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 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 an end-to-end learning framework to jointly optimize the gauge transformation 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.

翻译：神经场（如神经辐射场）的最新进展显著推动了场景表征学习的发展。为提高三维场景的计算效率和渲染质量，一类主流研究方向是将三维坐标系映射至其他测量系统（如二维流形和哈希表）以建模神经场。这种坐标系转换通常被称为规范变换，其映射函数（如正交投影或空间哈希函数）往往是预先定义的。由此引发一个关键问题：能否以端到端方式与神经场同步学习所需的规范变换？本文将问题扩展至包含离散与连续案例分类的通用范式，并构建了一个端到端学习框架以联合优化规范变换与神经场。针对规范变换学习易崩塌的问题，我们基于规范变换过程中的信息守恒原理推导了一种通用正则化机制。为避免引入正则化后规范学习的高计算成本，我们进一步直接推导出信息不变规范变换，该变换得以固有地保留场景信息并实现优越性能。