相关论文: From 9-IM Topological Operators to Qualitative Spa…

The Constructive Solid Geometry (CSG) is a data model providing a set of binary Boolean operators such as Union, Difference and Intersection. In this work, these operators are used to compute topological relations between objects defined by…

Lane-topology prediction is a critical component of safe and reliable autonomous navigation. An accurate understanding of the road environment aids this task. We observe that this information often follows conventions encoded in natural…

One of the essential tasks in connectomics is the morphology analysis of neurons and organelles like mitochondria to shed light on their biological properties. However, these biological objects often have tangled parts or complex branching…

Mobile robots require comprehensive scene understanding to operate effectively in diverse environments, enriched with contextual information such as layouts, objects, and their relationships. Although advances like neural radiation fields…

Human prowess in intuitive physics remains unmatched by machines. To bridge this gap, we argue for a fundamental shift towards brain-inspired computational principles. This paper introduces the Spatiotemporal Relational Neural Network…

Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different…

The recent adoption of artificial intelligence in robotics has driven the development of algorithms that enable autonomous systems to adapt to complex social environments. In particular, safe and efficient social navigation is a key…

This paper tackles the task of estimating the topology of road networks from aerial images. Building on top of a global model that performs a dense semantical classification of the pixels of the image, we design a Convolutional Neural…

Rationally null-homologous links in Seifert fibered spaces may be represented combinatorially via labeled diagrams. We introduce an additional condition on a labeled link diagram and prove that it is equivalent to the existence of a…

In this study, we explore the impact of network topology on the approximation capabilities of artificial neural networks (ANNs), with a particular focus on complex topologies. We propose a novel methodology for constructing complex ANNs…

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…

In this paper we present algorithms for computing the topology of planar and space rational curves defined by a parametrization. The algorithms given here work directly with the parametrization of the curve, and do not require to compute or…

In order to perform complex actions in human environments, an autonomous robot needs the ability to understand the environment, that is, to gather and maintain spatial knowledge. Topological map is commonly used for representing large…

The standard cosmological model with cold dark matter posits a hierarchical formation of structures. We introduce topological neural networks (TNNs), implemented as message-passing neural networks on higher-order structures, to effectively…

We consider how to directly extract a road map (also known as a topological representation) of an initially-unknown 2-dimensional environment via an online procedure that robustly computes a retraction of its boundaries. In this article, we…

In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered…

We develop a topological lens on relational schema design by encoding functional dependencies (FDs) as simplices of an abstract simplicial complex. This dependency complex exposes multi-attribute interactions and enables homological…

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…

We introduce the Rule Network with Selective Logical Operators (RNS), a novel neural architecture that employs \textbf{selective logical operators} to adaptively choose between AND and OR operations at each neuron during training. Unlike…