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Bart M.N. Smets

Applied Mathematician

Eindhoven University of Technology

Biography

I am a postdoctoral researcher in applied mathematics at the TU Eindhoven in the Geometric Learning and Differential Geometry group of dr.ir. R. Duits. I have a keen interest in both abstract mathematics and its application to new techniques in machine learning and image processing.

In my research I try to bridge neural networks with classic mathematical ideas from geometry and analysis, such as in the PDE-based G-CNN paper. Implementations of techniques I have developed are available as an open source extension to the popular PyTorch deep learning framework, named LieTorch.

Interests

  • Differential Geometry
  • Mathematical Image Analysis
  • Probability Theory
  • Machine Learning
  • Applied Analysis
  • Motorsport
  • History

Education

  • PhD in Applied Mathematics, 2024

    TU Eindhoven

  • MSc in Applied Mathematics, 2019

    TU Eindhoven

  • BSc in Applied Mathematics, 2017

    TU Eindhoven

Publications

Semiring Activation in Neural Networks

We introduce a class of trainable nonlinear operators based on semirings that are suitable for use in neural networks. These operators …

Geodesic Tracking of Retinal Vascular Trees with Optical and TV-Flow Enhancement in SE(2)

Retinal images are often used to examine the vascular system in a non-invasive way. Studying the behavior of the vasculature on the …

Analysis of (sub-)Riemannian PDE-G-CNNs

Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs …

Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking

We introduce a data-driven version of the plus Cartan connection on the 3D homogeneous space $\mathbb{M}_2$ of 2D positions and …

Talks

PDE-based CNNs with Morphological Convolutions

Convolutional neural networks have found wide adoption and great success in image processing yet have drawbacks such as needing huge …