Seminar Details
2026-09-22 (14:00) : FUTON: Fourier Tensor Network for Implicit Neural Representations
At Euler building (room A.002)
Duration: 60 minutes
Organized by Mathematical Engineering
Speaker :
Pooya Ashtari (University of Ghent)
Abstract :
Implicit neural representations (INRs) encode signals as continuous functions parameterized by neural networks that map coordinates to values, rather than as grids of discrete samples. Since they are resolution-free, compact, and differentiable with respect to their input coordinates, INRs have become attractive priors for inverse problems involving incomplete or irregularly sampled measurements. INRs are typically implemented as multilayer perceptrons (MLPs) with carefully designed activation functions, but such networks can converge slowly, overfit to noise, and extrapolate poorly.
This talk presents FUTON (Fourier Tensor Network), an INR that represents a signal as a generalized Fourier series with a coefficient tensor factorized using a low-rank decomposition. The two ingredients contribute complementary inductive biases: the orthonormal, separable basis favors smoothness and periodicity, while the low-rank factorization captures the low-dimensional spectral structure of natural signals. The resulting model is shallow and multilinear and requires no learned activation functions. I will show that FUTON is a universal approximator in L²; that evaluating it through an appropriate sequence of tensor contractions reduces an otherwise exponential computational cost to a tractable level; and that it outperforms state-of-the-art MLPs in image and volume representation, trains 2–5× faster, and generalizes better to image super-resolution, denoising, and CT/MRI reconstruction.