Related papers: Conformal Geometric Algebra as a Symbolic Interfac…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
Discrete motion tokenization has recently enabled Large Language Models (LLMs) to serve as versatile backbones for motion understanding and motion-language reasoning. However, existing pipelines typically decouple motion quantization from…
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…
Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying…
Text-to-3D generation has advanced rapidly, yet state-of-the-art models, encompassing both optimization-based and feed-forward architectures, still face two fundamental limitations. First, they struggle with coarse semantic alignment, often…
Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable…
Logarithmic representations of the conformal Galilean algebra (CGA) and the Exotic Conformal Galilean algebra ({\sc ecga}) are constructed. This can be achieved by non-decomposable representations of the scaling dimensions or the rapidity…
While recent advancements in machine learning, such as LLMs, are revolutionizing software development and creative industries, they have had minimal impact on engineers designing mechanical parts, which remains largely a manual process.…
In this work, we analyze the optimization dynamics of generative fine-tuning. We observe that under the Flow Matching framework, the standard MSE objective can be formulated as a Quadratic Form governed by a dynamically evolving Neural…
A 3D scene graph represents a compact scene model by capturing both the objects present and the semantic relationships between them, making it a promising structure for robotic applications. To effectively interact with users, an embodied…
Vision-Language models like CLIP have been widely adopted for various tasks due to their impressive zero-shot capabilities. However, CLIP is not suitable for extracting 3D geometric features as it was trained on only images and text by…
Graph reasoning agents operating from natural-language inputs must solve a coupled problem: they must reconstruct a structured graph instance from text, decide whether existing computational assets are sufficient, interact with tools under…
We present a framework that pioneers the prediction of photochemical conversion in complex three-dimensionally printed objects, introducing a challenging new computer vision task: predicting dense, non-visual volumetric physical properties…
Localizing objects and parts from natural language in 3D space is essential for robotics, AR, and embodied AI, yet existing methods face a trade-off between the accuracy and geometric consistency of per-scene optimization and the efficiency…
Global contexts in images are quite valuable in image-to-image translation problems. Conventional attention-based and graph-based models capture the global context to a large extent, however, these are computationally expensive. Moreover,…
This work presents the introduction of UniSG^GA, a novel integrated scenegraph structure, that to incorporates behavior and geometry data on a 3D scene. It is specifically designed to seamlessly integrate Graph Neural Networks (GNNs) and…
We revisit the geometric foundations of mesh representation through the lens of Plane-based Geometric Algebra (PGA), questioning its efficiency and expressiveness for discrete geometry. We find how $k$-simplices (vertices, edges, faces,…
This paper presents a new class of adaptive filters, namely Geometric-Algebra Adaptive Filters (GAAFs). They are generated by formulating the underlying minimization problem (a deterministic cost function) from the perspective of Geometric…
Recent advancements in large language models (LLMs) have demonstrated remarkable text generation capabilities. However, controlling specific attributes of generated text remains challenging without architectural modifications or extensive…
Automatically generating interactive 3D indoor scenes from natural language is crucial for virtual reality, gaming, and embodied AI. However, existing LLM-based approaches often suffer from spatial errors and collisions, in part because…