Supervisor: Professor Michael Farber
Project description:
In broad terms the project will be focused on themes of mathematical foundations of AI.
More specifically, the project will be centred around methods of learning of Boolean functions of many variables using recent progress in geometry of simplicial complexes.
In our recent work we developed theory of the Rado simplicial complex which is a universal and unique geometric object. We also developed theory of ample simplicial complexes which are finite approximations to the Rado complex and retain certain degree of universality. We analysed methods of generating ample simplicial complexes and criteria of ampleness. The proposed phd project will use the correspondence and explicit constructions relating Boolean functions of many variables with simplicial complexes and analysing the notions of universality and ampleness, translated into the language of Boolean functions. The Boolean functions corresponding to ample simplicial complexes will be of main interest as they may potentially lead to new efficient methods of machine learning. Such Boolean functions will have important extendability property which will allow growing Boolean functions by adding additional information and data.
Further information:
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Entry requirements
Fees and funding