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Recent breakthroughs have spurred claims that large language models (LLMs) match gold medal Olympiad to graduate level proficiency on mathematics benchmarks. In this work, we examine these claims in detail and assess the extent to which…
PyG (PyTorch Geometric) has evolved significantly since its initial release, establishing itself as a leading framework for Graph Neural Networks. In this paper, we present Pyg 2.0 (and its subsequent minor versions), a comprehensive update…
Training deep learning models on limited data while maintaining generalization is one of the fundamental challenges in molecular property prediction. One effective solution is transferring knowledge extracted from abundant datasets to those…
Equivariance is a powerful prior for learning physical dynamics, yet exact group equivariance can degrade performance if the symmetries are broken. We propose object-centric world models built with geometric algebra neural networks,…
Image Matching Challenge 2024 is a competition focused on building 3D maps from diverse image sets, requiring participants to solve fundamental computer vision challenges in image matching across varying angles, lighting, and seasonal…
Img2LaTeX is a practically important task that involves translating mathematical expressions and structured visual content from images into LaTeX code. In recent years, vision-language models (VLMs) have achieved remarkable progress across…
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…
In this work, we report on strategies and results of our initial approach for modernization of Titan2D code. Titan2D is a geophysical mass flow simulation code designed for modeling of volcanic flows, debris avalanches and landslides over a…
The Adam optimization method has achieved remarkable success in addressing contemporary challenges in stochastic optimization. This method falls within the realm of adaptive sub-gradient techniques, yet the underlying geometric principles…
Geometry theorem proving forms a major and challenging component in the K-12 mathematics curriculum. A particular difficult task is to add auxiliary constructions (i.e, additional lines or points) to aid proof discovery. Although there…
For analysing real-world networks, graph representation learning is a popular tool. These methods, such as a graph autoencoder (GAE), typically rely on low-dimensional representations, also called embeddings, which are obtained through…
Evaluating the symbolic reasoning of large language models (LLMs) calls for geometry benchmarks that require multi-step proofs grounded in both text and diagrams. However, existing benchmarks are often limited in scale and rarely provide…
We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…
This paper introduces GA-Unity, the first Unity package specifically designed for seamless integration of Geometric Algebra (GA) into collaborative networked applications. Indeed, in such contexts, it has been demonstrated that using…
AI models underpin data-centric applications from image and text processing to scientific discovery in biology, physics, and chemistry. Yet developing them remains heavily manual, requiring practitioners to design architectures, build…
Earth observation foundation models encode land surface information into dense embedding vectors, yet the geometric structure of these representations and its implications for downstream reasoning remain underexplored. We characterize the…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
We introduce the open-ended, modular, self-improving Omega AI unification architecture which is a refinement of Solomonoff's Alpha architecture, as considered from first principles. The architecture embodies several crucial principles of…
This paper presents a geometric approach to the classical isoperimetric problem by analysing the efficiency of regular polygons in enclosing maximum area for a fixed perimeter. Using efficiency metrics, it proves that regular polygons…
Trimming techniques are efficient ways to generate complex geometries in Computer-Aided Design(CAD). In this paper, an improved isogeometric analysis(IGA) method for trimmed geometries is proposed. We will show that the proposed method…