A 2-layers perceptual model

We have designed a model in order to study the interplay between a fully recurrent system and a spatio-temporal signal. This model is called ``ReST'' (i.e. Resonant Spatio-Temporal) model. The design of this architecture has been guided by two objectives : (i) give some insights in the global functioning of biological perceptual systems and (ii) lead to real-world applications (see section 5). The analogy with biological sensory structures is the following: we consider that a recognition process (odor, visual scene,...) may rely on the interplay between several structures, which are partly autonomous, and that correspond to different levels of generalization. Primary layers may produce basic treatments, while deeper (secondary) layers may correspond to a global treatment, linking spatial and temporal context of perception, and taking into account the memory of learned stimuli. The recognition of a given stimulus may then depend on the coherence (or dynamical coupling) between primary layers and secondary (and deeper) layers. Note that our point of view is distinct (and possibly complementary) from the feed-forward approach, see for instance [35]. We define an architecture with two layers (i.e. $P=2$): a primary layer of index 1 and a secondary layer of index 2. Population sizes $N^{(1)}$ and $N^{(2)}$ are supposed large (from 100 to 2000 neurons in our simulations) and are not necessarily equal. This system is simple in its design, but may produce complex dynamical behaviors. The two-layer architecture is shown on Fig.1. We can define three important classes of links: "feedforward links" $\mathbf{J}^{(21)}$ propagate the input signal towards the secondary layer, "inner links" $\mathbf{J}^{(22)}$ generate inner signal, and "feedback links" $\mathbf{J}^{(12)}$ send back the activity of the secondary layer towards the primary layer. In this model, primary lateral links $\mathbf{J}^{(11)}$ are equal to zero.

Figure: Architecture of the ReST model. Our model is composed of two layers. Their respective sizes are not necessarily equal. Only few links are represented. The primary layer is submitted to a spatio-temporal input pattern $\mathbf{I}^{(1)}$. The secondary layer has no input signal. The links are monodirectional. The activity of the secondary layer (inner signal) is chaotic. The activity on the primary layer depends both on the input signal and feedback signal from the secondary layer.