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Stein Variational Gradient Descent (SVGD) is a widely used in practice algorithm for scalable sampling with deterministic particle updates. We study its behavior in the singular limit where the kernel bandwidth tends to zero. In this…

Stein Variational Gradient Descent (SVGD) is a popular variational inference algorithm which simulates an interacting particle system to approximately sample from a target distribution, with impressive empirical performance across various…

This paper investigates coverage control for visual sensor networks based on gradient descent techniques on matrix manifolds. We consider the scenario that networked vision sensors with controllable orientations are distributed over 3-D…

3D Gaussian Splatting (3DGS) has emerged as a promising approach for 3D scene representation, offering a reduction in computational overhead compared to Neural Radiance Fields (NeRF). However, 3DGS is susceptible to high-frequency artifacts…

Stochastic Gradient Descent (SGD) is one of the most widely used techniques for online optimization in machine learning. In this work, we accelerate SGD by adaptively learning how to sample the most useful training examples at each time…

We propose and analyze a Stein variational reduced basis method (SVRB) to solve large-scale PDE-constrained Bayesian inverse problems. To address the computational challenge of drawing numerous samples requiring expensive PDE solves from…

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…

Provably solving stochastic convex optimization problems with constraints is essential for various problems in science, business, and statistics. Recently proposed XOR-Stochastic Gradient Descent (XOR-SGD) provides a convergence rate…

We present SAGE3D, a hybrid Transformer-based model for corner detection in airborne LiDAR point clouds. We propose a multi-stage solution built on a hierarchical encoder-decoder architecture that progressively downsamples point clouds…

Many robotic tasks involving some form of 3D visual perception greatly benefit from a complete knowledge of the working environment. However, robots often have to tackle unstructured environments and their onboard visual sensors can only…

Reconstructing 3D geometry from \emph{unoriented} point clouds can benefit many downstream tasks. Recent shape modeling methods mostly adopt implicit neural representation to fit a signed distance field (SDF) and optimize the network by…

We consider path planning for a rigid spatial robot with 6 degrees of freedom (6 DOFs), moving amidst polyhedral obstacles. A correct, complete and practical path planner for such a robot has never been achieved, although this is widely…

Gradient-based trajectory optimization (GTO) has gained wide popularity for quadrotor trajectory replanning. However, it suffers from local minima, which is not only fatal to safety but also unfavorable for smooth navigation. In this paper,…

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for real-time, high-resolution novel view synthesis. By representing scenes as a mixture of Gaussian primitives, 3DGS leverages GPU rasterization pipelines for efficient…

Accurate and affordable indoor 3D reconstruction is critical for effective robot navigation and interaction. Traditional LiDAR-based mapping provides high precision but is costly, heavy, and power-intensive, with limited ability for novel…

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be $SO(3)$ equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for…

In the field of 3D scene understanding, 3D scene graphs have emerged as a new scene representation that combines geometric and semantic information about objects and their relationships. However, learning semantic 3D scene graphs in a fully…

Generating grasp poses is a crucial component for any robot object manipulation task. In this work, we formulate the problem of grasp generation as sampling a set of grasps using a variational autoencoder and assess and refine the sampled…

Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for…

Grasping objects successfully from a single-view camera is crucial in many robot manipulation tasks. An approach to solve this problem is to leverage simulation to create large datasets of pairs of objects and grasp poses, and then learn a…