Related papers: Geometric Model Checking of Continuous Space
Advancing towards artificial superintelligence requires rich and intelligent perceptual capabilities. A critical frontier in this pursuit is overcoming the limited spatial understanding of Multimodal Large Language Models (MLLMs), where…
The possibility of obtaining an open set of regular cosmological models is discussed. Cylindrical stiff perfect fluid cosmologies are studied in detail. The condition for geodesic completeness is easy to check. A large family of…
Humans build shared spatial understanding by communicating partial, viewpoint-dependent observations. We ask whether Multimodal Large Language Models (MLLMs) can do the same, aligning distinct egocentric views through dialogue to form a…
Spatial consistency is a fundamental property of the visual world and a key requirement for models that aim to understand physical reality. Despite recent advances, multimodal large language models (MLLMs) often struggle to reason about 3D…
Multimodal language models (MLLMs) are increasingly being applied in real-world environments, necessitating their ability to interpret 3D spaces and comprehend temporal dynamics. Current methods often rely on specialized architectural…
In monitoring, we algorithmically check if a single behavior satisfies a property. Here, we consider monitoring for Multi-Lane Spatial Logic (MLSL). The behavior is given as a finite transition sequence of MLSL and the property is that a…
Multimodal large language models (MLLMs) have exhibited remarkable performance in various visual tasks, yet still struggle with spatial reasoning. Recent efforts mitigate this by injecting geometric features from 3D foundation models, but…
Loop closure, as one of the crucial components in SLAM, plays an essential role in correcting the accumulated errors. Traditional appearance-based methods, such as bag-of-words models, are often limited by local 2D features and the volume…
Reasoning about spatial relationships between objects is essential for many real-world robotic tasks, such as fetch-and-delivery, object rearrangement, and object search. The ability to detect and disambiguate different objects and identify…
Solid geometry problem solving demands spatial mathematical reasoning that integrates spatial intelligence and symbolic reasoning. However, most existing multimodal mathematical reasoning benchmarks focus primarily on 2D plane geometry,…
GeoGebra is an open source mathematics education software tool being used in thousands of schools worldwide. Since version 4.2 (December 2012) it supports symbolic computation of locus equations as a result of joint effort of mathematicians…
Recently there has been a great attention from the scientific community towards the use of the model-checking technique as a tool for test generation in the simulation field. This paper aims to provide a useful mean to get more insights…
Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…
Self-supervised learning (SSL) has emerged as a desirable paradigm in computer vision due to the inability of supervised models to learn representations that can generalize in domains with limited labels. The recent popularity of SSL has…
Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…
System development is not a linear, one-shot process. It proceeds through refinements and revisions. To support assurance that the system satisfies its requirements, it is desirable that continuous verification can be performed after each…
Geometric problem solving constitutes a critical branch of mathematical reasoning, requiring precise analysis of shapes and spatial relationships. Current evaluations of geometric reasoning in vision-language models (VLMs) face limitations,…
Reasoning about security properties involves reasoning about where the information of a system is located, and how it evolves over time. While most security analysis techniques need to cope with some notions of information locality and…
In this paper, we define notions of $P_{Z}(S)$-metric and $P_{Z}(S)$-metric space and we show that every $P_{Z}(S)$-metric Space, analogous to an ordinary metric space and generally, a $\Lambda$-metric space, is a topological space, and in…
Large vision-language models (VLMs) show strong multimodal understanding but still struggle with 3D spatial reasoning, such as distance estimation, size comparison, and cross-view consistency. Existing 3D-aware methods either depend on…