Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation
Janina Enrica Schütte and Martin Eigel, ICLR 2024 Workshop on AI4DifferentialEquations, 2024.
Adversarial flows: A gradient flow characterization of adversarial attacks
Lukas Weigand, Tim Roith, Martin Burger, 2024.
A Measure Theoretical Approach to the Mean-field Maximum Principle for Training NeurODEs
B. Bonnet, C. Cipriani, M. Fornasier and H. Huang. Nonlinear Analysis, 2023.
A Nonlocal Graph-PDE and Higher-Order Geometric Integration for Image Labeling
D. Sitenko, B. Boll and C. Schnörr. SIAM Journal on Imaging Sciences, 2023.
A Geometric Embedding Approach to Multiple Games and Multiple Populations (Preprint)
B. Boll, J. Cassel, P. Albers, S. Petra and C. Schnörr, 2024.
Algebraic Optimization of Sequential Decision Problems
M. Dressler, M. Garrote-Lopez, G. Montafur, J. Müller and K. Rose. Journal of Symbolic Computation, 2023.
Analysis of the Geometric Structure of Neural Networks and Neural ODEs via Morse Functions(Preprint)
Christian Kuehn, Sara-Viola Kuntz
Analysis of Convolutions, Non-linearity and Depth in Graph Neural Networks using Neural Tangent Kernel
M Sabanayagam P. Esser and D. Ghoshdastidar, Transactions on Machine Learning Research, 2024
Analyzing the Sample Complexity of Self-Supervised Image Reconstruction Methods (Preprint)
T. Klug, D. Atik and R. Heckel.
Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures(Preprint)
Martin Eigel, Charles Miranda, Janina Schütte, David Summer, 2023.
Approximation of Separable Control Lyapunov Functions with Neural Networks(Preprint)
Mario Sperl, Jonas Mysliwitz, Lars Grüne
A stochastic variant of replicator dynamics in zero-sum games and its invariant measures, to appear in Physics D: Nonlinear Phenomena
M. Engel, G. Piliouras
Computability of Optimizers (Preprint)
Y. Lee, H. Boche and G. Kutyniok.
Conditional Generative Models Are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problems
F. Altekrüger, P. Hagemann and G. Steidl. TMLR, 2023.
Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching(Preprint)
Jannis Chemseddine, Paul Hagemann, Gabriele Steidl, Christian Wald, 2024.
Continuous Limits of Residual Neural Networks in Case of Large Input Data
M. Herty, A. Thünen, T. Trimborn and G. Visconti. Communications in Applied and Industrial Mathematics, 2023.
Convergence Results for Gradient Flow and Gradient Descent Systems in the Artificial Neural Network Training (Preprint)
A. Ahmadova
Convergent Data-driven Regularizations for CT Reconstruction
S. Kabri, A. Auras, D. Riccio, H. Bauermeister, M. Benning, M. Moeller and M. Burger.
Coupling Analysis of the Asymptotic Behaviour of a Primal-Dual Langevin Algorithm
Martin Burger, Matthias J. Ehrhardt, Lorenz Kuger, Lukas Weigand, 2024.
Critical Points and Convergence Analysis of Generative Deep Linear Networks Trained with Bures-Wasserstein Loss
P. Brechet, K. Papagiannouli, J. An and G. Montafur. Proceeding of the 40th International Conference on Machine Learning, 2023.
Deep Learning Approximations for Non-Local Nonlinear PDEs with Neumann Boundary Conditions
V. Boussange, S. Becker, A. Jentzen, B. Kuckuck and L. Pellisier.
Deep Neural Networks With ReLU, Leaky ReLU, and Softplus Activation Provably Overcome the Curse of Dimensionality for Kolmogorov Partial Differential Equations With Lipschitz Nonlinearities in the Lp-Sense (Preprint)
J. Ackermann, A. Jentzen, T. Kruse, B. Kuckuck and J. L. Padgett.
Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations
L. Gonon and C. Schwab. Analysis and Applications, 2023.
Embedding Capabilities of Neural ODEs (Preprint)
C. Kuehn and S. Kuntz.
Enumeration of Max-pooling Responsed with Generalized Permutohedra (Preprint)
L. Escobar, P. Gallardo, J. Gonzales-Anaya, J. L. Gonzales, G. Montafur and A. H. Morales.
Examples for Separable Control Lyapunov Functions and Their Neural Network Approximation
L. Grüne and M. Sperl. IFAC-PapersOnLine, 2023.
Expected Gradients of Maxout Networks and Consequences to Parameter Initializations
