These Networks are already known in literature [Hinton, 1988]. The model of Recirculation Network (New RC) elaborated by Semeion is constituted by an architecture with four self-associated levels with a very peculiar functioning in three times and a matrix of weights. We have in fact, to distinguish between input and output units, visible and hidden, on one hand, and hypothetical and real on the other.

We define the input vector a_i^R as real visible input. Starting from a_i^R èit is possible, in a first time, to calculate a real hidden output a_o^R.
In a second time, acting backwards from the output to the input, it is possible to calculate, starting from a_o^R, a hypothetical visible input, a_i^I. In a third time, starting from a_i^I, it is possible to calculate a hypothetical hidden output a_o^I.

The dynamics of transfer of the signal in a RC happens, in three times:

t1: real visible input (a_i^R) → real hidden output (a_o^R)

t2: real hidden output (a_o^R) → hypothetical visible input (a_i^I)

t3: hypothetical visible input (a_i^I) → hypothetical hidden output (a_o^I)


The learning happens when he hypothetical visible input (a_i^I) reproduces each real visible input (a_i^R); this means that the two vectors of hidden units, a_o^I e a_o^R , formed an inner representation of the input vector a_i^R.

The matrix of the weights of a network RC is formed by connections at maximum gradient between the input and the output layer. The algorithm of learning of the RC happens in two times; every time the signal is filtered by the real input (a_i^R) to the hypothetical output (a_o^I), two corrections on the same matrix of the weights are operated: the first, considering the difference between real input and the hypothetical input, the second computing the difference between the real and the hypothetical output. In this way, the RC converges after a very low number of cycles.

We have developed a technique called “re-entry” [Buscema, 1994b, 1995a] for the recall phase. It deals with the response of a network on the phase of interrogation as a “process of re-entry in input of the information” in output, for a number of steps decided autonomously by the network itself, depending on the type of input that is processing.This mechanism allows to establish two important methodological concepts and the reaching of a practical benefit.

The first point of the method is the following: in reacting to some stimuli a network must, not only to manage the information inside, but also to perceive its own information management. This means to circulate inside the information produced by the new input stimulus, up to when these ones have not integrated (deformed) with the previous information that the network has encoded in its weights. This mechanism of Re-entry is internal to the network. It is impossible to know beforehand how many re-entries a network needs in order to establish its own output reply for any input.
The algorithm of each Re-entry is very simple: it consists in “replacing” the output just generated by the network as its new input, until the output generated stops changing.
It is as if the network had as desired target, at each cycle, the effective output of the previous cycle. In case this should not happen, we go on to the re-introduction of the output obtained in the input of the next cycle. This simple mechanism let the network to interpret the interpretations that he is supplying to some external stimuli and stabilizes its own response only when it has “digested” the external input trough a reflection on its own activity. The re-entry configures a meta activity of the networks, an activity of superior control on its own activities.

The second point of method is perspective. Trough the re-entry it is possible to imagine an activity of learning and one of answer of the network as a unique process. During this process the network learns, thinks, deforms and responds to the stimuli of input that continuously activate it. There is the practical advantage in the usage of the Re-entry when we use this network in the phase of recall: in front of an unknown input the network forces its interpretation as much as it can. This allows to read the Gestalts of many stimuli, in front of which the network without Re-entry are confused or trivialize their answer.

In an RC the technique of the Re-entry is particularly useful and simple: during the phase of the interrogation the real input is constituted by the type of question that we want to ask to the data base (DB). Thus, the real input vector is transformed first in real output and then in a hypothetical input, with the equations of transfer already described. At this point, we measure the distance between the two input vectors (real and hypothetical). If this distance is greater than a certain tolerance value (close to zero), the values of the hypothetical input are reintroduced in the real input for a second cycle. Also in this case the number of cycles of Re-entry, necessary to stabilise the system, is decided automatically by the RC.

The functional aim of an RC is different from the one of a Constraint Satisfaction (CS) network.
During the phase of learning the RC draws, through its own matrix of the weights, the hyper surface defined by all the variables contained in the DB. In the phase of interrogation, the Re-entry exploits this hyper surface to deform the new input in the input vector closer to those already defined by the matrix of the weights. The process of stabilization of the RC, happens through the minimisation of the inner energy of the network starting from the perturbation that this had in input .

For a more complete treatment of this model of network see the Technical Paper n. 24