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Large language models have seen widespread adoption in math problem-solving. However, in geometry problems that usually require visual aids for better understanding, even the most advanced multi-modal models currently still face challenges…
Large Multimodal Models (LMMs) have achieved impressive success in visual understanding and reasoning, remarkably improving the performance of mathematical reasoning in a visual context. Yet, a challenging type of visual math lies in the…
Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the…
The advancement of 3D language fields has enabled intuitive interactions with 3D scenes via natural language. However, existing approaches are typically limited to small-scale environments, lacking the scalability and compositional…
Vision Language Models (VLMs) exhibit a fundamental semantic-to-geometric gap in spatial reasoning: they excel at qualitative semantic inference but their reasoning operates within a lossy semantic space, misaligned with high-fidelity…
The advancement of Large Vision-Language Models (LVLMs) requires precise local region-based reasoning that faithfully grounds the model's logic in actual visual evidence. However, existing datasets face limitations in scalability due to…
Large Language Models (LLMs) with reasoning are trained to iteratively generate and refine their answers before finalizing them, which can help with applications to mathematics and code generation. We apply code generation with reasoning…
Spatial intelligence spans a rich suite of abilities, including visualising and transforming shapes, mentally rotating objects, judging relational positions and containment, and estimating numerosity. However, it still remains a critical…
Large Multimodal Models (LMMs) face limitations in geometric reasoning due to insufficient Chain of Thought (CoT) image-text training data. While existing approaches leverage template-based or LLM-assisted methods for geometric CoT data…
Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…
Space grounding refers to localizing a set of spatial references described in natural language instructions. Traditional methods often fail to account for complex reasoning -- such as distance, geometry, and inter-object relationships --…
Visual Language Models (VLMs) have increasingly become the main paradigm for understanding indoor scenes, but they still struggle with metric and spatial reasoning. Current approaches rely on end-to-end video understanding or large-scale…
This paper proposes a novel approach to analyzing multi-hop reasoning in language models through Hamiltonian mechanics. We map reasoning chains in embedding spaces to Hamiltonian systems, defining a function that balances reasoning…
Spatial reasoning remains a fundamental challenge for Vision-Language Models (VLMs), with current approaches struggling to achieve robust performance despite recent advances. We identify that this limitation stems from a critical gap:…
As textual reasoning with large language models (LLMs) has advanced significantly, there has been growing interest in enhancing the multimodal reasoning capabilities of large vision-language models (LVLMs). However, existing methods…
Diagram parsing is an important foundation for geometry problem solving, attracting increasing attention in the field of intelligent education and document image understanding. Due to the complex layout and between-primitive relationship,…
Document understanding with multimodal large language models (MLLMs) requires not only accurate answers but also explicit, evidence-grounded reasoning, especially in high-stakes scenarios. However, current document MLLMs still fall short of…
Geolocation, the task of identifying the geographic location of an image, requires abundant world knowledge and complex reasoning abilities. Though advanced large multimodal models (LMMs) have shown superior aforementioned capabilities,…
Grounded understanding of natural language in physical scenes can greatly benefit robots that follow human instructions. In object manipulation scenarios, existing end-to-end models are proficient at understanding semantic concepts, but…
Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…