H. Tseran and G. Montafur. Proceeding of the 40th International Conference on Machine Learning, 2023.
Finite Sample Identification of Wide Shallow Neural Networks with Biases (Preprint)
M. Fornasier, T. Klock, M. Mondelli and M. Rauchensteiner.
From NeurODEs to AutoencODEs: a Mean-field Control Framework for Width-varying Neural Networks (Preprint)
C. Cipriani, M. Fornasier and A. Scagliotti.
Function Space and Critical Points of Linear Convoluational Networks (Preprint)
K. Kohn, G. Montafur, V. Shahverdi and M. Trager.
Generalization Analysis of Message Passing Neural Networks on Large Random Graphs
S. Maskey, Y. Lee, R. Levie and G. Kutyniok. Advances in Neural Information Processing Systems, 2022.
Generalized normalizing flows via Markov Chains
P. Hagemann, J. Hertrich and G. Steidl. Cambridge University Press, 2023.
Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Data (Preprint)
B. Boll, D. Gonzalez-Alvarado, S. Petra and C. Schnörr, 2024.
Generative Sliced MMD Flows with Riesz Kernels
J. Hertrich, C. Wald, F. Altekrüger, P. Hagemann.
Generative Modeling of Discrete Joint Distributions by E-Geodesic Flow Matching on Assignment Manifolds (Preprint)
B. Boll, D. Gonzalez-Alvarado and C. Schnörr, 2024.
Generic Unsupervised Optimization for a Latent Variable Model With Exponential Family Observables.
Hamid Mousavi, Jakob Drefs, Florian Hirschberger and Jörg Lücke. Journal of Machine Learning Research , 2023.
Geometry and Convergence of Natural Policy Gradient Methods
J. Müller and G. Montafur. Information Geometry, 2023.
Guidelines for Data-driven Approaches to Study Transitions in Multiscale Systems: the Case of Lyapunov Vectors
A. Viennet, N. Vercauteren, M. Engel and D. Faranda. Chaos, 2022.
Hierarchical Randomized Smoothing
Yan Scholten, Jan Schuchardt, Aleksandar Bojchevski, Stephan Günnemann, 2023.
Improved Representation Learning Through Tensorized Autoencoders
P. Esser, S. Mukherjee, M. Sabanayagam and D. Ghoshdastidar. AISTATS, 2023.
Invariance-Aware Randomized Smoothing Certificates
J. Schuchardt and S. Günnemann. NeurIPS, 2022.
Implicit Bias of Gradient Descent for Mean Squared Error Regression with Wide Neural Networks
H. Jin and G. Montafur. Journal of Machine Learning Research, 2023.
Learning Provably Robust Estimators for Inverse Problems via Jittering (Preprint)
A. Krainovic, M. Soltanolkotabi and R. Heckel.
Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction(Preprint)
Moritz Piening, Fabian Altekrüger, Johannes Hertrich, Paul Hagemann, Andrea Walther, Gabriele Steidl
Learning Theory Can (Sometimes) Explain Generalisation in Graph Neural Networks
P. Esser, L. C. Vankadara and D. Ghoshdastidar. NeurIPS, 2021.
Learning Sparse Codes with Entropy-Based ELBOs
D. Velychko, S. Damm, A. Fischer and J. Lücke, AISTATS, 2024.
Localized Randomized Smoothing for Collective Robustness Certification
J. Schuchardt, T. Wollschläger, A. Bojchevski and S. Günnemann. ICLR, 2023.
Mildly Overparametrized ReLU Networks Have a Favorable Loss Landscape (Preprint)
K. Karhadkar, M. Murray, H. Tseran and G. Montafur.
Modeling Large-Scale Joint Distributions and Inference by Randomized Assignment
B. Boll, J. Schwarz, D. Gonzales-Alvarado, D. Sitenko, S. Petra and C. Schnörr. Scale Space and Variational Methods in Computer Vision, 2023.
Multilevel CNNs for Parametric PDEs (Preprint)
C. Heiß, I. Gühring and M. EIgel.
Mixed noise and posterior estimation with conditional deepGEM
P. Hagemann, J. Hertrich, M. Casfor, S. Heidenreich, G. Steidl , Machine Learning: Science and Technology, Vol 5, Number 3, 2024
Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation (Preprint)
P. Hagemann, L. Mildenberger, M. Ruthotto, G. Steidl and N.T. Yang.
Non-Parametric Representation Learning with Kernels (Preprint)
P. Esser, M. Fleissner and D. Ghoshdastidar.
Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems (Preprint)
Christian Beck, Arnulf Jentzen, Konrad Kleinberg , Thomas Kruse
On Certified Generalization in Structured Prediction (Preprint)
B. Boll and C. Schnörr.
On the Convergence of the ELBO to Entropy Sums (Preprint)
