Their algorithm has a time and space complexity of O ( dk) .

Their algorithm has a time and space complexity of O ( dk) .

In the kernel density estimation (KDE) problem, we are given a set $X$ of data points in $\mathbb{R}^d$, a kernel function $k: \mathbb{R}^d \times \mathbb{R}^d \rightarrow \mathbb{R}$, and a query point $\mathbf{q} \in \mathbb{R}^d$, and the objective is to quickly output an estimate of $\sum_{\mathbf{x} \in X} k(\mathbf{q}, \mathbf{x})$. In this paper, we consider $\textsf{KDE}$ in the dynamic setting, and introduce a data structure that efficiently maintains the estimates for a set of query points as data points are added to $X$ over time. Based on this, we design a dynamic data structure that maintains a sparse approximation of the fully connected similarity graph on $X$, and develop a fast dynamic spectral clustering algorithm. We further evaluate the effectiveness of our algorithms on both synthetic and real-world datasets.

Fully decentralized, safe, and deadlock-free multi-robot navigation in dynamic, cluttered environments is a critical challenge in robotics. Current methods require exact state measurements in order to enforce safety and liveness e.g. via control barrier functions (CBFs), which is challenging to achieve directly from onboard sensors like lidars and cameras. This work introduces LIVEPOINT, a decentralized control framework that synthesizes universal CBFs over point clouds to enable safe, deadlock-free real-time multi-robot navigation in dynamic, cluttered environments. Further, LIVEPOINT ensures minimally invasive deadlock avoidance behavior by dynamically adjusting agents' speeds based on a novel symmetric interaction metric. We validate our approach in simulation experiments across highly constrained multi-robot scenarios like doorways and intersections. Results demonstrate that LIVEPOINT achieves zero collisions or deadlocks and a 100% success rate in challenging settings compared to optimization-based baselines such as MPC and ORCA and neural methods such as MPNet, which fail in such environments. Despite prioritizing safety and liveness, LIVEPOINT is 35% smoother than baselines in the doorway environment, and maintains agility in constrained environments while still being safe and deadlock-free.

We introduce SAM2Point, a preliminary exploration adapting Segment Anything Model 2 (SAM 2) for zero-shot and promptable 3D segmentation. SAM2Point interprets any 3D data as a series of multi-directional videos, and leverages SAM 2 for 3D-space segmentation, without further training or 2D-3D projection. Our framework supports various prompt types, including 3D points, boxes, and masks, and can generalize across diverse scenarios, such as 3D objects, indoor scenes, outdoor environments, and raw sparse LiDAR. Demonstrations on multiple 3D datasets, e.g., Objaverse, S3DIS, ScanNet, Semantic3D, and KITTI, highlight the robust generalization capabilities of SAM2Point. To our best knowledge, we present the most faithful implementation of SAM in 3D, which may serve as a starting point for future research in promptable 3D segmentation. Online Demo: https://huggingface.co/spaces/ZiyuG/SAM2Point . Code: https://github.com/ZiyuGuo99/SAM2Point .

From rearranging objects on a table to putting groceries into shelves, robots must plan precise action points to perform tasks accurately and reliably. In spite of the recent adoption of vision language models (VLMs) to control robot behavior, VLMs struggle to precisely articulate robot actions using language. We introduce an automatic synthetic data generation pipeline that instruction-tunes VLMs to robotic domains and needs. Using the pipeline, we train RoboPoint, a VLM that predicts image keypoint affordances given language instructions. Compared to alternative approaches, our method requires no real-world data collection or human demonstration, making it much more scalable to diverse environments and viewpoints. In addition, RoboPoint is a general model that enables several downstream applications such as robot navigation, manipulation, and augmented reality (AR) assistance. Our experiments demonstrate that RoboPoint outperforms state-of-the-art VLMs (GPT-4o) and visual prompting techniques (PIVOT) by 21.8% in the accuracy of predicting spatial affordance and by 30.5% in the success rate of downstream tasks. Project website: https://robo-point.github.io.

Abstract-- Numerous mobile robots with mounted Ultraviolet-C (UV-C) lamps were developed recently, yet they cannot work in the same space as humans without irradiating them by UV-C. This paper proposes a novel modular and scalable Human-Aware Genetic-based Coverage Path Planning algorithm (GHACPP), that aims to solve the problem of disinfecting of unknown environments by UV-C irradiation and preventing human eyes and skin from being harmed. The system performance in effectiveness and human safety is validated and compared with one of the latest state-of-the-art online coverage path planning algorithms called SimExCoverage-STC. The experimental results confirmed both the high level of safety for humans and the efficiency of the developed algorithm in terms of decrease of path length (by 37.1%), number (39.5%) and size (35.2%) of turns, and time (7.6%) to complete the disinfection task, with a small loss in the percentage of area covered (0.6%), in comparison with the state-of-the-art approach. The irradiation-free area is marked in white. In the face of the COVID-19 world-girdling pandemic, B. Problem statement it has become apparent how important the disinfection of Nowadays, there are many types of effective path planning premises is to our lives.

Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes with gradient noise, often leading to specific step size and momentum choices in order to guarantee convergence, set aside acceleration. Proximal point methods, on the other hand, have gained much attention due to their numerical stability and elasticity against imperfect tuning. Their stochastic accelerated variants though have received limited attention: how momentum interacts with the stability of (stochastic) proximal point methods remains largely unstudied. To address this, we focus on the convergence and stability of the stochastic proximal point algorithm with momentum (SPPAM), and show that SPPAM allows a faster linear convergence to a neighborhood compared to stochastic proximal point algorithm (SPPA) with a better contraction factor, under proper hyperparameter tuning. In terms of stability, we show that SPPAM depends on problem constants more favorably than SGDM, allowing a wider range of step size and momentum that lead to convergence.

It is difficult to use subsampling with variational inference in hierarchical models since the number of local latent variables scales with the dataset. Thus, inference in hierarchical models remains a challenge at large scale. It is helpful to use a variational family with structure matching the posterior, but optimization is still slow due to the huge number of local distributions. Instead, this paper suggests an amortized approach where shared parameters simultaneously represent all local distributions. This approach is similarly accurate as using a given joint distribution (e.g., a full-rank Gaussian) but is feasible on datasets that are several orders of magnitude larger. It is also dramatically faster than using a structured variational distribution.