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Investigators

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Theoretical Foundations of Deep Learning

Parallel to the **impressive success of deep learning** in real-world applications ranging from autonomous driving to gaming intelligence and healthcare, deep learning-based methods are now also making a strong impact in science, replacing or complementing state-of-the-art classical model-based methods in solving mathematical problems such as inverse problems or partial differential equations.

However, despite the outstanding successes, most of the research on deep neural networks is empirically driven and their **theoretical-mathematical foundations are largely lacking**. The main goal of this priority program is to develop a comprehensive theoretical foundation of deep learning.

**The statistical perspective**, which views neural network training as a statistical learning problem and investigates expressivity, learning, optimization, and generalization,**The application perspective**, which focuses on security, robustness, interpretability, and fairness**The mathematical-methodological perspective**, which develops and theoretically analyzes novel Deep Learning-based approaches to solving inverse problems and partial differential equations.

The research questions to be addressed in this priority program are to a large extent **interdisciplinary** **in nature **and can only be solved by a joint effort of mathematics and computer science.

Mathematical methods and concepts from **all areas of mathematics** are required, including algebraic geometry, analysis, stochastics, approximation theory, differential geometry, discrete mathematics, functional analysis, optimal control, optimization, and topology. **Statistics** and **theoretical computer science** also play a fundamental role. In this sense, methods from mathematics, statistics and computer science form the core of this priority program.

The first annual meeting of the priority program provided a great opportunity to meet each other in person, exchange ideas and present current research.

We had a great start with the first iteration of the Junior Researcher Seminar, part of the priority program in Mathematical Foundations of AI.

The Junior Researcher Seminar series came to completion with exciting talks about various topics from deep learning theory.

Find the latest news and upcoming events from the various groups researching artificial intelligence and its applications at LMU Munich.

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