complexity-Aware Visual Token Compression for Vision-Language Modelscited by 2
  4. 2026Rational ANOVA Networkscited by 2
  5. 2026A Graph Meta-Network for Learning on Kolmogorov-Arnold Networkscited by 2
  6. 2025Reflective Confidence: Correcting Reasoning Flaws via Online Self-Correctioncited by 1
  7. 2026A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networkscited by 1
  8. 2026Partition-of-Unity Gaussian Kolmogorov-Arnold Networkscited by 1
  9. 2025GTMA: Dynamic Representation Optimization for OOD Vision-Language Modelscited by 0
  10. 2025PTTA: A Pure Text-to-Animation Framework for High-Quality Creationcited by 0
  11. 2025RevFFN: Memory-Efficient Full-Parameter Fine-Tuning of Mixture-of-Experts LLMs with Reversible Blockscited by 0
  12. 2025A Three-Level Alignment Framework for Large-Scale 3D Retrieval and Controlled 4D Generationcited by 0
6 more
  1. 2025Learning Dynamic Scene Reconstruction with Sinusoidal Geometric Priorscited by 0
  2. 2025Self-Rewarded Multimodal Coherent Reasoning Across Diverse Visual Domainscited by 0
  3. 2025Forgetting as a Feature: Cognitive Alignment of Large Language Modelscited by 0
  4. 2026Multi-Agent Cooperative Learning for Robust Vision-Language Alignment under OOD Conceptscited by 0
  5. 2026LogicGaze: Benchmarking Causal Consistency in Visual Narratives via Counterfactual Verificationcited by 0
  6. 2026Adaptive RBF-KAN: A Comparative Evaluation of Dynamic Shape Parameters in Kolmogorov-Arnold Networkscited by 0