Related papers: Conformal Geometric Algebra as a Symbolic Interfac…

Modern ultra-high-resolution image synthesis relies heavily on the robust generative capacity of large-scale pre-trained Latent Diffusion Models (LDMs). While recent representation alignment methods have proven effective by distilling…

3D scene reconstruction and understanding have gained increasing popularity, yet existing methods still struggle to capture fine-grained, language-aware 3D representations from 2D images. In this paper, we present GALA, a novel framework…

Geometric Algebra (GA) presents challenges to learners due to its highly abstract mathematical structure and complex operational rules, as translating algebraic manipulations into concrete geometric interpretations is a non-intuitive…

Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have…

Large Language Models (LLMs) have demonstrated strong performance across a wide range of tasks, yet they still struggle with complex mathematical reasoning, a challenge fundamentally rooted in deep structural dependencies. To address this…

Knowledge graph completion (KGC) aims to infer new knowledge and make predictions from knowledge graphs. Recently, large language models (LLMs) have exhibited remarkable reasoning capabilities. LLM-enhanced KGC methods primarily focus on…

Identifying affordance regions on 3D objects from semantic cues is essential for robotics and human-machine interaction. However, existing 3D affordance learning methods struggle with generalization and robustness due to limited annotated…

In order to provide a robot with the ability to understand and react to a user's natural language inputs, the natural language must be connected to the robot's underlying representations of the world. Recently, large language models (LLMs)…

We show that if PGA is understood as a subalgebra of CGA in mathematically correct sense, then the flat objects share the same representation in PGA and CGA. Particularly, we treat duality in PGA. This leads to unification of PGA and CGA…

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…

Plane Geometry Problem Solving (PGPS) is a multimodal reasoning task that aims to solve a plane geometric problem based on a geometric diagram and problem textual descriptions. Although Large Language Models (LLMs) possess strong reasoning…

In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform…

Despite significant advancements in text generation and reasoning, Large Language Models (LLMs) still face challenges in accurately performing complex arithmetic operations. Language model systems often enable LLMs to generate code for…

A new simplified approach for teaching electromagnetism is presented using the formalism of geometric algebra (GA) which does not require vector calculus or tensor index notation, thus producing a much more accessible presentation for…

Alignment in large language models (LLMs) is still largely static: after training, the policy is frozen. DPO, GRPO methods typically imprint one behavior into the weights, leaving little runtime control beyond prompt hacks or expensive…

Knowledge graph representation learning approaches provide a mapping between symbolic knowledge in the form of triples in a knowledge graph (KG) and their feature vectors. Knowledge graph embedding (KGE) models often represent relations in…

We propose GALA, a novel representation of 3D shapes that (i) excels at capturing and reproducing complex geometry and surface details, (ii) is computationally efficient, and (iii) lends itself to 3D generative modelling with modern,…

We introduce Graphical Algebraic Geometry (GAG), a family of diagrammatic languages extending the Graphical Linear Algebra programme. We construct several languages within this family and prove that they are universal and complete for the…

Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial…

Vision-language models like CLIP have demonstrated remarkable zero-shot transfer capabilities. However, their susceptibility to imperceptible adversarial perturbations remains a critical security concern. While test-time defenses offer a…