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Mathematics of Machine Learning

Leon Bungert, Prof. Dr.

Prof. Dr. Leon Bungert

W2 Professor with Tenure Track to W3
Professorship for Mathematics III (Mathematics of Machine Learning)
Emil-Fischer-Straße 40
97074 Würzburg
Building: Mathematik Ost (40)
Room: 01.008
Phone: +49 931 31-82849
Fax: +49 931 31-81492

Personal Website

Portrait Leon Bungert

The following links provide information on

Professor (Tenure Track) at the University of Würzburg since 2023

Previous Positions:

  • Junior Research Group Leader at the Technical University of Berlin (2023)
  • Postdoctoral Researcher at the Hausdorff Center for Mathematics, University of Bonn (2021 - 2023)
  • Postdoctoral Researcher at the University of Erlangen-Nürnberg (2020 - 2021)

Education:

  • Ph.D. (summa cum laude) from the University of Erlangen-Nürnberg (2020), title of the thesis: "Nonlinear spectral theory with variational methods"
  • M.Sc. in Mathematics from the University of Erlangen-Nürnberg (2017)
  • B.Sc. in Mathematics from the University of Erlangen-Nürnberg (2016)

Publications

  • 1.
    Convergence rates for Poisson learning to a Poisson equation with measure data
    Bungert, L., Calder, J., Mihailescu, M., Houssou, K., Yuan, A.
    https://arxiv.org/abs/2407.06783 (2024)
  • 1.
    Convergence rates of the fractional to the local Dirichlet problem
    Bungert, L., del Teso, F.
    https://arxiv.org/abs/2408.03299 (2024)
  • 1.
    It begins with a boundary: A geometric view on probabilistically robust learning
    Bungert, L., Trillos, N. G., Jacobs, M., McKenzie, D., Nikolić, Đorđe, Wang, Q.
    https://arxiv.org/abs/2305.18779 (2023)
  • 1.
    Neural Architecture Search via Bregman Iterations
    Bungert, L., Roith, T., Tenbrinck, D., Burger, M.
    https://arxiv.org/abs/2106.02479 (2021)
  • 1.
    The lion in the attic -- A resolution of the Borel--Kolmogorov paradox
    Bungert, L., Wacker, P.
    (2020)

