Homotopy type theory, relating Martin-Löf’s dependent type theory to homotopy theory, was originally based in large part on Voevodsky’s model of type theory in simplicial sets.  More recently, models in cubical sets have turned out to enjoy various computational and technical advantages; meanwhile, models have also been given in large classes of suitably-structured (∞,1)-categories, although these are as yet less well understood.  From the point of view of logic, this offers new ways to understand equality (in the form of Martin-Löf's identity type); from the point of view of topology, it provides a powerful language for reasoning axiomatically about spaces.

This course will give an introduction to homotopy type theory, with a focus on its models.  We will not assume prior knowledge of type theory, but will start with a brief introduction focusing on homotopical aspects.  Similarly, we will not assume prior experience of homotopical algebra, but will introduce tools as they are required.

Due to its remarkable predictive capabilities, deep learning (DL) becomes the most rapidly developing field in data science, machine learning and modern statistics. Despite its success, DL methods remain largely as “black boxes” in terms of how and why they work. This course provides the entry ticket to crack open the working principles of DL methods from the viewpoint of information theory (IT), aiming to deeply understand how information is processed inside neural network (NN) models. During the course, basic and relevant concepts in DL and IT will be reviewed, followed by a systematic study of recent frameworks, debates and perspectives on the information processes of deep NNs and their optimization processes. Instead of predictions and technicalities, focuses of the course will be put on understanding, explanation, validation and generalization of the DL methods. In the later part of the course, recent exciting developments of “AI scientists” that can discover the laws of nature will be covered with a scrutinization of the underlying mechanism of information processing.


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IMPORTANT: Due to the participation of students from other Universities, the course will be carried out in Zoom. Zoom ID: 622 7799 3636

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