Symmetric properties of neural networks for control applications

Applications of neural networks to control impose hard constraints on the symmetric properties of the functional that is to be learned by a neural network. Traditional sigmoid units are not able to satisfy these constraints. A new type of unit, the modulated sigmoid unit, is presented that can simultaneously represent symmetries with regard to some inputs and asymmetries to others. The importance of symmetric relationships and the use of this unit is illustrated on applications to control and system identification