Chaos-Free Networks are Stable Recurrent Neural Networks
This provides a stable architecture for identifying nonlinear dynamical systems, addressing a domain-specific issue in machine learning for control or system identification.
The paper tackled the problem of chaotic dynamics in gated recurrent neural networks (RNNs) used for nonlinear system identification by introducing the Decoupled-Gate Network (DGN), a variant that unconditionally satisfies incremental input-to-state stability (delta-ISS) while maintaining modeling capabilities.
Gated Recurrent Neural Networks (RNNs) are widely used for nonlinear system identification due to their high accuracy, although they often exhibit complex, chaotic dynamics that are difficult to analyze. This paper investigates the system-theoretic properties of the Chaos-Free Network (CFN), an architecture originally proposed to eliminate the chaotic behavior found in standard gated RNNs. First, we formally prove that the CFN satisfies Input-to-State Stability (ISS) by design. However, we demonstrate that ensuring Incremental ISS (delta-ISS) still requires specific parametric constraints on the CFN architecture. Then, to address this, we introduce the Decoupled-Gate Network (DGN), a novel structural variant of the CFN that removes internal state connections in the gating mechanisms. Finally, we prove that the DGN unconditionally satisfies the delta-ISS property, providing an incrementally stable architecture for identifying nonlinear dynamical systems without requiring complex network training modifications. Numerical results confirm that the DGN maintains the modeling capabilities of standard architectures while adhering to these rigorous stability guarantees.