This study deals with the evolution of the so called intelligent networks (insect society without leader, cells of an organism, brain…) during their apprenticeship period..
The used formalism draws one’s inspiration from the one of the Quantum field theory (Principle of stationary action, gauge fields, invariance by symmetry transformations…).

After a recall of some definitions, we consider at first the free network, that is to say which does not exchange any information with outside.
Then we study the evolution of the network connected with its environment, that is to say immersed into an information field created by this environment which so dictates to it the apprenticeship constraints.
At that time, we obtain Lagrange equations which solutions describe the network evolution during the whole apprenticeship period.
Finally, while proceeding with the same formalism inspiration, we suggest other study ways capable of evolving the knowledge in the considered scope.

Note: This study has not yet been translated in English.