There is an introduction to my research for non-mathematicians and mathematicians from other research areas, including general themes and a few words on selected publications. Other pages in this section may use some terminology and concepts of advanced mathematics.
Currently, I am mostly interested in various topics in machine learning, among them - Functions which are well approximated by deep, but not shallow neural networks.
- Convolutional neural networks and the use of symmetry in machine learning.
- Various optimization algorithms for the weights of a neural network and the impact of parameter initialization.
The techniques involved stem from optimal transport theory, PDEs, the calculus of variations, high-dimensional probability, statistical learning theory, and functional analysis. Other interests of mine are differential geometry, geometric measure theory, and the continuum mechanics of solids.
You can find a complete list of my publications here, on Orcid and ArXiv. Some publications are also available on cvgmt or DeepAI respectively.
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