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.

3D Gaussian Splatting (3DGS) has begun incorporating rich information from 2D foundation models. However, most approaches rely on a bottom-up optimization process that treats raw 2D features as ground truth, incurring increased computational costs. We propose a top-down pipeline for constructing compact and fast 3D Gaussian feature fields, namely, CF3. We first perform a fast weighted fusion of multi-view 2D features with pre-trained Gaussians. This approach enables training a per-Gaussian autoencoder directly on the lifted features, instead of training autoencoders in the 2D domain. As a result, the autoencoder better aligns with the feature distribution. More importantly, we introduce an adaptive sparsification method that optimizes the Gaussian attributes of the feature field while pruning and merging the redundant Gaussians, constructing an efficient representation with preserved geometric details. Our approach achieves a competitive 3D feature field using as little as 5% of the Gaussians compared to Feature-3DGS.