Stochastic Preconditioning for Neural Field Optimization

TL;DR

This paper introduces a simple stochastic preconditioning technique for neural fields that improves training convergence and robustness by sampling with Gaussian offsets, outperforming or matching complex hierarchical methods across various tasks.

Contribution

It formalizes stochastic preconditioning as implicit blurring in neural field optimization, offering a simple, cost-free, and effective alternative to complex hierarchy-based methods.

Findings

Improves convergence and robustness in neural field training.

Nearly matches or outperforms existing hierarchical methods.

Provides a universal, simple approach applicable across multiple neural field representations.

Abstract

Neural fields are a highly effective representation across visual computing. This work observes that fitting these fields is greatly improved by incorporating spatial stochasticity during training, and that this simple technique can replace or even outperform custom-designed hierarchies and frequency space constructions. The approach is formalized as implicitly operating on a blurred version of the field, evaluated in-expectation by sampling with Gaussian-distributed offsets. Querying the blurred field during optimization greatly improves convergence and robustness, akin to the role of preconditioners in numerical linear algebra. This implicit, sampling-based perspective fits naturally into the neural field paradigm, comes at no additional cost, and is extremely simple to implement. We describe the basic theory of this technique, including details such as handling boundary conditions, and extending to a spatially-varying blur. Experiments demonstrate this approach on representations including coordinate MLPs, neural hashgrids, triplanes, and more, across tasks including surface reconstruction and radiance fields. In settings where custom-designed hierarchies have already been developed, stochastic preconditioning nearly matches or improves their performance with a simple and unified approach; in settings without existing hierarchies it provides an immediate boost to quality and robustness.