On the stability, storage capacity, and design of nonlinear continuous neural networks

The s t a b i l i t y , c a p a c i t y , and design o f a n o n l i n e a r , continuous neural netwark are analyzed. S u f f i c i e n t c o n d i t i o n s f o r e x i s t e n c e and asymptotic s t a b i l i t y o f t h e network's equi-l i b r i a are reduced t o a s e t o f piecewise l i n e a r i n e q u a l i t y r e 1 a t i ons whi ch can be s o l ved by a feedforward b i nary network, o r by methods such as F o u r i e r E l i m i n a t i o n. The s t a b i l i t y and c a p a c i t y o f t h e network i s c h a r a c t e r i z e d by t h e post s y n a p t i c f i r i n g r a t e f u n c t i o n. An N neuron netwo k w i t h sigmoidal o f which N+1 a r b i t r a r y p o i n t s may always be made s t a b l e. This o f f e r s a h i g h e r c a p a c i t y than t h e (0.1-0.2)N obtained i n t h e b i n a r y H o p f i e l d network. Moreover, i t i s shown t h a t by a proper s e l e c t i o n o f t h e p o s t s y n a p t i c f i r i n g r a t e f u n c t i o n , one can s i g n i f i c a n t l y extend …