Related papers: VoronoiNet: General Functional Approximators with …

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…

In this paper, we study a generalization of the classical Voronoi diagram, called clustering induced Voronoi diagram (CIVD). Different from the traditional model, CIVD takes as its sites the power set $U$ of an input set $P$ of objects. For…

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an…

A Voronoi diagram is a basic geometric structure that partitions the space into regions associated with a given set of sites, such that all points in a region are closer to the corresponding site than to all other sites. While being…

Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction,…

Implicit Neural Representations (INRs) have emerged in the last few years as a powerful tool to encode continuously a variety of different signals like images, videos, audio and 3D shapes. When applied to 3D shapes, INRs allow to overcome…

Vision-and-Language Navigation (VLN) has long been constrained by the limited diversity and scalability of simulator-curated datasets, which fail to capture the complexity of real-world environments. To overcome this limitation, we…

The discovery of new catalysts is one of the significant topics of computational chemistry as it has the potential to accelerate the adoption of renewable energy sources. Recently developed deep learning approaches such as graph neural…

Recently, implicit graph neural networks (GNNs) have been proposed to capture long-range dependencies in underlying graphs. In this paper, we introduce and justify two weaknesses of implicit GNNs: the constrained expressiveness due to their…

Deep neural networks have usually to be compressed and accelerated for their usage in low-power, e.g. mobile, devices. Recently, massively-parallel hardware accelerators were developed that offer high throughput and low latency at low power…

We study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the…

In this work, we introduce a novel deep learning architecture, Variable Length Embeddings (VLEs), an autoregressive model that can produce a latent representation composed of an arbitrary number of tokens. As a proof of concept, we…

We introduce a NeRF-based active mapping system that enables efficient and robust exploration of large-scale indoor environments. The key to our approach is the extraction of a generalized Voronoi graph (GVG) from the continually updated…

Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we…

In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models. We propose a graph embedding network that projects propositional formulae (and assignments) onto a manifold via an augmented Graph…

Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a…

In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (108 points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in…

We use Lie sphere geometry to describe two large categories of generalized Voronoi diagrams that can be encoded in terms of the Lie quadric, the Lie inner product, and polyhedra. The first class consists of diagrams defined in terms of…

In current deep network architectures, deeper layers in networks tend to contain hundreds of independent neurons which makes it hard for humans to understand how they interact with each other. By organizing the neurons by correlation,…