Discussion

We have presented a model where dynamical encoding and processing can not be reduced to a simple feed-forward process. Our system is recurrent, and consequently presents an operational closure [36], so that the inner constraints dominate the external signal. One can also say that the inner dynamics corresponds to a ``simulation'' of the external world, which is updated according to the input signal. In any way, the traditional input-output dependency is modified: the predictability of a sensory-motor scheme is dependent on the fitting between the inner dynamics and the input-output flow. When such fitting is observed (dynamical or structural coupling, resonance), one can predict the behavior of the whole system as in traditional input-output systems. On the contrary, when the fitting is bad, the whole system is found to produce complex inner dynamics and unpredictable sensory-motor behaviors. Even if the link with biology is a delicate matter with our simple analog neuronal units, we will try in this part to exhibit some plausible analogies with real biological neural structures and functions, and also to estimate the limits of such analogy. The question of recognition is central in our system, and corresponds to ``acceptance'' or ``rejection'' of some spatio-temporal configurations arriving on the primary layers. Most of the signals are rejected, or ignored, while some of them allow the activation of a specific resonant feedback signal. This property relates to the question of dynamical binding [37,4], i.e. the ability to link together separate elements. In our model, the individual elements composing a sequence are not significant by themselves. The activation of a feedback signal needs a specific spatio-temporal disposition of these individual elements, which are thus processed and ``perceived'' as a whole. This hypothesis of dynamical binding is present at different scales in neurophysiological studies [16,23,27]. Our model is one of the possible implementations of the dynamical binding hypothesis, and thus a candidate for explaining how such binding occurs in the brain. The possible role of chaotic dynamics in brain processing is also a matter of interest for neurophysiologists. The principal hypothesis on the functional role of chaos in olfactory perception systems was stated by [32]. In their article, they interpret the recognition of an olfactory stimulus as the stabilization of an unstable orbit of a chaotic attractor. Chaos is thus seen as a reservoir of cycles, where every unstable orbit corresponds to the encoding of a specific odor. Our model is not fully compatible with Freeman's model, even if the ideas are globally comparable. In particular, as the input dynamics takes part in the dynamical process, the different attractors associated to every different stimulus do not correspond to a subpart of a global chaotic attractor. In our model, due to structural instability, there is no global attractor, but a lot of transitions between distinct attractors, chaotic or not, depending on the input signal, on the inner constraints and on previous learning. It is difficult to claim high links between our model and some specific cortical or sub-cortical regions. However, the 3-populations ReST model, which is devoted to navigation, has connections with the hippocampus architecture. Other works by the ETIS team have already taken inspiration from the hippocampal architecture for the design of control architecture for the Koala mobile robot [26,13]. The ReST model has been inserted in this architecture and takes the place of the area denoted as CA3. Structurally, this area is known for its important recurrent links. Functionally, (i) it has been found to display a functional remapping in case of environmental contextual changes [3] and (ii) it is supposed to be the place where locations and/or temporal sequences are learned when the animal is performing an action. These observations and hypotheses are compatible with the dynamical organization and computational abilities of our system. This analogy has to be more deeply invested, but may already give new insights in the way the CA3 region processes information. In the same way, the analogy with the visual system (V1 and V2) is not straightforward, but our model may however give clues for people who are interested in the role of feedback links in visual perception. First, it is known that 80 % of the LGN entries correspond to feedback connections from the visual cortex. According to [7], this feedback information is supposed to enhance the sensitivity of some neurons, according to the expectations of the cortex on the visual flow. Second, some recent studies [21] have shown that V1 $\rightarrow$ V2 feedback connections may play a role in the process of figure/ground segregation. Some theoretical models have yet been proposed, see [28], for explaining the psychological phenomena of illusionary contour detection. Our model, even coarser, brings the idea that feedback signal may also be implied in the reinforcement, by anticipation, of the primary treatment of dynamical scenes and objects. At last, one can ask the question of the temporal scales of the phenomenons we want to model. This question is not trivial. Our system uses its own discrete-time parallel updating, which is not associated to a particular temporal unit. The time scale is not defined a priori, so that one have to consider the specific field of application to determine an ``external'' temporal reference. The visual and perceptual analogies suggest for instance to interpret synchronization and dynamical binding at the millisecond scale. On the contrary, sensory-motor experiments take place in the range of seconds. In future works, and with the same global structures, it may be necessary to distinguish between the modeling of sensory perception, with the use of spiking neurons with biologically-compatible temporal scales, and control models that may correspond to the modeling of global structures, at broader temporal scales. Nevertheless, the compatibility between these two interpretations illustrates in some way the genericity and ``universality'' of our model of dynamical perception.