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Scaling Continuous Kernels with Sparse Fourier Domain Learning

Clayton Harper, Luke Wood, Peter Gerstoft, Eric C. Larson

TL;DR

This work proposes a novel approach that leverages sparse learning in the Fourier domain that enables the efficient scaling of continuous kernels, drastically reduces computational and memory requirements, and mitigates spectral bias by exploiting the Gibbs phenomenon.

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.

Scaling Continuous Kernels with Sparse Fourier Domain Learning

TL;DR

This work proposes a novel approach that leverages sparse learning in the Fourier domain that enables the efficient scaling of continuous kernels, drastically reduces computational and memory requirements, and mitigates spectral bias by exploiting the Gibbs phenomenon.

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.
Paper Structure (9 sections, 1 equation, 3 figures, 4 tables)

This paper contains 9 sections, 1 equation, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Fourier Domain Motivation
  4. CF-Conv Parameterizations
  5. Scaling CF-Convs
  6. Sparse Updates
  7. Experiments and Results
  8. Discussion
  9. Conclusion

Figures (3)

  • Figure 1: Illustration of different potential parameterizations for CF-Conv layers, where MLPs are conditioned on various axes. The number of MLPs (represented by different colors) and the corresponding parameter counts vary based on the chosen parameterization.
  • Figure 2: Sparse sampling visualization for more efficient training of CF-Conv layers. Uniformly random sampled positions for a single training step are shown in red.
  • Figure 3: Cats vs. Dogs architectural overview using CF-Convs.