Stabilization of Hebbian neural nets by inhibitory learning
Hebbian neural models with simultaneously active pre- and postsynaptic neurons are considered which are stabilized by recurrent inhibition via modifiable inhibitory synapses. A one synapse model which is a system of two differential equations incorporating Hebb's principle is described to introduce the main definitions. Adding to the model first fixed feed- forward inhibition, then dynamic feed-forward and then fixed recurrent one, it is shown that there is no stable steady state solution. With modifiable recurrent inhibition a non-zero solution exists when the input exceeds a certain intensity. When the zero solution is the only one, it is stable, but when the non-zero solution exists it is stable and the zero solution is unstable. The equations are extended to time varying input and to many neuron systems. The linearized equations are tensor invariant under a class of rotations of the state space. The response to stimulation may be derived as a set of independent modes of activity distributed over the net, which may be identified with cell assemblies. Analytic solutions of the three layer system are given.
continuously infinite set of equivalent solutions
simultaneously active pre- and postsynaptic neurons
Analytic solutions of the three layer system
scientific article; zbMATH DE number 3880490