I'm interested in applying mathematics in artificial intelligence but only by solving purely mathematical problems.
Is this possible? And what fields of mathematics are most applicable?
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You might be interested in Markov decision process and things like convergence properties of Q-learning. – Shashi Sep 12 '19 at 12:54
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Another area is applications of Probabilistic Graphical Models to Deep Learning. While PGMs were typically used in the early development of deep learning, concepts from the field such as variational learning and learning distributions of parameters through Bayesian methods are starting to gain traction again to help Neural Networks confront uncertainty. This is opposed to the frequentist Maximum likelihood learning (point estimates of parameters ). – dylan7 Sep 12 '19 at 13:15
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There is also explainbility of "black box" methods such as neural networks. There has been research that used fields from Topology, Differential Geometry and knot theory to analysis to understand how Nueral Networks manipulate feature space and well as pinpoint which features are considered most important. As well find bounds on learning, and develop possible alternative feature extractors to Neural Networks. In addition, there is Geometric Deep Learning, which tackles data that forms complex manifolds. – dylan7 Sep 12 '19 at 13:37
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Formalizing the concrete problems in machine learning and AI is a pure math problem. – reuns Sep 12 '19 at 14:24