Kolmogorov-Arnold Fourier Networks

• URL: http://arxiv.org/abs/2502.06018v1
• Date: Sun, 09 Feb 2025 20:21:43 GMT
• Title: Kolmogorov-Arnold Fourier Networks
• Authors: Jusheng Zhang, Yijia Fan, Kaitong Cai, Keze Wang,
• Abstract summary: Kolmogorov-Arnold-Fourier Network (KAF) integrates trainable Random Fourier Features (RFF) and a novel hybrid GELU-Fourier activation mechanism.<n>Key technical contributions include merging KAN's dual-matrix structure through matrix association properties to substantially reduce parameters.<n>Experiments demonstrate the superiority of our KAF across various domains including vision, NLP, audio processing, and differential equation-solving tasks.
• Score: 9.17466024566914
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Although Kolmogorov-Arnold based interpretable networks (KAN) have strong theoretical expressiveness, they face significant parameter explosion and high-frequency feature capture challenges in high-dimensional tasks. To address this issue, we propose the Kolmogorov-Arnold-Fourier Network (KAF), which effectively integrates trainable Random Fourier Features (RFF) and a novel hybrid GELU-Fourier activation mechanism to balance parameter efficiency and spectral representation capabilities. Our key technical contributions include: (1) merging KAN's dual-matrix structure through matrix association properties to substantially reduce parameters; (2) introducing learnable RFF initialization strategies to eliminate spectral distortion in high-dimensional approximation tasks; (3) implementing an adaptive hybrid activation function that progressively enhances frequency representation during the training process. Comprehensive experiments demonstrate the superiority of our KAF across various domains including vision, NLP, audio processing, and differential equation-solving tasks, effectively combining theoretical interpretability with practical utility and computational efficiency.

Related papers

• R-Sparse: Rank-Aware Activation Sparsity for Efficient LLM Inference [77.47238561728459]
  R-Sparse is a training-free activation sparsity approach capable of achieving high sparsity levels in advanced LLMs. Experiments on Llama-2/3 and Mistral models across ten diverse tasks demonstrate that R-Sparse achieves comparable performance at 50% model-level sparsity.
  arXiv  Detail & Related papers  (2025-04-28T03:30:32Z)
• Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential [9.699640804685629]
  We introduce the Fourier Multi-Component and Multi-Layer Neural Network (FMMNN) We show that FMMNNs consistently achieve superior accuracy and efficiency across various tasks.
  arXiv  Detail & Related papers  (2025-02-26T09:12:52Z)
• STAF: Sinusoidal Trainable Activation Functions for Implicit Neural Representation [7.2888019138115245]
  Implicit Neural Representations (INRs) have emerged as a powerful framework for modeling continuous signals. The spectral bias of ReLU-based networks is a well-established limitation, restricting their ability to capture fine-grained details in target signals. We introduce Sinusoidal Trainable Functions Activation (STAF) STAF inherently modulates its frequency components, allowing for self-adaptive spectral learning.
  arXiv  Detail & Related papers  (2025-02-02T18:29:33Z)
• DiffFNO: Diffusion Fourier Neural Operator [8.895165270489167]
  We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO) We show that DiffFNO achieves state-of-the-art (SOTA) results, outperforming existing methods across various scaling factors by a margin of 2 to 4 dB in PSNR. Our approach sets a new standard in super-resolution, delivering both superior accuracy and computational efficiency.
  arXiv  Detail & Related papers  (2024-11-15T03:14:11Z)
• Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks [4.499833362998488]
  Implicit neural representations (INRs) use neural networks to provide continuous and resolution-independent representations of complex signals.<n>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.<n> Experimental results show that our proposed FKAN model outperforms three state-of-the-art baseline schemes.
  arXiv  Detail & Related papers  (2024-09-14T05:53:33Z)
• Parameter-Efficient Fine-Tuning for Continual Learning: A Neural Tangent Kernel Perspective [125.00228936051657]
  We introduce NTK-CL, a novel framework that eliminates task-specific parameter storage while adaptively generating task-relevant features. By fine-tuning optimizable parameters with appropriate regularization, NTK-CL achieves state-of-the-art performance on established PEFT-CL benchmarks.
  arXiv  Detail & Related papers  (2024-07-24T09:30:04Z)
• Spatial Annealing for Efficient Few-shot Neural Rendering [73.49548565633123]
  We introduce an accurate and efficient few-shot neural rendering method named textbfSpatial textbfAnnealing regularized textbfNeRF (textbfSANeRF)<n>By adding merely one line of code, SANeRF delivers superior rendering quality and much faster reconstruction speed compared to current few-shot neural rendering methods.
  arXiv  Detail & Related papers  (2024-06-12T02:48:52Z)
• A Sampling Theory Perspective on Activations for Implicit Neural Representations [73.6637608397055]
  Implicit Neural Representations (INRs) have gained popularity for encoding signals as compact, differentiable entities. We conduct a comprehensive analysis of these activations from a sampling theory perspective. Our investigation reveals that sinc activations, previously unused in conjunction with INRs, are theoretically optimal for signal encoding.
  arXiv  Detail & Related papers  (2024-02-08T05:52:45Z)
• Fractional Concepts in Neural Networks: Enhancing Activation Functions [0.6445605125467574]
  This study integrates fractional calculus into neural networks by introducing fractional order derivatives (FDO) as tunable parameters in activation functions. We evaluate these fractional activation functions on various datasets and network architectures, comparing their performance with traditional and new activation functions.
  arXiv  Detail & Related papers  (2023-10-18T10:49:29Z)
• Adaptive Frequency Filters As Efficient Global Token Mixers [100.27957692579892]
  We show that adaptive frequency filters can serve as efficient global token mixers. We take AFF token mixers as primary neural operators to build a lightweight neural network, dubbed AFFNet.
  arXiv  Detail & Related papers  (2023-07-26T07:42:28Z)
• Hybrid Spectral Denoising Transformer with Guided Attention [34.34075175179669]
  We present a Hybrid Spectral Denoising Transformer (HSDT) for hyperspectral image denoising. Our HSDT significantly outperforms the existing state-of-the-art methods while maintaining low computational overhead.
  arXiv  Detail & Related papers  (2023-03-16T02:24:31Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Fourier Space Losses for Efficient Perceptual Image Super-Resolution [131.50099891772598]
  We show that it is possible to improve the performance of a recently introduced efficient generator architecture solely with the application of our proposed loss functions. We show that our losses' direct emphasis on the frequencies in Fourier-space significantly boosts the perceptual image quality. The trained generator achieves comparable results with and is 2.4x and 48x faster than state-of-the-art perceptual SR methods RankSRGAN and SRFlow respectively.
  arXiv  Detail & Related papers  (2021-06-01T20:34:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.