Related papers: Geometric Model Checking of Continuous Space

Although large multimodal models (LMMs) have demonstrated remarkable capabilities in visual scene interpretation and reasoning, their capacity for complex and precise 3-dimensional spatial reasoning remains uncertain. Existing benchmarks…

Spatial reasoning plays a vital role in both human cognition and machine intelligence, prompting new research into language models' (LMs) capabilities in this regard. However, existing benchmarks reveal shortcomings in evaluating…

Cross-modal alignment plays a crucial role in vision-language pre-training (VLP) models, enabling them to capture meaningful associations across different modalities. For this purpose, numerous masked modeling tasks have been proposed for…

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption…

Evaluating the symbolic reasoning of large language models (LLMs) calls for geometry benchmarks that require multi-step proofs grounded in both text and diagrams. However, existing benchmarks are often limited in scale and rarely provide…

Spatial competence is the quality of maintaining a consistent internal representation of an environment and using it to infer discrete structure and plan actions under constraints. Prevailing spatial evaluations for large models are limited…

In many scientific and technological contexts we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal…

This paper investigates Large Language Models (LLMs) ability to assess the economic soundness and theoretical consistency of empirical findings in spatial econometrics. We created original and deliberately altered "counterfactual" summaries…

Understanding the latent space geometry of large language models (LLMs) is key to interpreting their behavior and improving alignment. Yet it remains unclear to what extent LLMs linearly organize representations related to semantic…

This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…

We propose Map2Thought, a framework that enables explicit and interpretable spatial reasoning for 3D VLMs. The framework is grounded in two key components: Metric Cognitive Map (Metric-CogMap) and Cognitive Chain-of-Thought (Cog-CoT).…

Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. This is applied by Du (2010) [A note on cone…

This paper deals with two aspects of relativistic cosmologies with closed (compact and boundless) spatial sections. These spacetimes are based on the theory of General Relativity, and admit a foliation into space sections S(t), which are…

The demand for semantically rich 3D models of indoor scenes is rapidly growing, driven by applications in augmented reality, virtual reality, and robotics. However, creating them from sparse views remains a challenge due to geometric…

Multi-modal Large Language Models (MLLMs) exhibit impressive problem-solving abilities in various domains, but their visual comprehension and abstract reasoning skills remain under-evaluated. To this end, we present PolyMATH, a challenging…

Online services rely on CAPTCHAs as a first line of defense against automated abuse, yet recent advances in multi-modal large language models (MLLMs) have eroded the effectiveness of conventional designs that focus on text recognition or 2D…

The task of 3D semantic scene completion using monocular cameras is gaining significant attention in the field of autonomous driving. This task aims to predict the occupancy status and semantic labels of each voxel in a 3D scene from…

Establishing dense correspondence across 3D shapes is crucial for fundamental downstream tasks, including texture transfer, shape interpolation, and robotic manipulation. However, learning these mappings without manual supervision remains a…

As a voxel-wise labeling task, semantic scene completion (SSC) tries to simultaneously infer the occupancy and semantic labels for a scene from a single depth and/or RGB image. The key challenge for SSC is how to effectively take advantage…

Automated building facade inspection is a critical component of urban resilience and smart city maintenance. Traditionally, this field has relied on specialized discriminative models (e.g., YOLO, Mask R-CNN) that excel at pixel-level…