Partner laboratories: LIP6 – Sorbonne Université, Dept. of Statistics – Stanford University
The discovery of hyperbolic geometry was a fairly important event in the history of mathematics and science in general. Indeed, hyperbolic spaces have many applications in various branches of science such as general relativity (with Minkowski's notion of space-time), in cosmology (FLRW models are the main candidates for modeling the shape of the universe as a whole), in number theory (modular shapes have solved several number theory riddles) etc. In recent years new applications of hyperbolic geometry in the field of artificial intelligence and deep learning have emerged.
Several research studies have shown that hyperbolic spaces are more capable of capturing complex data such as graphs, texts and images than their Euclidean counterparts.
In this context, the project "Machine learning with hyperbolic neural networks" aims to
• explore the efficiency of hyperbolic neural networks for concrete applications,
• compare their performances with Euclidean neural networks,
• determine whether hyperbolic algorithms provide more robust, interpretable and safe results than their Euclidean analogs.
This project is carried out in collaboration with Université de Sorbonne and Stanford university.