Project period

01 April 2024 to 31 March 2025 (12 months)

Project description

Within the scientific discipline of machine learning, methods as well as concepts from several areas of computer science and mathematics are employed. These involve theoretical frameworks from the intersection of statistics and mathematical logic, learning in dynamical systems and applied techniques from numerical optimization. While in each of these areas questions in their own interest are pursued, problems arising in the theory and application of machine learning bear the potential to bring together scientists in this wide range of diverse disciplines.

The concepts lying at the core of this network platform are the description and application of formal learning processes. These processes take place in artificial systems with the aim to solve a problem by learning from examples and generalizing them after the learning phase. Learning processes involve several distinct steps, in which the aforementioned areas from computer science and mathematics come into play. The overall aim of this network platform is to benefit from a clustered series of round-table discussions on topics within the broad area of learning theory in order to reveal problems that the involved internal and external researchers can approach together, each from the angle of their own discipline.

Consider examples such as efficiently learning optimal policies for controlled dynamical systems from data, a core aspect of ‘reinforcement learning’. This problem category involves both statistical challenges (efficient learning) and computational challenges (solving underlying optimization problems efficiently). Other examples revolve around determining which properties can be learned from data and under what conditions – for instance, discerning when causal effects can be inferred from data and how. Additionally, we are intrigued by the fundamental limits of various learning tasks, seeking answers to questions such as which quantities can be learned and which cannot be determined based on a given dataset. This notably involves establishing explicit bounds on the sample complexity of the underlying learning problem.

In the foundational area of mathematical logic, we aim to develop mathematical frameworks, i.e., mathematical descriptions, of the concept of learning. One approach is to observe applied methods and formalize them in a suitable logical language. A main question that we ask in this context is whether the given formal framework is foundationally sound. For instance, we scrutinize mathematical procedures that we observe in applications and deliver a more general theoretical description of the procedure isolating the applied concept rather than the context-specific deployed algorithms and functions. In turn, the question follows whether these general theoretical descriptions can lead to further applications via practical implementation.

In empirical research, formal learning theory as sketched above is beneficial for the analysis of network data (i.e., overlapping dyadic data). Such analyses usually involve staggered processes (pipelines) of computational data transformations, e.g., geometrical embeddings, distance/walk/similarity-based clusterings, or just database operations. Under-standing the inferential logics and inferential statistics of whole pipelines is helpful in coping with reproducibility issues in empirical research. A possible long-term outcome could be a theoretical foundation of interpretable pipelines, e.g., for learning clusterings in dynamical networks.

Although all participants in this network platform are active in the intersection between computer science and mathematics, each individual researcher is highly specialized in their own particular area within the exact sciences. Each of these specializations requires a solid understanding of an extensive background theory, which complicates a swift exchange of ideas and tackling problems together. The innovation of this network platform lies in our mutual endeavor to face this challenge: Thorough discussions within a biweekly research colloquium will stimulate the exchange of ideas and concepts among the internal researchers and external guests. Over a long-term period, we hope to identify problems stemming from learning theory, which lead the participants of this network platform to initiate new interdisciplinary collaborations.

Structural and local integration of  the network platform

The round-table discussions of this network platform take place in the form of an interdisciplinary research colloquium. This colloquium is held approximately every two weeks during the lecture period of the summer semester 2024. Both internal and external researchers are invited as speakers to present a specific problem and corresponding methods from their scientific standpoint. Each speaker is specifically instructed to make their theoretical and applied approaches accessible to the interdisciplinary audience.

The co-operation between the different parties of this network platform ensures that a wide range of topics dealing with different aspects of learning theory is presented. Moreover, each involved group can activate their broad scientific network in order to attract researchers from a variety of institutions and areas. We invite several external researchers – most being at a postdoctoral stage of their scientific career – as guest speakers for our research colloquium. Some of the potential guests are already involved in active collaborations with participants of this network platform.