FUTON: Fourier Tensor Network for Implicit Neural Representations

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 empirically linear complexity in both 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× faster.