Learning of correlated patterns by simple perceptrons
  Learning behavior of simple perceptrons is analyzed for a teacher-student scenario in which output labels are provided by a teacher network for a set of possibly correlated input patterns, and such that teacher and student networks are of the same type. Our main concern is the effect of statistical correlations among the input patterns on learning performance. For this purpose, we extend to the teacher-student scenario a methodology for analyzing randomly labeled patterns recently developed in {\em J. Phys. A: Math. Theor.} {\bf 41}, 324013 (2008). This methodology is used for analyzing situations in which orthogonality of the input patterns is enhanced in order to optimize the learning performance. 
Takashi Shinzato and Yoshiyuki Kabashima