Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence

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Generalization of Deep Neural Networks


Master's thesis / Bachelor's thesis / guided research



  • Strong machine learning knowledge
  • Solid knowledge in probability theory
  • Proficiency with Python
  • (Preferred) Proficiency with deep learning frameworks (TensorFlow or PyTorch)


Deep neural networks (DNNs) have shown success in various domains (such as image classification, speech recognition, playing games, etc.) over the last decades. However, the theoretical properties of DNNs, particularly their remarkable generalization abilities, largely remain unclear to the scientific community. DNNs used in practice are usually strongly over-parametrized, i.e., they have many more parameters than training samples. According to classical statistical learning theory, such models are prone to overfitting, i.e., they perform much worse on test data than on training data. Surprisingly, DNNs often do generalize well to test data in practice, directly challenging classical statistical learning theory. Therefore, we need a new theory of DNNs' generalization and more thorough experiments that precede the theory.