Implicit neural representations are powerful for geometric modeling, but their practical use is often limited by the high computational cost of network evaluations. We observe that implicit representations require progressively lower accuracy as query points move farther from the target surface, and that even within the same iso-surface, representation difficulty varies spatially with local geometric complexity. However, conventional neural implicit models evaluate all query points with the same network depth and computational cost, ignoring this spatial variation and thereby incurring substantial computational waste. Motivated by this observation, we propose an efficient neural implicit geometry representation framework with spatially adaptive network depth (SAND). SAND leverages a volumetric network-depth map together with a tailed multi-layer perceptron (T-MLP) to model implicit representation. The volumetric depth map records, for each spatial region, the network depth required to achieve sufficient accuracy, while the T-MLP is a modified MLP designed to learn implicit functions such as signed distance functions, where an output branch, referred to as a tail, is attached to each hidden layer. This design allows network evaluation to terminate adaptively without traversing the full network and directs computational resources to geometrically important and complex regions, improving efficiency while preserving high-fidelity representations. Extensive experimental results demonstrate that our approach can significantly improve the inference-time query speed of implicit neural representations.

翻译：隐式神经表示在几何建模中表现出强大的能力，但其实际应用常受限于网络评估的高计算成本。我们观察到，隐式表示对查询点远离目标曲面时所需精度逐渐降低，且即使在相同等值面内，表示难度也会随局部几何复杂度而空间变化。然而，传统神经隐式模型对所有查询点采用相同的网络深度与计算开销，这种忽略空间变化的设计导致了大量计算浪费。基于上述观察，我们提出一种具有空间自适应网络深度的高效神经隐式几何表示框架SAND。SAND利用体素网络深度图与带尾部的多层感知机（T-MLP）共同建模隐式表示：体素深度图为每个空间区域记录达成足够精度所需的网络深度，而T-MLP是一种改进型MLP，旨在学习符号距离函数等隐式函数，其中每个隐藏层附加一个称为尾部的输出分支。该设计允许网络评估自适应终止而无需遍历完整网络，从而将计算资源导向几何重要且复杂的区域，在保持高保真表示的同时提升效率。大量实验结果表明，本方法可显著提升隐式神经表示的推理时查询速度。