  • 1.
    A mean curvature flow arising in adversarial training
    Bungert, L., Laux, T., Stinson, K.
    Journal de Mathématiques Pures et Appliquées 192, 103625 (2024)
  • 1.
    Polarized consensus-based dynamics for optimization and sampling
    Bungert, L., Roith, T., Wacker, P.
    Mathematical Programming (2024)
  • 1.
    Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian
    Bungert, L., Calder, J., Roith, T.
    Annals of Applied Probability 34, 3870-3910 (2024)
  • 1.
    Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning
    Bungert, L., Stinson, K.
    Calculus of Variations and Partial Differential Equations 63, 114 (2024)
  • 1.
    The infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
    Bozorgnia, F., Bungert, L., Tenbrinck, D.
    Journal of Scientific Computing 98, 40 (2024)
  • 1.
    The convergence rate of $p$-harmonic to infinity-harmonic functions
    Bungert, L.
    Communications in Partial Differential Equations 48, 1323-1339 (2024)
  • 1.
    The geometry of adversarial training in binary classification
    Bungert, L., García Trillos, N., Murray, R.
    Information and Inference: A Journal of the IMA 12, 921-968 (2023)
  • 1.
    The inhomogeneous $p$-Laplacian equation with Neumann boundary conditions in the limit $ ptoinfty$
    Bungert, L.
    Advances in Continuous and Discrete Models 2023, 1-17 (2023)
  • 1.
    Uniform convergence rates for Lipschitz learning on graphs
    Bungert, L., Calder, J., Roith, T.
    IMA Journal of Numerical Analysis 43, 2445-2495 (2023)
  • 1.
    Complete Deterministic Dynamics and Spectral Decomposition of the Linear Ensemble Kalman Inversion
    Bungert, L., Wacker, P.
    SIAM/ASA Journal on Uncertainty Quantification (2023)
  • 1.
    Eigenvalue problems in $mathrmL^infty$: optimality conditions, duality, and relations with optimal transport
    Bungert, L., Korolev, Y.
    Communications of the American Mathematical Society 2, 345–373 (2022)
  • 1.
    Continuum Limit of Lipschitz Learning on Graphs
    Roith, T., Bungert, L.
    Foundations of Computational Mathematics (2022)
  • 1.
    A Bregman Learning Framework for Sparse Neural Networks
    Bungert, L., Roith, T., Tenbrinck, D., Burger, M.
    Journal of Machine Learning Research 23, 1-43 (2022)
  • 1.
    Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals
    Bungert, L., Burger, M., Chambolle, A., Novaga, M.
    Analysis & PDE 14, 823-860 (2021)
  • 1.
    Nonlinear power method for computing eigenvectors of proximal operators and neural networks
    Bungert, L., Hait-Fraenkel, E., Papadakis, N., Gilboa, G.
    SIAM Journal on Imaging Sciences 14, 1114-1148 (2021)
  • 1.
    Structural analysis of an $L$-infinity variational problem and relations to distance functions
    Bungert, L., Korolev, Y., Burger, M.
    Pure and Applied Analysis 2, 703–738 (2020)
  • 1.
    Localization of Passive 3-D Coils as an Inverse Problem: Theoretical Analysis and a Numerical Method
    Doß, M., Bungert, L., Cichon, D., Brauer, H., Psiuk, R.
    IEEE Transactions on Magnetics 56, 1-10 (2020)
  • 1.
    Asymptotic profiles of nonlinear homogeneous evolution equations of gradient flow type
    Bungert, L., Burger, M.
    Journal of Evolution Equations 20, 1061-1092 (2020)
  • 1.
    Variational regularisation for inverse problems with imperfect forward operators and general noise models
    Bungert, L., Burger, M., Korolev, Y., Schönlieb, C.-B.
    Inverse Problems 36, 125014 (2020)
  • 1.
    Robust Image Reconstruction with Misaligned Structural Information
    Bungert, L., Ehrhardt, M. J.
    IEEE Access 8, 222944-222955 (2020)
  • 1.
    Solution paths of variational regularization methods for inverse problems
    Bungert, L., Burger, M.
    Inverse Problems 35, 105012 (2019)
  • 1.
    Robust Blind Image Fusion for Misaligned Hyperspectral Imaging Data
    Bungert, L., Ehrhardt, M. J., Reisenhofer, R.
    PAMM 18, e201800033 (2018)
  • 1.
    Blind image fusion for hyperspectral imaging with the directional total variation
    Bungert, L., Coomes, D. A., Ehrhardt, M. J., Rasch, J., Reisenhofer, R., Schönlieb, C.-B.
    Inverse Problems 34, 044003 (2018)
  • 1.
    Comparison of two local discontinuous Galerkin formulations for the subjective surfaces problem
    Aizinger, V., Bungert, L., Fried, M.
    Computing and Visualization in Science 18, 193-202 (2018)
  • 1.
    A discontinuous Galerkin method for the subjective surfaces problem
    Bungert, L., Aizinger, V., Fried, M.
    Journal of Mathematical Imaging and Vision 58, 147-161 (2017)

  • 1.
    Improving Robustness against Real-World and Worst-Case Distribution Shifts through Decision Region Quantification
    Schwinn, L., Bungert, L., Nguyen, A., Raab, R., Pulsmeyer, F., Precup, D., Eskofier, B., Zanca, D.
    In: Chaudhuri, K., Jegelka, S., Song, L., Szepesvari, C., Niu, G., and Sabato, S. (eds.) Proceedings of the 39th International Conference on Machine Learning. pp. 19434-19449. PMLR (2022)
  • 1.
    Chapter 13 - Gradient flows and nonlinear power methods for the computation of nonlinear eigenfunctions
    Bungert, L., Burger, M.
    In: Trélat, E. and Zuazua, E. (eds.) Numerical Control: Part A. pp. 427-465. Elsevier (2022)
  • 1.
    Identifying untrustworthy predictions in neural networks by geometric gradient analysis
    Schwinn, L., Nguyen, A., Raab, R., Bungert, L., Tenbrinck, D., Zanca, D., Burger, M., Eskofier, B.
    In: de Campos, C. and Maathuis, M. H. (eds.) Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence. pp. 854-864. PMLR (2021)
  • 1.
    CLIP: Cheap Lipschitz Training of Neural Networks
    Bungert, L., Raab, R., Roith, T., Schwinn, L., Tenbrinck, D.
    In: Elmoataz, A., Fadili, J., Quéau, Y., Rabin, J., and Simon, L. (eds.) Scale Space and Variational Methods in Computer Vision. pp. 307-319. Springer International Publishing, Cham (2021)
  • 1.
    Computing nonlinear eigenfunctions via gradient flow extinction
    Bungert, L., Burger, M., Tenbrinck, D.
    In: International Conference on Scale Space and Variational Methods in Computer Vision. pp. 291-302. Springer (2019)