Continual Learning of Dynamical Systems in Recurrent Neural Networks through Recyclable Unit Gating

Researchers introduced Continually-Recyclable Unit-Gating (CRUG), a continual learning method for dynamical systems reconstruction that achieves zero forgetting while conserving network capacity, according to an arXiv paper (arXiv:2609.38356v1). CRUG uses differentiable gates trained with an L0-based penalty to select task-specific units and recycle unused ones for later tasks, and it produced the strongest reconstruction-capacity trade-off among tested methods on a heterogeneous sequence of nonlinear and chaotic systems. The authors also report that forward transfer is more pronounced when tasks share similar underlying dynamics, and that CRUG's advantages extend to sequential cognitive tasks.

arXiv:2609.38356v1 Announce Type: new Abstract: Dynamical Systems Reconstruction DSR aims to infer models from observed time series that reproduce a system's qualitative long-term behavior. Continual DSR cDSR requires learning new systems while preserving previously learned dynamics, yet even small parameter updates in recurrent models can qualitatively alter their behavior over long autonomous rollouts. We benchmark established continual learning CL methods spanning parameter regularization, replay, and parameter isolation on the fully trainable and interpretable Almost-Linear RNN AL-RNN . Parameter isolation preserves earlier dynamics most effectively, but excessive task-specific allocations can rapidly exhaust a fixed-size network. We therefore introduce Continually-Recyclable Unit-Gating CRUG , which conserves capacity through compact allocation and forward transfer. Differentiable gates trained with an $L 0$-based penalty select task-specific units, while unused units are recycled for subsequent tasks. Directed connections allow later tasks to reuse earlier representations without affecting the dynamics of previously committed units. CRUG achieves the strongest reconstruction--capacity trade-off among the tested methods with zero forgetting and reliably learns a heterogeneous sequence of nonlinear and chaotic systems. Furthermore, we show that forward transfer is more pronounced and useful when tasks share similar underlying dynamics. Lastly, we demonstrate that CRUG's advantages extend beyond autonomous cDSR to sequential cognitive tasks.