258 citations · 2.4k across the 118 of their papers we have counts for
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Lipschitz constant estimation for general neural network architectures using control tools
Patricia Pauli, Dennis Gramlich, Frank Allgöwer
This paper is devoted to the estimation of the Lipschitz constant of general neural network architectures using semidefinite programming. For this purpose, we interpret neural netw…
Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activations
Patricia Pauli, Aaron Havens, Alexandre Araujo +4
Recently, semidefinite programming (SDP) techniques have shown great promise in providing accurate Lipschitz bounds for neural networks. Specifically, the LipSDP approach (Fazlyab…
Lipschitz-bounded 1D convolutional neural networks using the Cayley transform and the controllability Gramian
Patricia Pauli, Ruigang Wang, Ian R. Manchester +1
We establish a layer-wise parameterization for 1D convolutional neural networks (CNNs) with built-in end-to-end robustness guarantees. In doing so, we use the Lipschitz constant of…
Lipschitz constant estimation for 1D convolutional neural networks
Patricia Pauli, Dennis Gramlich, Frank Allgöwer
In this work, we propose a dissipativity-based method for Lipschitz constant estimation of 1D convolutional neural networks (CNNs). In particular, we analyze the dissipativity prop…
Neural network training under semidefinite constraints
Patricia Pauli, Niklas Funcke, Dennis Gramlich +2
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particu…
Training robust neural networks using Lipschitz bounds
Patricia Pauli, Anne Koch, Julian Berberich +2
Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in…