This paper starts by revisiting some founding, classical ideas for Neural Networks as Artificial Intelligence devices. The basic functionality of these devices is given by stability related properties such as the gradient-like and other collective qualitative behaviors. These properties can be linked to the structural - connectionist - approach. A version of this approach is offered by the hyperstability theory which is presented in brief (its essentials) in the paper. The hyperstability of an isolated Hopfield neuron and the interconnection of these neurons in hyperstable structures are discussed. It is shown that the so-called "triplet" of neurons has good stability properties with a non-symmetric weight matrix. This suggests new approaches in developing of Artificial Intelligence devices based on the triplet interconnection of elementary systems (neurons) in order to obtain new useful emergent collective computational properties.