J. Lücke and J. Warnken.
On the Effectiveness of Persistent Homology
R. Turkes, G. Montafur and N. Otter. NeurIPS, 2022.
On the Generalization Analysis of Adversarial Learning
W. Mustafa, Y. Lei and M. Kloft. PMLR, 2023.
PatchNR: Learning From Very Few Images by Patch Normalizing Flow Regularization
F. Altekrüger, A. Denker, P. Hagemann, J. Hertrich, P. Maass and G. Steidl. Inverse Problems, 2023.
Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise
D. Chemnitz and M. Engel, 2023.
(Provable) Adversarial Robustness for Group Equivariant Tasks: Graphs, Point Clouds, Molecules, and More
Jan Schuchardt, Yan Scholten, Stephan Günnemann, 2023
Quantum State Assignment Flows
J. Schwarz, B. Boll, D. Gonzales-Alvarado, D. Sitenko, M. Gärttner, P. Albers and C. Schnörr. Scale Space and Variational Methods in Computer Science, 2023.
Quantum State Assignment Flows
J. Schwarz, J. Cassel, B. Boll, M. Gärttner, P. Albers and C. Schnörr. Entropy, 2023.
Random Feature Neural Networks Learn Black-Scholes Type PDEs Without Curse of Dimensionality
L. Gonon. Journal of Machine Learning Research, 2023.
Randomized Message-Interception Smoothing: Gray-Box Certificates for Graph Neural Networks
Y. Scholten, J. Schuchardt, S. Geisler, A. Bojchevski and S. Günnemann. NeurIPS Proceedings, 2022.
Recent Trends on Nonlinear Filtering for Inverse Problems
M. Herty, E. Iacomini, and G. Visconti. Communications in Applied and Industrial Mathematics, 2022.
Representation Learning Dynamics of Self-Supervised Models (Preprint)
P. Esser, S. Mukherjee and D. Ghoshdastidar.
Reproducing Kernel Hilbert Spaces in the Mean Field Limit
C. Fiedler, M. Herty, M. Rom, C. Segala and S. Trimpe. Kinetic and Related Models, 2023.
Resolution-Invariant Image Classification Based on Fourier Neural Operators
S. Kabri, T. Roith, D. Tenbrick and M. Burger. International Conference on Scale Space and Variational Methods in Computer Vision, 2023.
Robustness and exploration of variational and machine learning approaches to inverse problems: An overview
A. Auras, K. Vaishnavi Gandikota, H. Droege, M. Moeller. GAMM-Mitteilungen, Volume 47, Issue 4, 2024.
Scaling Laws for Deep Learning Based Image Reconstruction
T. Klug and R. Heckel. ICLR, 2023.
Self-Certifying Classification by Linearized Deep Assignment
B. Boll, A. Zeilmann, S. Petra and C. Schnörr. PAMM, 2023.
Separable approximations of optimal value functions under a decaying sensitivity assumption (Preprint)
M. Sperl, L. Saluzzi, L. Grüne and D. Kalise.
Stable Recovery of Entangled Weights: Towards Robust Identification of Deep Neural Networks from Minimal Samples
C. Fiedler, M. Fornasier, T. Klock and M. Rauchensteiner. Applied and Computational Harmonic Analysis, 2023.
Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint
P. Hagemann, J. Hertrich and G. Steidl. SIAM/ASA Journal on Uncertainty Quantification, 2022.
Structure Preserving Neural Networks: A Case Study in the Entropy Closure of the Boltzmann Equation
S. Schotthöfer, T. Xiao, M. Frank and C. Hauck. PMLR, 2022.
Supermodular Rank: Set Function Decomposition and Optimization (Preprint)
R. Sonthalia, A. Seigal and G. Montafur.
The ELBO of Variational Autoencoders Converges to a Sum of Entropies
S. Damm, D. Forster, D. Velychko, Z. Dai, A. Fischer and J. Lücke. PMLR, 2023.
The Lyapunov Spectrum for Conditioned Random Dynamical Systems (Preprint)
M. M. Castro, D. Chemnitz, H. Chu, M. Engel, J. S. W. Engel and M. Rasmussen.
Turnpike Properties of Optimal Boundary Control Problems with Random Linear Hyperbolic Systems
M. Gugat and M. Herty. ESAIM: Control, Optimisation and Calculus of Variations, 2023.
Using neural networks to accelerate the solution of the Boltzmann equation
T. Xiao and M. Frank. Journal of Computational Physics, 2021.
When can we Approximate Wide Contrastive Models with Neural Tangent Kernels and Principal Component Analysis?(Preprint)
Gautham Govind Anil, Pascal Esser, Debarghya Ghoshdastidaral, 2024.
Which Spaces can be Embedded in Reproducing Kernel Hilbert Spaces?
Max Schölle, Ingo Steinwart, 2023.
