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[2602.13414] FUTON: Fourier Tensor Network for Implicit Neural Representations
Summary
The paper introduces FUTON, a Fourier Tensor Network designed to enhance implicit neural representations (INRs) by improving convergence speed and generalization capabilities over traditional MLP-based models.
Why It Matters
FUTON addresses key limitations in existing INR models, such as slow convergence and overfitting, making it a significant advancement in image processing and machine learning. Its theoretical guarantees and practical performance improvements could influence future research and applications in these fields.
Key Takeaways
- FUTON models signals using generalized Fourier series with low-rank tensor decomposition.
- It offers faster training times (2-5x) compared to state-of-the-art MLP-based INRs.
- FUTON demonstrates better generalization in inverse problems like image denoising and super-resolution.
- The paper provides theoretical guarantees through a universal approximation theorem.
- An inference algorithm is derived with linear complexity in spectral resolution and input dimension.
Electrical Engineering and Systems Science > Image and Video Processing arXiv:2602.13414 (eess) [Submitted on 13 Feb 2026] Title:FUTON: Fourier Tensor Network for Implicit Neural Representations Authors:Pooya Ashtari, Pourya Behmandpoor, Nikos Deligiannis, Aleksandra Pizurica View a PDF of the paper titled FUTON: Fourier Tensor Network for Implicit Neural Representations, by Pooya Ashtari and 2 other authors View PDF HTML (experimental) Abstract:Implicit neural representations (INRs) have emerged as powerful tools for encoding signals, yet dominant MLP-based designs often suffer from slow convergence, overfitting to noise, and poor extrapolation. We introduce FUTON (Fourier Tensor Network), which models signals as generalized Fourier series whose coefficients are parameterized by a low-rank tensor decomposition. FUTON implicitly expresses signals as weighted combinations of orthonormal, separable basis functions, combining complementary inductive biases: Fourier bases capture smoothness and periodicity, while the low-rank parameterization enforces low-dimensional spectral structure. We provide theoretical guarantees through a universal approximation theorem and derive an inference algorithm with complexity linear in the spectral resolution and the input dimension. On image and volume representation, FUTON consistently outperforms state-of-the-art MLP-based INRs while training 2--5$\times$ faster. On inverse problems such as image denoising and super-resolution, FUTON gener...
