AI in Mathematics Group

Lectures in Winter Semester

Our working group offers the following lectures in the winter semester 2022/23:

Mathematical Methods in AI


The course introduces the relevant mathematical concepts and methods in the field of artificial intelligence (AI) and conveys the practical skills to apply these methods in guided practical projects dealing with real life data and issues.The recurrent theme is in establishing a joint stochastic/statistic perspective based on optimization paradigm and complexity estimates - for various mathematical methods and algorithms deployed in machine learning (ML) and AI.

The topics covered include:

  • Introduction, biological, neurophysiological and mathematical foundations of living neural networks, mathematical implications of differences between living and common synthetic classes of artificial neural networks;
  • Euclidean, non-Euclidean and information-theoretical measures in ML/AI;
  • transformation of measures, embedding theorems (Whitney and Takens);
  • deterministic vs. stochastic approximation of functions and integrals;
  • deterministic vs. stochastic unconstrained optimization methods in AI;
  • constrained optimization methods in AI, soft vs. hard constraints, necessary concepts from linear and quadratic programming;
  • mathematical foundations of Markovian and Bayesian learning;
  • dimension reduction and feature selection in ML/AI as an optimization problem for various measures;
  • ill-posedness and “small data learning challenge”, information-theoretic vs. more common (L1/L2) regularizations in learning problems;
  • mathematical concepts in eXplainable AI (XAI), Scalable Probabilistic Approximation family of learning methods and its extensions.

Contact Hours

4 SWS / 56 h Lectures
2 SWS / 28 h Exercise Classes

Prerequisites (Contents)

A profound knowledge and skills in the following areas of mathematics are required:

  • Analysis
  • Linear Algebra
  • Probability Theory and Statistics

Optional requirements (nice to have):

It is desirable (but not mandatory) that students participating in this course have basic knowledge and experience in programming with one out of the following three languages: MATLAB, Python, Julia. We recommend MATLAB.

Helpful for the course would also be mastering principles of more advanced Frechet-calculus with matrices (from the "matrix cookbook").

Frequency of occurence

The lecture is irregularly given.

Link to KIS: [KIS]

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