Preconditioners for the Stochastic Training of Neural Fields

TL;DR

This paper introduces a theoretical framework for using curvature-aware diagonal preconditioners to accelerate the stochastic training of neural fields, improving efficiency in various applications like image reconstruction and NeRF.

Contribution

It proposes a novel framework for preconditioning neural field training with curvature-aware methods, addressing limitations of traditional second-order approaches in stochastic settings.

Findings

Preconditioners significantly speed up training times.

Effective across diverse neural field applications.

Framework demonstrates improved convergence without accuracy loss.

Abstract

Neural fields encode continuous multidimensional signals as neural networks, enabling diverse applications in computer vision, robotics, and geometry. While Adam is effective for stochastic optimization, it often requires long training times. To address this, we explore alternative optimization techniques to accelerate training without sacrificing accuracy. Traditional second-order methods like L-BFGS are unsuitable for stochastic settings. We propose a theoretical framework for training neural fields with curvature-aware diagonal preconditioners, demonstrating their effectiveness across tasks such as image reconstruction, shape modeling, and Neural Radiance Fields (NeRF).