相关论文: On Low Discrepancy Samplings in Product Spaces of …

Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point sets with small discrepancy are called low-discrepancy and are known to efficiently fill the space in a uniform manner. Low-discrepancy…

Low discrepancy point sets have been widely used as a tool to approximate continuous objects by discrete ones in numerical processes, for example in numerical integration. Following a century of research on the topic, it is still unclear…

We study the $L^{\infty}$ discrepancy of point sets generated by determinantal point processes on all compact, connected two-point homogeneous spaces, namely spheres and projective spaces. Using concentration inequalities and variance…

Learning neural implicit fields of 3D shapes is a rapidly emerging field that enables shape representation at arbitrary resolutions. Due to the flexibility, neural implicit fields have succeeded in many research areas, including shape…

We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…

In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…

Low-discrepancy designs play a central role in quasi-Monte Carlo methods and are increasingly influential in other domains such as machine learning, robotics and computer graphics, to name a few. In recent years, one such low-discrepancy…

This work proposes a nonlinear stochastic filter evolved on the Special Orthogonal Group SO(3) as a solution to the attitude filtering problem. One of the most common potential functions for nonlinear deterministic attitude observers is…

Sampling-based motion planning methods, while effective in high-dimensional spaces, often suffer from inefficiencies due to irregular sampling distributions, leading to suboptimal exploration of the configuration space. In this paper, we…

Monte Carlo sampling has become a major vehicle for approximate inference in Bayesian networks. In this paper, we investigate a family of related simulation approaches, known collectively as quasi-Monte Carlo methods based on deterministic…

We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to…

Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…

Sampling-based algorithms are widely used for motion planning in high-dimensional configuration spaces. However, due to low sampling efficiency, their performance often diminishes in complex configuration spaces with narrow corridors.…

In the subdivision approach to robot path planning, we need to subdivide the configuration space of a robot into nice cells to perform various computations. For a rigid spatial robot, this configuration space is $SE(3)=\mathbb{R}^3\times…

The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive,…

In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…

Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…

When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…

The L infinity star discrepancy is a measure for how uniformly a point set is distributed in a given space. Point sets of low star discrepancy are used as designs of experiments, as initial designs for Bayesian optimization algorithms, for…

Score distillation sampling (SDS) and its variants have greatly boosted the development of text-to-3D generation, but are vulnerable to geometry collapse and poor textures yet. To solve this issue, we first deeply analyze the SDS and find…