Human beings have an innate ability to learn from samples without conscious effort, yet teaching computers to do the same has long been a challenging task. In recent years, the field of artificial intelligence evolved rapidly. The most well-known tool is deep learning, a method for training deep neural networks (DNNs). Inspired by the human brain, DNNs consist of multiple layers that learn different levels of representation and abstraction, enabling machines to understand speech, classify images, drive autonomously, and excel at complex games. DNNs are often referred to as "black boxes" as it is challenging to understand empirically and theoretically how the reasoning within a trained DNN works.
To address this issue, our research focuses on developing regression and (image) classification models that allow for the analysis and explanation of DNN behavior. Proving theoretical properties of the deep learning optimization algorithm is extremely challenging. We investigate how different algorithmic regularization methods affect training and study the implicit regularisation effect that occurs during the training. Finally, we also delve into the theory of biological neural networks by considering the brain as a statistical method for supervised learning.
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