用连续时间神经网络提升动态3D高斯点云的时序平滑性
Liquid Neural Networks as a Drop-in Continuous-Time Deformation Field for Dynamic 3D Gaussian Splatting
- 用闭式连续时间细胞重构变形场，实现显式连续时间建模
- 在8个D-NeRF和7个NeRF-DS数据集上性能持平或超越基线
- 特别擅长处理高频关节运动场景，无需额外计算开销
可变形3D高斯点云（D-3DGS）通过时间编码的MLP对标准3D高斯分布进行变形，以从单目视频重建动态场景。尽管输入为连续变量，该MLP架构未显式建模时间依赖，仅通过优化隐含实现时序平滑。本文将变形场重设计为闭式连续时间（CfC）细胞堆叠的液态神经网络（LNN），其为液态时间常数微分方程的闭式解，同时保留原有D-3DGS流水线。每个细胞包含一个sigmoid时间门，可在两个候选隐藏状态间插值，将学习到的平滑响应嵌入损失景观，无需数值求解器。在8个D-NeRF和7个NeRF-DS场景中，液态场达到或超过MLP基线，尤其在具有高频关节运动的场景中提升显著。结果实现零摩擦架构升级，将离散的MLP变形场转为显式的连续时间函数。
原文摘要 · Abstract (English)
Deformable 3D Gaussian Splatting (D-3DGS) re-constructs dynamic scenes from monocular video by deforming a canonical set of 3D Gaussians through a positional-encoded MLP of frame time t. Although fitted to a continuous variable, the MLP couples no two values of t in its architecture and effectively predicts discrete per-frame offsets, leaving temporal smoothness to emerge only as a byproduct of optimisation. We redesign the deformation field as a stack of Closed-form Continuous-time (CfC) cells, a Liquid Neural Network (LNN), that is the closed-form solution of the Liquid Time-constant ODE while preserving every other part of the D-3DGS pipeline. Each cell exposes a sigmoidal time gate that interpolates between two candidate hidden states, baking a learned smooth response to t into the loss landscape without invoking any numerical solver. On the eight D-NeRF and seven NeRF-DS scenes the liquid field matches or exceeds the MLP baseline in aggregate, with its largest gains concentrated on the scenes with the most high-frequency articulated motion. The result is a near-zero-friction architectural design that turns the discrete MLP deformation field into an explicit continuous-time function of t.
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