Absence of Cycles in Symmetric Neural Networks
For a given recurrent neural network, a discrete-time model may have asymptotic dynamics different from the one of a related continuous-time model. In this article, we consider a discrete-time model that discretizes the continuous-time leaky integrator model and study its parallel, sequential, block-sequential, and distributed dynamics for symmetric networks. We provide sufficient (and in many cases necessary) conditions for the discretized model to have the same cycle-free dynamics of the corresponding continuous-time model in symmetric networks.
Wang, X., Jagota, A., Botelho, F., & Garzon, M. (1998). Absence of Cycles in Symmetric Neural Networks. Neural Computation, 10 (5), 1235-1249. https://doi.org/10.1162/089976698300017430