Related papers: Geometry-Aware Probabilistic Circuits via Voronoi …
Winner-takes-all training is a simple learning paradigm, which handles ambiguous tasks by predicting a set of plausible hypotheses. Recently, a connection was established between Winner-takes-all training and centroidal Voronoi…
The application of Voronoi and Delaunay tessellation based methods for reconstructing continuous fields from discretely sampled data sets is discussed. The succesfull operation as ``multidimensional interpolation'' method is corroborated…
We show that most arithmetic circuit lower bounds and relations between lower bounds naturally fit into the representation-theoretic framework suggested by geometric complexity theory (GCT), including: the partial derivatives technique…
The purpose of this note is to clarify the effect of the finite size of spherical particles upon the characteristics of their spatial distribution through a random Poisson process (RPP). This information is of special interest when using…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
VORO++ is a software library written in C++ for computing the Voronoi tessellation, a technique in computational geometry that is widely used for analyzing systems of particles. VORO++ was released in 2009 and is based on computing the…
Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…
Probabilistic atlases (PAs) have long been used in standard segmentation approaches and, more recently, in conjunction with Convolutional Neural Networks (CNNs). However, their use has been restricted to relatively standardized structures…
Spatial statistical analysis of multivariate volumetric data can be challenging due to scale, complexity, and occlusion. Advances in topological segmentation, feature extraction, and statistical summarization have helped overcome the…
The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative randomized algorithm facilitating the approximation of Voronoi…
We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs of the neural networks are not directly observable, and…
We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to…
We present a technique to adaptively bin sparse X-ray data using weighted Voronoi tesselations (WVTs). WVT binning is a generalisation of Cappellari & Copin's (2001) Voronoi binning algorithm, developed for integral field spectroscopy. WVT…
Deep generative models (DGMs) have recently demonstrated remarkable success in capturing complex probability distributions over graphs. Although their excellent performance is attributed to powerful and scalable deep neural networks, it is,…
In Computer Vision, edge detection is one of the favored approaches for feature and object detection in images since it provides information about their objects boundaries. Other region-based approaches use probabilistic analysis such as…
Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…
We introduce a non-parametric density estimator deemed Radial Voronoi Density Estimator (RVDE). RVDE is grounded in the geometry of Voronoi tessellations and as such benefits from local geometric adaptiveness and broad convergence…
Interpretability methods for deep neural networks mainly focus on the sensitivity of the class score with respect to the original or perturbed input, usually measured using actual or modified gradients. Some methods also use a…
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
Probabilistic spin logic (PSL) is a recently proposed computing paradigm based on unstable stochastic units called probabilistic bits (p-bits) that can be correlated to form probabilistic circuits (p-circuits). These p-circuits can be used…