Related papers: Geometric Model Checking of Continuous Space
In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed topological properties. This leads to satisfactory topological characterizations of closed…
Spatial intelligence, which refers to the ability to reason about geometric and physical structure from visual observations, remains a core challenge for multimodal large language models. Despite promising performance, recent multimodal…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
Graph-based representations such as Scene Graphs enable localization in structured indoor environments by matching a locally observed graph, constructed from sensor data, to a prior map. This process is particularly challenging in…
This paper is a study of the interaction between the combinatorics of boundaries of convex polytopes in arbitrary dimension and their metric geometry. Let S be the boundary of a convex polytope of dimension d+1, or more generally let S be a…
As language models are increasingly used in scientific workflows, evaluating their ability to propose sets of explanations-not just a single correct answer-becomes critical. Many scientific problems are underdetermined: multiple,…
Declarative spatial reasoning denotes the ability to (declaratively) specify and solve real-world problems related to geometric and qualitative spatial representation and reasoning within standard knowledge representation and reasoning (KR)…
Multimodal learning is an essential paradigm for addressing complex real-world problems, where individual data modalities are typically insufficient to accurately solve a given modelling task. While various deep learning approaches have…
Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have…
An S-approximation space is a novel approach to study systems with uncertainty that are not expressible in terms of inclusion relations. In this work, we further examined these spaces, mostly from a topological point of view by a…
Simultaneous Localisation and Mapping (SLAM) is one of the fundamental problems in autonomous mobile robots where a robot needs to reconstruct a previously unseen environment while simultaneously localising itself with respect to the map.…
This article describes a volumetric approach for procedural shape modeling and a new Procedural Shape Modeling Language (PSML) that facilitates the specification of these models. PSML provides programmers the ability to describe shapes in…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
For safety and robustness of AI systems, we introduce topological parallax as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure.…
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…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined…
Spatial cognition is fundamental to real-world multimodal intelligence, allowing models to effectively interact with the physical environment. While multimodal large language models (MLLMs) have made significant strides, existing benchmarks…
Geometry problem-solving (GPS), a challenging task requiring both visual comprehension and symbolic reasoning, effectively measures the reasoning capabilities of multimodal large language models (MLLMs). Humans exhibit strong reasoning…
Hyperproperties extend trace properties to express properties of sets of traces, and they are increasingly popular in specifying various security and performance-related properties in domains such as cyber-physical systems, smart grids, and…