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Establishing the correspondences between newly acquired points and historically accumulated data (i.e., map) through nearest neighbors search is crucial in numerous robotic applications. However, static tree data structures are inadequate…
We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R^2) or the skip octree (for point data in R^d, with constant d>2). Our data structure combines the best features of two well-known data…
Maintaining spatial data (points in two or three dimensions) is crucial and has a wide range of applications, such as graphics, GIS, and robotics. To handle spatial data, many data structures, called spatial indexes, have been proposed,…
We investigate the multi-step prediction of the drivable space, represented by Occupancy Grid Maps (OGMs), for autonomous vehicles. Our motivation is that accurate multi-step prediction of the drivable space can efficiently improve path…
Modeling and understanding the environment is an essential task for autonomous driving. In addition to the detection of objects, in complex traffic scenarios the motion of other road participants is of special interest. Therefore, we…
A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional…
Structured adaptive mesh refinement (AMR), commonly implemented via quadtrees and octrees, underpins a wide range of applications including databases, computer graphics, physics simulations, and machine learning. However, octrees enforce…
Attention mechanisms have revolutionized sequence learning but suffer from quadratic computational complexity. This paper introduces \model, a novel recurrent neural network (RNN) mechanism that leverages the inherent low-rank structure of…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
When introducing physics-constrained deep learning solutions to the volumetric super-resolution of scientific data, the training is challenging to converge and always time-consuming. We propose a new hierarchical sampling method based on…
This paper proposes an efficient data structure, ikd-Tree, for dynamic space partition. The ikd-Tree incrementally updates a k-d tree with new coming points only, leading to much lower computation time than existing static k-d trees.…
\begin{abstract} The advent of multitemporal high resolution data, like the Copernicus Sentinel-2, has enhanced significantly the potential of monitoring the earth's surface and environmental dynamics. In this paper, we present a novel deep…
Containment-based trees encompass various handy structures such as B+-trees, R-trees and M-trees. They are widely used to build data indexes, range-queryable overlays, publish/subscribe systems both in centralized and distributed contexts.…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we…
Lidar datasets are becoming more and more common. They are appreciated for their precise 3D nature, and have a wide range of applications, such as surface reconstruction, object detection, visualisation, etc. For all this applications,…
As an adaptive, interpretable, robust, and accurate meta-algorithm for arbitrary differentiable loss functions, gradient tree boosting is one of the most popular machine learning techniques, though the computational expensiveness severely…
Contemporary machine learning models, including large language models, exhibit remarkable capabilities in static tasks yet falter in non-stationary environments due to rigid architectures that hinder continual adaptation and lifelong…