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Found 7 papers, 2 papers with code
Perspectives on Contractivity in Control, Optimization, and Learning
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms.
Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees
Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty.
Positive Competitive Networks for Sparse Reconstruction
Our analysis leverages contraction theory to characterize the behavior of a family of firing-rate competitive networks for sparse reconstruction with and without non-negativity constraints.
Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach
Third, we use the upper bounds of the Lipschitz constants and the upper bounds of the tight inclusion functions to design two algorithms for the training and robustness verification of implicit neural networks.
Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks
We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs).
Robustness Certificates for Implicit Neural Networks: A Mixed Monotone Contractive Approach
First, given an implicit neural network, we introduce a related embedded network and show that, given an $\ell_\infty$-norm box constraint on the input, the embedded network provides an $\ell_\infty$-norm box overapproximation for the output of the given network.
Robust Implicit Networks via Non-Euclidean Contractions
Additionally, we design a training problem with the well-posedness condition and the average iteration as constraints and, to achieve robust models, with the input-output Lipschitz constant as a regularizer.
