DNRF Chair Amir Yehudayoff

Machine learning (ML) and artificial intelligence (AI) have an amazing impact on our world. It brings promises but also dangers. How does it work? Can we trust it? As in many scientific endeavors, a solid mathematical foundation is crucial for finding answers. The research aims to significantly contribute to the mathematical foundations of ML.

As in many scientific endeavors, a solid mathematical foundation is crucial for finding answers. Building rigorous foundations for ML is important for understanding its capabilities, controlling its outcomes, and steering it in preferable directions. It can make ML more efficient and allow us to use less resources. It is also important for effective communication between researchers and developers.

One central goal is providing provable guarantees for specific learning algorithms. Such mathematical guarantees are crucial for trusting the behavior and outcomes of ML and AI. A different goal is to develop and analyze mathematical models for ML. Choosing the correct definitions is crucial for making progress.

The research aims at two main significant contributions to the mathematical foundations of ML. One goal is a better understanding of compression in the context of ML. The second goal is to further develop the theory of list learning, and to subsequently improve our understanding of stability, privacy, and replicability. This could lead to ML algorithms that do not leak sensitive data, and to the ability to replicate the outcomes of ML and AI. We have recently identified that the mathematical field topology can be a powerful tool for achieving both of our goals, and we plan to pursue this further.