“Theoretical Foundations of Deep Learning” (SPP 2298)
Deadline: 1. Dezember 2023
In May 2020, the Senate of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) established the Priority Programme “Theoretical Foundations of Deep Learning” (SPP 2298). The programme is designed to run for six years. The present call invites proposals for the second (and last) three-year funding period.
We currently witness the impressive success of deep learning in real-world applications, ranging from autonomous driving to game intelligence to the health care sector. At the same time, deep learning-based methods have a similarly strong impact on science, often replacing state-of-the-art classical model-based methods to solve mathematical problems such as inverse problems or partial differential equations. However, despite this outstanding success, most of the research on deep neural networks is empirically driven and mathematical foundations are largely missing. Moreover, in several special but important cases these techniques dramatically fail under small perturbations such as adversarial examples in image classification, which calls for improvements driven by a theoretical underpinning.
The key goal of this Priority Programme is the development of a comprehensive theoretical foundation of deep learning. The research within the programme will be structured along three complementary points of view, namely
- the statistical point of view regarding neural network training as a statistical learning problem and studying expressivity, learning, optimisation and generalisation,
- the applications point of view focusing on safety, robustness, interpretability and fairness, and
- the mathematical methodologies point of view relating to developing and theoretically analysing novel deep learning-based approaches to solve inverse problems and partial differential equations.
The research questions to be addressed within this Priority Programme are of a truly interdisciplinary nature and can only be solved by a joint effort of mathematics and computer science. Mathematical methods and models throughout mathematics are required, including algebraic geometry, analysis, applied probability, approximation theory, differential geometry, discrete mathematics, functional analysis, optimal control, optimisation and topology.
A fundamental role is similarly played by statistics as well as theoretical computer science. In this sense, methods from mathematics, statistics and computer science are at the core of this Priority Programme. Successful proposals address a genuine contribution to the understanding and the theoretical foundations of deep learning along the above-mentioned three complementary points of view. Projects aiming “only” at the application of existing methods of deep learning or their further development without theoretical foundations may not be funded within the framework of the programme.
