arXiv Computer Vision

Spatial-Frequency-Aware Implicit Neural Representation of Multidimensional Signals via MLP-KAN Fusion

The paper introduces a spatial-frequency-aware implicit neural representation that fuses a Multi‑Layer Perceptron (MLP) branch with a Kolmogorov‑Arnold network (KAN) branch. The MLP captures low‑frequency, smooth structures while the KAN captures high‑frequency, localized details, and their outputs are combined using discrete wavelet transform (DWT) and inverse DWT. A wavelet‑domain band‑separation regularization encourages complementary frequency behavior, and experiments on 1D–4D signals show improved reconstruction fidelity.

arXiv AI
Sep 1

Frequency Selective Neural Networks as a Foundation Architecture for Time Series Learning

The paper introduces the Frequency Selective Neural Network (FSNN), a new foundation architecture for time‑series learning that embeds advanced signal‑processing mathematics into its neural topology. By using a fully differentiable Wiener‑like filter bank optimized with complex‑domain backpropagation, FSNN autonomously discovers and isolates the precise physical modes of a given task, thereby avoiding the spectral entanglement that plagues CNNs, RNNs, and Transformers. Extensive evaluations show that FSNN achieves state‑of‑the‑art predictive performance, attaining 77.0 % average accuracy on the 10 multivariate UEA datasets and leading all major metrics on the imbalanced PTB‑XL ECG benchmark, while converging directly on physically meaningful frequency bands such as the cardiac QRS complex.

By Hui Huang, Ye Sun, Shiyan Hu
arXiv Machine Learning
Oct 8

CAFE+FNO: Fourier Kernel Generation via Multiplicative Feature Composition

The paper introduces CAFE+FNO, a Fourier Neural Operator variant that enhances kernel generation by combining Fourier–Chebyshev features through parallel affine branches and a Hadamard product. This method produces frequency interactions explicitly, allowing a kernel MLP to map each normalized spectral coordinate to a complex channel‑mixing matrix while keeping the number of trainable parameters independent of the number of modes. Experiments on five PDE benchmarks and ablation studies demonstrate the effectiveness of the proposed basis configuration, multiplicative composition, and bandwidth learnability.

By Hyungjoon Juen, Minwoo Shin
arXiv Machine Learning
Oct 7

Learnable Spectral Activations

arXiv:2610.07419v1 Announce Type: new Abstract: Implicit neural representations (INRs) are shaped by the spectral structure induced by their input encodings and activation functions. Existing methods...

By Tamir Shor, Or Litany, Alex Bronstein
arXiv Machine Learning
Oct 3

PI-AMFM: Permutation-Invariant Learning for Variable-Cardinality AM-FM Mode Decomposition in Biomedical Signal Analysis

The paper introduces PI-AMFM, a permutation‑invariant neural framework that learns to decompose biomedical signals into variable‑cardinality amplitude‑ and frequency‑modulated (AM‑FM) modes. It combines a multiscale temporal encoder, a Mamba backbone, and component‑presence estimation, using Hungarian matching during training to handle unknown numbers of components. Experiments on synthetic AM‑FM signals and photoplethysmographic recordings show that PI‑AMFM outperforms existing methods in decomposition accuracy and successfully captures cardiac and respiratory dynamics without prior knowledge of mode count.

By Youngsun Kong, Ki H. Chon
arXiv Computer Vision
Sep 3

LaST-SR: Laplace-Inspired Steady-Transient Complex-Frequency Decomposition for Single Image Super-Resolution

LaST‑SR introduces a Laplace‑inspired steady‑transient complex‑frequency decomposition for single‑image super‑resolution. The method couples a global full‑spectrum Fourier branch with a window‑conditioned local complex‑frequency branch, and fuses them via a Steady‑Transient Collaborative Aggregation module. Experiments on five benchmarks demonstrate that LaST‑SR achieves the highest PSNR/SSIM for ×2 and ×4 upscaling, with ablation studies confirming the effectiveness of its architecture.

By Linhao Li, Zhaojie Pan, Langkun Chen