324 citations · 1.4k across the 135 of their papers we have counts for
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Robust identifiability for symbolic recovery of differential equations
Hillary Hauger, Philipp Scholl, Gitta Kutyniok
Recent advancements in machine learning have transformed the discovery of physical laws, moving from manual derivation to data-driven methods that simultaneously learn both the str…
Computability of Classification and Deep Learning: From Theoretical Limits to Practical Feasibility through Quantization
Holger Boche, Vit Fojtik, Adalbert Fono +1
The unwavering success of deep learning in the past decade led to the increasing prevalence of deep learning methods in various application fields. However, the downsides of deep l…
Compositional Construction of Barrier Functions for Switched Impulsive Systems
Katharina Bieker, Hugo Tadashi Kussaba, Philipp Scholl +4
Many systems occurring in real-world applications, such as controlling the motions of robots or modeling the spread of diseases, are switched impulsive systems. To ensure that the…
Generalization Bounds for Message Passing Networks on Mixture of Graphons
Sohir Maskey, Gitta Kutyniok, Ron Levie
We study the generalization capabilities of Message Passing Neural Networks (MPNNs), a prevalent class of Graph Neural Networks (GNN). We derive generalization bounds specifically…
Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning
Raffaele Paolino, Sohir Maskey, Pascal Welke +1
We introduce -loopy Weisfeiler-Leman (-WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, -MPNN, that can count cycles up…
Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations
Beatrice Lorenz, Aras Bacho, Gitta Kutyniok
This paper provides rigorous error bounds for physics-informed neural networks approximating the semilinear wave equation. We provide bounds for the generalization and training err…
Mathematical Algorithm Design for Deep Learning under Societal and Judicial Constraints: The Algorithmic Transparency Requirement
Holger Boche, Adalbert Fono, Gitta Kutyniok
Deep learning still has drawbacks in terms of trustworthiness, which describes a comprehensible, fair, safe, and reliable method. To mitigate the potential risk of AI, clear obliga…