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Vision-Language Models (VLMs) still lack robustness in spatial intelligence, demonstrating poor performance on spatial understanding and reasoning tasks. We attribute this gap to the absence of a visual geometry learning process capable of…

We consider path planning for a rigid spatial robot with 6 degrees of freedom (6 DOFs), moving amidst polyhedral obstacles. A correct, complete and practical path planner for such a robot has never been achieved, although this is widely…

Recent studies have extended the application of large language models (LLMs) to geographic problems, revealing surprising geospatial competence even without explicit spatial supervision. However, LLMs still face challenges in spatial…

Large language models (LLMs) are increasingly adopted for a variety of tasks with implicit graphical structures, such as planning in robotics, multi-hop question answering or knowledge probing, structured commonsense reasoning, and more.…

Large language models (LLMs) have shown great success in text modeling tasks across domains. However, natural language exhibits inherent semantic hierarchies and nuanced geometric structure, which current LLMs do not capture completely…

We introduce compute-grounded reasoning (CGR), a design paradigm for spatial-aware research agents in which every answerable sub-problem is resolved by deterministic computation before a language model is asked to generate. Spatial Atlas…

Automated theorem proving in Euclidean geometry, particularly for International Mathematical Olympiad (IMO) level problems, remains a major challenge and an important research focus in Artificial Intelligence. In this paper, we present a…

Internet image collections containing photos captured by crowds of photographers show promise for enabling digital exploration of large-scale tourist landmarks. However, prior works focus primarily on geometric reconstruction and…

Multi-step theorem prediction is a central challenge in automated reasoning. Existing neural-symbolic approaches rely heavily on supervised parametric models, which exhibit limited generalization to evolving theorem libraries. In this work,…

Recent advancements in Large Language Models (LLMs) have sparked interest in their formal reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used to assess the mathematical reasoning of models on…

Large Language Models (LLMs) for Graph Reasoning have been extensively studied over the past two years, involving enabling LLMs to understand graph structures and reason on graphs to solve various graph problems, with graph algorithm…

Large language models (LLMs) are increasingly used for tasks that implicitly reduce to Boolean satisfiability (SAT), yet their reasoning ability on SAT remains unclear. We present a systematic study of LLMs on 2-SAT and 3-SAT, together with…

Robots collaborating with humans must convert natural language goals into actionable, physically grounded decisions. For example, executing a command such as "go two meters to the right of the fridge" requires grounding semantic references,…

We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…

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…

Current multimodal large language models (MLLMs) often underperform on mathematical problem-solving tasks that require fine-grained visual understanding. The limitation is largely attributable to inadequate perception of geometric…

Logic provides a controlled testbed for evaluating LLM-based reasoners, yet standard SAT-style benchmarks often conflate surface difficulty (length, wording, clause order) with the structural phenomena that actually determine…

Three-dimensional geospatial analysis is critical for applications in urban planning, climate adaptation, and environmental assessment. However, current methodologies depend on costly, specialized sensors, such as LiDAR and multispectral…

This research focuses on assessing the ability of large language models (LLMs) in representing geometries and their spatial relations. We utilize LLMs including GPT-2 and BERT to encode the well-known text (WKT) format of geometries and…

Reasoning segmentation is a challenging vision-language task that aims to output the segmentation mask with respect to a complex, implicit, and even non-visual query text. Previous works incorporated multimodal Large Language Models (MLLMs)…