Saturation at high gain in discrete time recurrent networks

✍ Scribed by Morris W. Hirsch

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 451 KB
• Volume: 7
• Category: Article
• ISSN: 0893-6080
• DOI: 10.1016/0893-6080(94)90078-7

✦ Synopsis

We develop analogs of the saturation theorems of Grossberg and Hopfield for networks operating in discrete time with continuous activation dynamics. At certain units, called output nodes, the transfer functions gj are like sums of classical sigmoids with gain parameter ~. There is no restriction on transfer functions at other units; they need not be monotone, and are not affected by the gain. To each output node there is associated a finite set of numbers called its level values. For a broad class of nets we show that if the gain is sufficiently high, and if each output node is self-exciting, or each is self-inhibiting, then for any stable fixed point p of the activation dynamics, at each output node the outgoing signal gj( pj) is saturated, that is, close to a level vahw.