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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…
We address the problems of measuring geometric similarity between 3D scenes, represented through point clouds or range data frames, and associating them. Our approach leverages macro-scale 3D structural geometry - the relative configuration…
Engineers widely rely on simulation platforms like COMSOL or ANSYS to model and optimise processes. However, setting up such simulations requires expertise in defining geometry, generating meshes, establishing boundary conditions, and…
This paper introduces the new interactive Java sketching software KamiWaAi, recently developed at the University of Fukui. Its graphical user interface enables the user without any knowledge of both mathematics or computer science, to do…
We characterize a compositional architecture of literary primitives in two instruction-tuned large language models (Llama 3.1 8B-Instruct and Gemma 2 9B-IT) via sparse autoencoders on mid-depth residual streams. Four feature classes emerge:…
Generating editable, parametric CAD models from a single image holds great potential to lower the barriers of industrial concept design. However, current multi-modal large language models (MLLMs) still struggle with accurately inferring 3D…
Contrastive learning (CL) aims to preserve relational structure between samples by learning representations that reflect a similarity graph. Yet, the geometry of the resulting embeddings remains poorly understood. Here we show that weighted…
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…
We present an algebraic semantics for governed execution in which governance is axiomatized, compositional, and coterminous with expressibility. The framework, mechanized in 32 Rocq modules (~12,000 lines, 454 theorems, 0 admitted), is…
Content Warning: This paper may contain unsafe or harmful content generated by LLMs that may be offensive to readers. Large Language Models (LLMs) increasingly serve as tooling platforms through structured output APIs, but the…
The Galilean Conformal Algebra (GCA) arises in taking the non-relativistic limit of the symmetries of a relativistic Conformal Field Theory in any dimensions. It is known to be infinite-dimensional in all spacetime dimensions. In…
Large language models (LLMs) have been proposed as powerful tools for detecting software vulnerabilities, where task-specific fine-tuning is typically employed to provide vulnerability-specific knowledge to the LLMs. However, existing…
In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…
Can a Large Language Model (LLM) solve simple abstract reasoning problems? We explore this broad question through a systematic analysis of GPT on the Abstraction and Reasoning Corpus (ARC), a representative benchmark of abstract reasoning…
Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either…
Tracking objects in 3D space and predicting their 6DoF pose is an essential task in computer vision. State-of-the-art approaches often rely on object texture to tackle this problem. However, while they achieve impressive results, many…
Generating high-quality geometry problems is both an important and challenging task in education. Compared to math word problems, geometry problems further emphasize multi-modal formats and the translation between informal and formal…
Creating interactive scenes often involves complex programming tasks. Although large language models (LLMs) like ChatGPT can generate code from natural language, their output is often error-prone, particularly when scripting interactions…
Compilers use control flow graph (CFG) representations of low-level programs because they are suited to program analysis and optimizations. However, formalizing the behavior and metatheory of CFG programs is non-trivial: CFG programs don't…
This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main…