Multi-population recurrent model

The class of neural networks we start from are recurrent systems, whose weights are set according to a random draw (Random Recurrent Neural Networks, ``RRNN's''). We present in this section a generic formalism for the design of multi-population random recurrent systems. This formalism will help to specify the sensory architecture we use in section 3. Random neural networks were introduced by Amari [2] in a study of their large size properties. Predictions on the mean field of such systems can be obtained in the limit of large sizes under an hypothesis of independence of the individual signals [33,6]. This convergence towards mean-field equations has recently been formally proved [25]. The arising of several sorts of synchronized dynamics can thus be proven, in a model with excitatory and inhibitory populations [9]. Here, we will mainly consider our random networks as finite-size dynamical systems, that can display a generic quasi-periodicity route to chaos with a continuous tuning of gain parameter [11]. Note that dynamical neural networks have some specific time constraints that distinguish them from pure feedforward associative systems. In particular, the time necessary to reach an attractor is not determined. One needs ``several time steps'' or ``a certain time'' to reach a neighborhood of the attractor. This transient time, which may be short, is necessary, and takes place as soon as a change occurs in the environment of the system.