用随机模糊提升神经场优化速度与稳定性，无需复杂设计。
Stochastic Preconditioning for Neural Field Optimization
- 训练时引入高斯偏移采样，隐式实现场的模糊化优化。
- 在表面重建和辐射场任务中显著加速收敛并提升鲁棒性。
- 方法简单通用，适合各类神经场模型且无需额外计算开销。
神经场在视觉计算中表现优异。本文发现，在训练中引入空间随机性可大幅提升其拟合效果，且该简单技巧能取代或超越定制化的层级结构与频率空间设计。该方法被形式化为对场的模糊版本进行隐式操作，通过高斯分布偏移采样在期望下评估。在优化过程中查询模糊场显著改善收敛性和鲁棒性，类似数值线性代数中的预条件器作用。这种基于采样的隐式视角自然契合神经场范式，无需额外成本，实现极其简便。我们阐述了该技术的基本理论，包括边界条件处理及空间可变模糊的扩展。实验覆盖坐标MLP、神经哈希网格、三平面等表示，涵盖表面重建与辐射场等任务。在已有定制层级结构的场景中，随机预条件法几乎持平或优于原有性能；在无现有层级结构的场景中，立即带来质量与鲁棒性的显著提升。
原文摘要 · Abstract (English)
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.
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