The Geometrization of AI: Bridging the Gap Between Geometric Structures and Statistical Models

This year-long theme aims to explore how geometric concepts, such as geodesics, curvature, symmetries, and metrics, are being used to shape the future of artificial intelligence and statistical learning about two TDAI strategic research directions: Foundations of AI and Responsible and Ethical Data Science. The sub-themes below blend theoretical exploration with practical application, inspiring discussions and innovations at the intersection of geometry and AI.

1. Curvature in Statistics: Geometry Meets AI
2. Latent Spaces and Hidden Realities: Geometry in Generative Models
3. Latent Geometry: Enabling Knowledge Transfer and Data Integration
4. Quantum Meets Geometry: Towards the Future of AI
5. Learning Robust Models with Little Data: Domain Knowledge and Geometric Constraints
6. Privacy and Efficiency: Group Theory in AI
7. Fairness and Safety: Geometric Approaches to Ethical AI

These programmatic components are designed to build a vibrant, collaborative ecosystem that drives forward the understanding and application of geometric concepts in AI. By combining research, education, and funding, this proposal aims to create a space where interdisciplinary ideas can thrive and shape the future of AI through the lens of geometry.

The proposed Geometrization of AI initiative has the potential to fundamentally reshape the theoretical foundations of AI by integrating advanced geometric insights into machine learning, statistical modeling, and responsible AI development. By investigating curvature, latent spaces, quantum-inspired geometry, and privacy-preserving techniques, this program will tackle critical challenges in AI interpretability, robustness, and efficiency.