Scene understanding based on 3DGaussian Splatting (3DGS) has recently achieved notable advances. Although 3DGS related methods have efficient rendering capabilities, they fail to address the inherent contradiction between the anisotropic color representation of gaussian primitives and the isotropic requirements of semantic features, leading to insufficient cross-view feature consistency. To overcome the limitation, we proposes FHGS (Feature-Homogenized Gaussian Splatting), a novel 3D feature distillation framework inspired by physical models, which freezes and distills 2D pre-trained features into 3D representations while preserving the realtime rendering efficiency of 3DGS. Specifically, our FHGS introduces the following innovations: Firstly, a universal feature fusion architecture is proposed, enabling robust embedding of large-scale pre-trained models' semantic features (e.g., SAM, CLIP) into sparse 3D structures. Secondly, a non-differentiable feature fusion mechanism is introduced, which enables semantic features to exhibit viewpoint independent isotropic distributions.

Recent advances in text-based image editing have motivated the extension of these techniques into the 3D domain. However, existing methods typically apply 2D diffusion models independently to multiple viewpoints, resulting in significant artifacts, most notably the Janus problem, due to inconsistencies across edited views. To address this, we propose a novel approach termed DFFSplat, which integrates a 3D-consistent diffusion feature field into the editing pipeline. By rendering and injecting these 3D-consistent structural features into intermediate layers of a 2D diffusion model, our method effectively enforces geometric alignment and semantic coherence across views. However, averaging 3D features during the feature field learning process can lead to the loss of fine texture details. To overcome this, we introduce a dual-encoder architecture to disentangle view-independent structural information from view-dependent appearance details. By encoding only the disentangled structure into the 3D field and injecting it during 2D editing, our method produces semantically and multi-view coherent edited images while maintaining high text fidelity. Additionally, we employ a time-invariance objective to ensure consistency across diffusion timesteps, enhancing the stability of learned representations. Experimental results demonstrate that our method achieves state-of-the-art performance in terms of text-fidelity, and better preserves structural and semantic consistency compared to existing approaches.

Results from experiments on three large real-world benchmark datasets demonstrate that OptFeature performs well in terms of accuracy and efficiency. Additional studies support the feasibility of our method.

A general solution of the kernel space constraint is given for arbitrary representations of the Euclidean groupE(2) and its subgroups.

Attention mechanism has shown great performance and efficiency in a lot of deep learning models, in which relative position encoding plays a crucial role. However, when introducing attention to manifolds, there is no canonical local coordinate system to parameterize neighborhoods.

Deep sparse networks are widely investigated as a neural network architecture for prediction tasks with high-dimensional sparse features, with which feature interaction selection is a critical component. While previous methods primarily focus on how to search feature interaction in a coarse-grained space, less attention has been given to a finer granularity. In this work, we introduce a hybrid-grained feature interaction selection approach that targets both feature field and feature value for deep sparse networks. To explore such expansive space, we propose a decomposed space which is calculated on the fly. We then develop a selection algorithm called OptFeature, which efficiently selects the feature interaction from both the feature field and the feature value simultaneously. Results from experiments on three large real-world benchmark datasets demonstrate that OptFeature performs well in terms of accuracy and efficiency. Additional studies support the feasibility of our method.

Clifford-Steerable CNNs (CSCNNs) provide a unified framework that allows incorporating equivariance to arbitrary pseudo-Euclidean groups, including isometries of Euclidean space and Minkowski spacetime. In this work, we demonstrate that the kernel basis of CSCNNs is not complete, thus limiting the model expressivity. To address this issue, we propose Conditional Clifford-Steerable Kernels, which augment the kernels with equivariant representations computed from the input feature field. We derive the equivariance constraint for these input-dependent kernels and show how it can be solved efficiently via implicit parameterization. We empirically demonstrate an improved expressivity of the resulting framework on multiple PDE forecasting tasks, including fluid dynamics and relativistic electrodynamics, where our method consistently outperforms baseline methods.

Comprehensive visual, geometric, and semantic understanding of a 3D scene is crucial for successful execution of robotic tasks, especially in unstructured and complex environments. Additionally, to make robust decisions, it is necessary for the robot to evaluate the reliability of perceived information. While recent advances in 3D neural feature fields have enabled robots to leverage features from pretrained foundation models for tasks such as language-guided manipulation and navigation, existing methods suffer from two critical limitations: (i) they are typically scene-specific, and (ii) they lack the ability to model uncertainty in their predictions. We present UniFField, a unified uncertainty-aware neural feature field that combines visual, semantic, and geometric features in a single generalizable representation while also predicting uncertainty in each modality. Our approach, which can be applied zero shot to any new environment, incrementally integrates RGB-D images into our voxel-based feature representation as the robot explores the scene, simultaneously updating uncertainty estimation. We evaluate our uncertainty estimations to accurately describe the model prediction errors in scene reconstruction and semantic feature prediction. Furthermore, we successfully leverage our feature predictions and their respective uncertainty for an active object search task using a mobile manipulator robot, demonstrating the capability for robust decision-making.