Related papers: Geometric Model Checking of Continuous Space
Large language models (LLMs) show strong performance across natural language processing (NLP), mathematical reasoning, and programming, and recent large reasoning models (LRMs) further emphasize explicit reasoning. Yet their computational…
Model checking has been successfully used in many computer science fields, including artificial intelligence, theoretical computer science, and databases. Most of the proposed solutions make use of classical, point-based temporal logics,…
Cyber-Physical Systems (CPS) consist of inter-wined computational (cyber) and physical components interacting through sensors and/or actuators. Computational elements are networked at every scale and can communicate with each other and with…
This paper shows that a variety of software model-checking algorithms can be seen as proof-search strategies for a non-standard proof system, known as a cyclic proof system. Our use of the cyclic proof system as a logical foundation of…
The goal of the Semantic Scene Completion (SSC) task is to simultaneously predict a completed 3D voxel representation of volumetric occupancy and semantic labels of objects in the scene from a single-view observation. Since the…
This paper introduces GeoChain, a large-scale benchmark for evaluating step-by-step geographic reasoning in multimodal large language models (MLLMs). Leveraging 1.46 million Mapillary street-level images, GeoChain pairs each image with a…
Among the approximation methods for the verification of counter systems, one of them consists in model-checking their flat unfoldings. Unfortunately, the complexity characterization of model-checking problems for such operational models is…
Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead…
Large vision-language models (VLMs) still struggle with reliable 3D spatial reasoning, a core capability for embodied and physical AI systems. This limitation arises from their inability to capture fine-grained 3D geometry and spatial…
Large language models (LLMs) have demonstrated strong reasoning capabilities in text-based mathematical problem solving; however, when adapted to visual reasoning tasks, particularly geometric problem solving, their performance…
Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…
Large Language Models (LLMs) demonstrate ever-increasing abilities in mathematical and algorithmic tasks, yet their geometric reasoning skills are underexplored. We investigate LLMs' abilities in constructive geometric problem-solving one…
Spatial labeling assigns labels to specific spatial locations to characterize their spatial properties and relationships, with broad applications in scientific research and practice. Measuring the similarity between two spatial labelings is…
New era has unlocked exciting possibilities for extending Large Language Models (LLMs) to tackle 3D vision-language tasks. However, most existing 3D multimodal LLMs (MLLMs) rely on compressing holistic 3D scene information or segmenting…
Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…
Network centrality measures play a crucial role in understanding graph structures, assessing the importance of nodes, paths, or cycles based on directed or reciprocal interactions encoded by vertices and edges. Estrada and Ross extended…
Establishing accurate point-to-point correspondences between non-rigid 3D shapes remains a critical challenge, particularly under non-isometric deformations and topological noise. Existing functional map pipelines suffer from ambiguities…
Polyhedral meshes (PM) - meshes having planar faces - have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate.…
Geospatial Location Embedding (GLE) helps a Large Language Model (LLM) assimilate and analyze spatial data. GLE emergence in Geospatial Artificial Intelligence (GeoAI) is precipitated by the need for deeper geospatial awareness in our…
This paper presents ModelGuard, a sampling-based approach to runtime model validation for Lipschitz-continuous models. Although techniques exist for the validation of many classes of models the majority of these methods cannot be applied to…