DeGenseGS: Geometrically and Semantically Decoupled Surgical Scene Understanding in 4D Gaussian Splatting

Real-time, text-promptable 4D reconstruction is indispensable for autonomous surgical interaction. Severe misalignment between semantic meaning and physical anatomy still persists, largely because existing solutions integrate Vision-Language Models into deformable fields via a rigid coupling scheme that tightly binds semantic features to geometric warping. In this paper, we propose DeGenseGS, Geometrically and Semantically Decoupled Surgical Scene Understanding in 4D Gaussian Splatting, a novel framework that independently models semantic evolution and geometric deformation. Specifically, we propose a HexPlane-based spatiotemporal entanglement module that uses shared kinematic latents to synchronize semantic mutations with scene dynamics, while explicitly disentangling semantic updates from geometric deformation. To further ensure robustness against reconstruction artifacts, we devise a Rasterization-Native Semantic Extraction mechanism that infers semantics from topologically continuous feature maps. Additionally, we incorporate an angular-aligned optimization strategy that conforms to the native hyperspherical latent space, thereby preventing semantic distortion. Extensive evaluations on the CholecSeg8k and EndoVis18 datasets demonstrate that DeGenseGS achieves state-of-the-art performance. Our framework yields enhanced geometric completeness and robust semantic-anatomic alignment, enabling spatially continuous segmentation despite drastic tissue deformation and topological transitions.

Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks

In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such as physics-informed neural networks, depend on automatic differentiation and the sampling of collocation points, which can result in a lack of interpretability and lower accuracy compared to traditional numerical methods. To address this issue, we propose two approaches for learning discontinuous Galerkin solutions to PDEs using small linear convolutional neural networks. Our first approach is supervised and depends on labeled data, while our second approach is unsupervised and does not rely on any training data. In both cases, our methods use substantially fewer parameters than similar numerics-based neural networks while also demonstrating comparable accuracy to the true and DG solutions for elliptic problems.