Scaling Continuous Kernels with Sparse Fourier Domain Learning

TL;DR

This paper introduces a sparse Fourier domain learning method to efficiently scale continuous kernels, reducing computational costs and spectral bias, thereby enhancing their ability to capture high-frequency details.

Contribution

The paper presents a novel sparse Fourier domain approach that improves the scalability and spectral fidelity of continuous kernel learning methods.

Findings

Significantly reduces computational and memory demands.

Mitigates spectral bias to better capture high-frequency details.

Enables practical application of continuous kernels in large-scale settings.

Abstract

We address three key challenges in learning continuous kernel representations: computational efficiency, parameter efficiency, and spectral bias. Continuous kernels have shown significant potential, but their practical adoption is often limited by high computational and memory demands. Additionally, these methods are prone to spectral bias, which impedes their ability to capture high-frequency details. To overcome these limitations, we propose a novel approach that leverages sparse learning in the Fourier domain. Our method enables the efficient scaling of continuous kernels, drastically reduces computational and memory requirements, and mitigates spectral bias by exploiting the Gibbs phenomenon.