Evolving recurrent neural networks are super-Turing

The computational power of recurrent neural networks is intimately related to the nature of their synaptic weights. In particular, neural networks with static rational weights are known to be Turing equivalent, and recurrent networks with static real weights were proved to be super-Turing. Here, we study the computational power of a more biologically-oriented model where the synaptic weights can evolve rather than stay static. We prove that such evolving networks gain a super-Turing computational power, equivalent to that of static real-weighted networks, regardless of whether their synaptic weights are rational or real. These results suggest that evolution might play a crucial role in the computational capabilities of neural networks.