Stability of State and Costate Dynamics in Continuous Time Recurrent Neural Networks

The notion of stability plays a crucial role in ensuring the safe development of a model in a lifelong learning context.This paper investigates the fundamental aspects of stability in a class of continuous-time recurrent neural networks which include both state and costate variables.The latter are directly inherited from optimal control theory, and they act as adjoint variables closely related to gradient terms.Stability is investigated both in terms of state and of costate dynamics, showing the key conditions that must be satisfied to produce bounded dynamics in the forward and learning stages.* This work was