发表机构
School of Information Technology, Monash University（莫纳什大学信息技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将动态3D高斯溅射的变形场替换为带高斯扰动的CfC单元，提出随机液体变形场，在合成场景上性能优于MLP基线，明确了噪声项的适用场景。
AI 中文摘要
可变形三维高斯溅射（D-3DGS）通过帧时间的变形场对一组标准三维高斯进行变形，以重建动态场景。将其多层感知机（MLP）替换为闭式连续时间（CfC）单元堆栈——一种以闭式求解液体时间常数常微分方程的液体神经网络——可使该场在前馈计算成本下获得连续时间行为。然而，该闭式形式仅是噪声驱动系统的确定性极限，丢失了通常被认为对液体网络鲁棒性至关重要的随机项。我们将该随机项重新引入：为每个CfC单元的时间门添加小的高斯扰动，使确定性场转变为简单的随机微分方程（SDE）场。该噪声仅在训练期间使用，无需求解器，且关闭时可精确还原为CfC。在合成D-NeRF场景上，该随机场在多数场景中与确定性CfC表现相当且优于MLP基线；在真实世界NeRF-DS场景上，确定性极限已表现最优，添加噪声无增益。本研究因此提供了将CfC场解读为SDE的清晰方式，并明确了纯噪声项何时有效、何时无效。
英文摘要
Deformable 3D Gaussian Splatting (D-3DGS) reconstructs dynamic scenes by deforming a canonical set of 3D Gaussians through a deformation field of frame time. Replacing its MLP with a stack of Closed-form Continuous-time (CfC) cells-a Liquid Neural Network that solves the Liquid Timeconstant ODE in closed form-gives the field continuous-time behaviour at feed-forward cost. That closed form, however, is only the deterministic limit of a noise-driven system, and drops the stochastic term usually credited for the robustness of liquid networks. We put it back: a small Gaussian perturbation is added to the time gate of every CfC cell, turning the deterministic field into a simple stochastic (SDE) one. The noise is used only during training, needs no solver, and reduces exactly to the CfC when switched off. On the synthetic D-NeRF scenes the stochastic field is on par with the deterministic CfC and beats the MLP baseline on most scenes; on the real-world NeRF-DS scenes the deterministic limit is already best and adding noise does not help. The study thus gives both a clean way to read the CfC field as an SDE and an honest account of when a plain noise term helps and when it does not.
CommentsAPSIPA ASC 2026 accepted paper
