Related papers: Geometric Model Checking of Continuous Space

Statistical Model Checking (SMC) is a trade-off between testing and formal verification. The core idea of the approach is to conduct some simulations of the system and verify if they satisfy some given property. In this paper we show that…

Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user…

Algorithmic meta-theorems explain the tractability of large classes of computational problems by linking logical expressibility with structural graph properties. While extensions of first-order logic such as FO+dp admit efficient model…

We introduce cs-topologies, or topologies of open complemented subsets, as a new approach to constructive topology that preserves the duality between open and closed subsets of classical topology. Complemented subsets were used successfully…

Geometric models and Teichm\"uller structures have been introduced for the space of smooth expanding circle endomorphisms and for the space of uniformly symmetric circle endomorphisms. The latter one is the completion of the previous one…

3D Visual Grounding (3DVG) focuses on locating objects in 3D scenes based on natural language descriptions, serving as a fundamental task for embodied AI and robotics. Recent advances in Multi-modal Large Language Models (MLLMs) have…

A challenge in advancing Visual-Language Models (VLMs) is determining whether their failures on abstract reasoning tasks, such as Bongard problems, stem from flawed perception or faulty top-down reasoning. To disentangle these factors, we…

Language models have become very popular recently and many claims have been made about their abilities, including for commonsense reasoning. Given the increasingly better results of current language models on previous static benchmarks for…

Symbolic and graphical tools, such as Mathematica, enable precise visualization and analysis of void spaces in sphere packings. In the cubic close packing (CCP, or face-centred cubic packing; FCC) arrangement these voids can be partitioned…

Regular model checking is a well-established technique for the verification of regular transition systems (RTS): transition systems whose initial configurations and transition relation can be effectively encoded as regular languages. In…

Standard statistical learning theory predicts that Large Language Models (LLMs) should overfit because their parameter counts vastly exceed the number of training tokens. Yet, in practice, they generalize robustly. We propose that the…

(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we introduce an…

We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Buesemann, our concept also applies to metric spaces that might…

Precise spatial understanding from multi-view images remains a fundamental challenge for Multimodal Large Language Models (MLLMs), as their visual representations are predominantly semantic and lack explicit geometric grounding. While…

Spatial reasoning is a fundamental capability of multimodal large language models (MLLMs), yet their performance in open aerial environments remains underexplored. In this work, we present Open3D-VQA, a novel benchmark for evaluating MLLMs'…

Vision-Language Models (VLMs) have recently emerged as powerful tools, excelling in tasks that integrate visual and textual comprehension, such as image captioning, visual question answering, and image-text retrieval. However, existing…

As an emerging task that integrates perception and reasoning, topology reasoning in autonomous driving scenes has recently garnered widespread attention. However, existing work often emphasizes "perception over reasoning": they typically…

Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…

Verifying quantum systems has attracted a lot of interest in the last decades.In this paper, we study the quantitative model-checking of quantum continuous-time Markov chains (quantum CTMCs). The branching-time properties of quantum CTMCs…

Explainable AI (XAI) is crucial for building transparent and trustworthy machine learning systems, especially in high-stakes domains. Concept Bottleneck Models (CBMs) have emerged as a promising ante-hoc approach that provides…