Strengthening the mathematical foundations of modern AI approaches is of utmost importance to unleash their power, but also to understand their limitations. Many new developments in the field, such as Multi-Task Learning, Generative AI or large language models are applied in a rather heuristic way and methods are optimized often based on try-and-error procedures only, or for specific applications lacking generalizability. We here aim at improving the situation by building a solid foundation of AI methods and applications.

Research Focus

We create, extend, and refine mathematical techniques in three major fields.

• We aim for a comprehensive, mathematically sound framework for learning transformation rules in abstract rewriting systems,
• We develop new methods for stochastic models addressing the often-observed problem of outliers in classification or stochastic time series, and
• We advance the field of learning theory in various respects.

Newly developed methods and approaches are shared with the ScaDS.AI Dresden/Leipzig partners to support their research. In particular, we cooperate with ScaDS.AI Dresden/Leipzig partners in:

• Life Science and Medicine,
• Earth and Environmental Sciences,
• Big Data Analytics,
• Knowledge Representation and Engineering,
• Graph-based Artificial Intelligence, and
• Methods and Hardware for Neuro-inspired Computing.

Aims

Emerging topics which we aim to address by our future work comprise for example:

• Development of geometric methods for data analysis and representation learning
• Language models for social media analysis and philology
• Combining AI and natural intelligence based time-series models
• General approaches for graph transformation systems