5 papers
Scalable Incremental Robustness Analysis of Neural Network Feedback Systems
Zichen Wang, Peter Seiler, Geir Dullerud +1
Semidefinite programming (SDP) certificates for feedback systems containing deep neural networks (NNs) typically scale with the total number of neurons, whereas small-gain tests ar…
An Exact, Finite Dimensional Representation for Full-Block, Circle Criterion Multipliers
Felix Biertümpfel, Bin Hu, Geir Dullerud +1
This paper provides the first finite-dimensional characterization for the complete set of full-block, circle criterion multipliers. We consider the interconnection of a discrete-ti…
Discrete-Time Stability Analysis of ReLU Feedback Systems via Integral Quadratic Constraints
Sahel Vahedi Noori, Bin Hu, Geir Dullerud +1
This paper analyzes internal stability of a discrete-time feedback system with a ReLU nonlinearity. This feedback system is motivated by recurrent neural networks. We first review…
A Complete Set of Quadratic Constraints for Repeated ReLU and Generalizations
Sahel Vahedi Noori, Bin Hu, Geir Dullerud +1
This paper derives a complete set of quadratic constraints (QCs) for the repeated ReLU. The complete set of QCs is described by a collection of matrix copositivity conditions. We a…
Stability and Performance Analysis of Discrete-Time ReLU Recurrent Neural Networks
Sahel Vahedi Noori, Bin Hu, Geir Dullerud +1
This paper presents sufficient conditions for the stability and -gain performance of recurrent neural networks (RNNs) with ReLU activation functions. These conditions are d…