Generative System Dynamics in Recurrent Neural Networks
This work addresses the challenge of designing RNNs with improved memorization skills for complex temporal dependencies, though it appears incremental as it builds on known dynamics principles.
The study tackled the problem of enabling perpetual oscillatory behavior in Recurrent Neural Networks (RNNs) without convergence to static fixed points, establishing that skew-symmetric weight matrices and hyperbolic tangent-like activation functions are fundamental for stable limit cycles and enhanced numerical stability.
In this study, we investigate the continuous time dynamics of Recurrent Neural Networks (RNNs), focusing on systems with nonlinear activation functions. The objective of this work is to identify conditions under which RNNs exhibit perpetual oscillatory behavior, without converging to static fixed points. We establish that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations. We further demonstrate that hyperbolic tangent-like activation functions (odd, bounded, and continuous) preserve these oscillatory dynamics by ensuring motion invariants in state space. Numerical simulations showcase how nonlinear activation functions not only maintain limit cycles, but also enhance the numerical stability of the system integration process, mitigating those instabilities that are commonly associated with the forward Euler method. The experimental results of this analysis highlight practical considerations for designing neural architectures capable of capturing complex temporal dependencies, i.e., strategies for enhancing memorization skills in recurrent models.