Non-Euclidean Foundation Models and Geometric Learning: Advancing AI Beyond Euclidean Frameworks

In the era of foundation models and Large Language Models (LLMs), Euclidean space is the de facto geometric setting of our machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental limitations. Non-Euclidean learning is quickly gaining traction. Non-Euclidean spaces, such as hyperbolic, spherical, and mixed-curvature spaces, have been shown to provide more efficient and effective representations for data with intrinsic geometric properties, like hierarchy, symmetry, and heterogeneity.

Integrating foundation models with non-Euclidean spaces has great potential to enhance their ability to capture and model the underlying structures and relationships in complex real-world data, leading to better performance, generalization, and interpretability. This workshop focuses on the intersection of Non-Euclidean representation learning and Foundation Models, exploring its potential benefits, challenges, and future directions.