Related papers: From axial C-hedra to general P-nets
Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shapes with mathematical…
Generic polyhedra are interesting mathematical objects to study in their own right. In this paper, we initialize a systematic study of two-dimensional generic polyhedra with an eye towards applications to low-dimensional topology,…
Discrete Koenigs nets are a special class of discrete surfaces that play a fundamental role in discrete differential geometry, in particular in the study of discrete isothermic and minimal surfaces. Recently, it was shown by Bobenko and…
Given a bi-invariant metric on a group, we construct a version of an asymptotic cone without using ultrafilters. The new construction, called the directional asymptotic cone, is a contractible topological group equipped with a complete…
In contrast to the somewhat abstract, group theoretical approach adopted by many papers, our work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions. This derivation is based on…
Convolutional Neural Networks (CNNs) can provide accurate object classification. They can be extended to perform object detection by iterating over dense or selected proposed object regions. However, the runtime of such detectors scales as…
We propose a classification of polyhedra (planar, $3$-connected graphs) according to their type i.e., their set of quantities of common neighbours for each pair of distinct vertices. For every (finite) set of non-negative integers, we…
We study a new class of networks, generated by sequences of letters taken from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary…
This paper systematically investigates the geometry of fundamental quantum cones, the separable cone ($\mathscr{P}_+$) and the Positive Partial Transpose (PPT) cone ($\mathcal{P}_{\mathrm{PPT}}$), under generalized non-commutative…
In this work, merging ideas from compatible discretisations and polyhedral methods, we construct novel fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. The spaces and operators that appear in these…
We introduce a new general-purpose approach to deep learning on 3D surfaces, based on the insight that a simple diffusion layer is highly effective for spatial communication. The resulting networks are automatically robust to changes in…
In this paper, we introduce Channel-wise recurrent convolutional neural networks (RecNets), a family of novel, compact neural network architectures for computer vision tasks inspired by recurrent neural networks (RNNs). RecNets build upon…
A graph associahedron is a polytope dual to a simplicial complex whose elements are induced connected subgraphs called tubes. Graph associahedra generalize permutahedra, associahedra, and cyclohedra, and therefore are of great interest to…
In this paper we study G-surfaces, a rather unknown surface class originally defined by Calapso, and show that the coordinate surfaces of a Guichard net are G-surfaces. Based on this observation, we present distinguished Combescure…
This paper presents a new clustering algorithm for symmetric positive semi-definite (SPSD) matrices, called K-Tensors. The method identifies structured subsets of the SPSD cone characterized by common principal component (CPC)…
The categorical modeling of Petri nets has received much attention recently. The Dialectica construction has also had its fair share of attention. We revisit the use of the Dialectica construction as a categorical model for Petri nets…
Implicit surface representations, such as signed-distance functions, combined with deep learning have led to impressive models which can represent detailed shapes of objects with arbitrary topology. Since a continuous function is learned,…
We generalize regular subdivisions (polyhedral complexes resulting from the projection of the lower faces of a polyhedron) introducing the class of recursively-regular subdivisions. Informally speaking, a recursively-regular subdivision is…
Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we…
Motivated by the design of flexible nets, we classify all nets of arbitrary size m x n that admit a continuous family of area-preserving Combescure transformations. There are just two different classes. The nets in the first class are…