

![0_image_0.png](0_image_0.png)

 $ \underline{\underline{\cdot\ 1}}\quad\text{if}t_c\leq t_{max}\quad\text{(2)}$  $ \quad\ \ \ \text{otherwise}$  ... 
where S
out i,µ and ξ out i,µ **are respectively the computed and the wanted output**
for the µ**-th pattern of** ε 6**. The addiction of a term for transient will justify**
the passage from a computationally slow attractor neural network, prototypical of data-driven processes, to a faster and oriented one representative of schema-driven processes. Each asymptotic configuration having E **= 0,**
is one of the possible configurations able to solve the n **incoming instances**
of the problem and therefore the presented task.

As there aren't clues as the way ζ tmeas **have to be modified, we choose to**
proceed by trial and error. Consequently, the learning problem can be associated with a problem of global optimization, where E **is the object function**
to be minimized. The choice of the optimization strategy will produce different behaviors of the network during the learning phase and consequently, we will be able to associate them to different cognitive strategies of task resolution.

Haphazard trials. **No optimization strategy is applied. Starting from**
an arbitrary generated condition, a series of local perturbations are produced, by modifying just one entry either in W or b **selected at random**
with uniformly distributed probability. For each perturbation, the corresponding E(ζ tmeas **) is calculated. The resulting trend is a random walk of**
E. This non strategic behavior is directly affected by the N **involved functional areas, namely by the size of the solution space. Consequently this**
strategy can need a very long time to reach the solution of the **problem and**
to produce the correct response to the task.

Emergence of mental schemes. The optimized asymptotical configuration must be able to store the n **presented instances as mental schemes,**
which future activation will produce a fast and cognitively **cheap response.**
We choose to formalize the emergence of mental schemes as a simulated annealing procedure with geometrical cooling ratio cl**, fixed once for all at 0**.6, and by using E **as energy. By starting from the arbitrary generated** ζ t**meas**,
a local perturbation is produced with same modalities of the haphazard trials**. The resulting** ζ
′
tmeas differs in E of a value ∆E **from the previous one.**
For the acceptation of the new configuration, we refer to the Metropolis 6