The recent advance of neural fields, such as neural radiance fields, has significantly pushed the boundary of scene representation learning. Aiming to boost the computation efficiency and rendering quality of 3D scenes, a popular line of research maps the 3D coordinate system to another measuring system, e.g., 2D manifolds and hash tables, for modeling neural fields. The conversion of coordinate systems can be typically dubbed as \emph{gauge transformation}, which is usually a pre-defined mapping function, e.g., orthogonal projection or spatial hash function. This begs a question: can we directly learn a desired gauge transformation along with the neural field in an end-to-end manner? In this work, we extend this problem to a general paradigm with a taxonomy of discrete \& continuous cases, and develop a learning framework to jointly optimize gauge transformations and neural fields. To counter the problem that the learning of gauge transformations can collapse easily, we derive a general regularization mechanism from the principle of information conservation during the gauge transformation. To circumvent the high computation cost in gauge learning with regularization, we directly derive an information-invariant gauge transformation which allows to preserve scene information inherently and yield superior performance. Project: https://fnzhan.com/Neural-Gauge-Fields

翻译：神经场（如神经辐射场）的最新进展显著推动了场景表示学习的发展边界。为了提升三维场景的计算效率与渲染质量，主流研究方向将三维坐标系映射至另一种度量系统（如二维流形与哈希表）以建模神经场。这种坐标系的转换通常被称为**规范变换**，其通常为预定义的映射函数（如正交投影或空间哈希函数）。这引出一个问题：能否以端到端方式直接学习所需的规范变换与神经场？本研究将问题扩展至离散与连续情况分类的通用范式，并开发了联合优化规范变换与神经场的学习框架。针对规范变换学习易坍塌的问题，我们基于规范变换中的信息守恒原理推导出通用正则化机制。为规避带正则化的规范学习中高昂的计算成本，我们直接推导出信息不变性规范变换，该变换能天然保持场景信息且获得更优性能。项目主页：https://fnzhan.com/Neural-Gauge-Fields