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.
General Salient Object Detection (SOD) aims to identify and segment visually interesting objects from uni-modality or multi-modality scenes, recently advanced by cutting-edge State Space Models (SSMs). However, a critical limitation of current approaches is their neglect of the inherent spectral biases exhibited by different neural network paradigms. By digging to the dataset-level spectral analysis of Convolutional Neural Networks (CNNs) and SSMs, their semantic representations are inherently complementary based on their complementary frequency preferences. Inspired by this, we harmonize heterogeneous representations from SSMs and CNNs to bridge their spectral biases for general salient object detection. To this end, inspired by the dynamic information propagation of Liquid Neural Networks (LNNs), we introduce a liquid fusion to dynamically integrates features from two backbones, including VMamba and ConvNeXt, referred to Liquid Fusion Network (LFNet). Concretely, by treating the continuous VMamba features and ConvNeXt features as evolving states and exogenous stimulus, respectively, LFNet employs a dynamic gating mechanism for content-aware feature aggregation. Crucially, this state-stimulus paradigm enables to scale to multi-modal cues, resulting in flexibility in general SOD. Besides, a Saliency-Guided Upsampling (SGU) operator to propagate the features to the shallow layer, which leverages a spectral-spatial co-design to suppress upsampling artifacts while preserving semantics. Extensive experiments across five diverse tasks (RGB, RGB-D, RGB-T, VSOD, and VDT) demonstrate that LFNet achieves state-of-the-art performance, offering a superior trade-off between detection accuracy and model efficiency. Code has been released at https://github.com/cke520/LFNet.