On the correlation dimension of recurrent neural networks

Recurrent sigmoidal neural networks with asymmetric weight matrices and recurrent neural networks with nonmonotone transfer functions can exhibit ongoing uctuations rather than settling into point attractors. It is, however, an open question if these uctuations are the sign of low dimensional chaos or if they can be considered as close to stochastic. We report on the calculation of the correlation dimension of time series generated by those networks. The numerical calculation indicate a limited correlation dimension of around D2 = 6 in both networks which has to be considered as high dimensional chaos yet far from the stochastic limit. First results of this calculation were reported in [1].