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arXiv · 2603.17137

Integral Quadratic Constraints for Repeated ReLU

Sahel Vahedi Noori·Bin Hu·Geir Dullerud·Peter Seiler
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Abstract

This paper presents a new dynamic integral quadratic constraint (IQC) for the repeated Rectified Linear Unit (ReLU). These dynamic IQCs can be used to analyze stability and induced $\ell_2$-gain performance of discrete-time, recurrent neural networks (RNNs) with ReLU activation functions. These analysis conditions can be incorporated into learning-based controller synthesis methods, which currently rely on static IQCs. We show that our proposed dynamic IQCs for repeated ReLU form a superset of the dynamic IQCs for repeated, slope-restricted nonlinearities. We also prove that the $\ell_2$-gain bounds are nonincreasing with respect to the horizon used in the dynamic IQC filter. A numerical example using a simple (academic) RNN shows that our proposed IQCs lead to less conservative bounds than existing IQCs.

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Sahel Vahedi Noori, Bin Hu, Geir Dullerud, Peter Seiler. 2026-03-17. Integral Quadratic Constraints for Repeated ReLU. https://arxiv.org/abs/2603.17137

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