CONSTRUCTION OF MINIMAL N-2-N ENCODERS FOR ANY N

The encoding problem (Rumelhart and McClelland 1986) is an important c anonical problem. It has been widely used as a benchmark. Here, we hav e analytically derived minimal-sized nets necessary and sufficient to solve encoding problems of arbitrary size. The proofs are constructive : we construct n-2-n encoders and show that two hidden units are also necessary for n > 2. Moreover, the geometric approach employed is gene ral and has much wider applications. For example, this method has also helped us derive lower bounds on the redundancy necessary for achievi ng complete fault tolerance (Phatak and Koren 1992a,b).