Some nonlinear networks capable of learning a spatial pattern of arbitrary complexity.

(1) Introduction,-This note describes some nonlinear net\vorks ,vhich caD learn a spatial pattern, in "black and white," of arbitrary size and complexity. These networks are a special case of a collection of learning machines ~ which were introduced in reference 1, where a machine capable of learxung a list of "letters" or "events" was described, We list in heuristic terminology some of the properties which arise in the learning of patterns: (a) "Practice makes perfect": Given a "black and white" pattern of arbitral'y size and complexity, a nonlinear network fit can be found \vhich learns this pattern to any prescribed degree of accuracy, (b) An isolated machine never forgets: If the pattern is leal'ned to a fixed degree of accuracy by 3Tl:, then fit will remember the pattern to at least this degree of accuracy until a new pattern is imposed upon fit. (c) Overt practice is unnecessary: fit remembers the pattern without practicing it overtly, (d) Contour enhancement: If fit learns the pattern to a "moderate" degree of accuracy, then fit's memory of the pa~tern spontaneously improves after practices ceases, As a result, when fit recalls the pattern, its contours are enhanced in the sense that "darks get darker" and "lights get lighter." (e) A new pattern can always be learned: Even if 3Tl: kno\vs one pattern to an arbitrary degree of accuracy, this pattern can be replaced by any other pattern by a sufficient amount of practice. (2) The Machine,-The nonlinear network which describes fit is defined as follows for any fixed number n ?:. 1 of states and any reaction time l' ?:. O.