Analysis of Chaotic Elman Network

Elman network is a descrete-time 3 layer neural network which is able to realize stochastic finite-state automaton. In this study, chaotic neuron model proposed by K.Aihara is introduced in its hidden layer, namely the chaotic Elman network. The chaotic Elman network includes the ordinal Elman network as a special case. Choosing parameters, the dynamics shows chaotic itinerancy among stored patterns. I will first show the analysis using invariant subspaces, explaining the chaotic itinerancy as crisis-induced intermittency of periodic orbit. Second, We consider the case where Hebbian learning is added during the itinerancy. Using only the local information of neuron dynamics, the network can converge attractor basins, simplify and modify the hierarchical structure of invariant subspaces. This implies an analogy of dialectic, which escapes from formal logic.

I would also talk on some intuitional view to analize chaotic itinerancy using information geometry, inspired by Nihat Ay's work.