1. A digital, adaptive information processing system comprising, in combination: a. digital input register means for storing a plurality (N) of digital numbers s.sub.1, s.sub.2.. . s.sub.j,. .. s.sub.N, representing an input signal; b. digital output register means for storing a plurality (n) of digital numbers r.sub.1, r.sub.2.. . r.sub.i,. . .r.sub.n, representing an output response; and c. digital information processing apparatus connecting said input register means with said output register means, said apparatus comprising: 1. digital memory means for storing a plurality (n .times. N) of digital weighting numbers A.sub.11, A.sub.12.. .A.sub.ij,. .. A.sub.nN ; 2. digital multiplier means, coupled to said input register means and to said memory means, for multiplying selected ones s.sub.j of said numbers located in said input register means with selected ones A.sub.ij of said weighting numbers to produce digital product numbers s'.sub.j in accordance with the formula: EQU s'.sub.j = A.sub.ij s.sub.j ; 3. digital adder means, coupled to said multiplier means and to said output register means, for adding together selected ones of said product numbers s'.sub.j produced by said multiplier means to produce digital sum numbers r.sub.i in accordance with the formula: ##EQU3## said sum numbers r.sub.i being stored in said output register means; and digital modifier means, coupled to said input register means, said output register means and to said memory means, for changing at least one of said weighting numbers A.sub.ij in accordance with the formula: EQU A.sub.ij (t) = .gamma.A.sub.ij (t-1) + .eta.s.sub.j r.sub.i ; where A.sub.ij (t) is the new number stored in said memory means, A.sub.ij (t-1) is the number previously stored in said memory means, .gamma. is a decay constant in the range o.ltoreq..gamma..ltoreq.1, .eta. is a learning constant for which o.ltoreq..eta., s.sub.j is the number stored in said input register means, r.sub.i is the member stored in said output register means, and i and j are integers from 1 to n and N, respectively.