This is a reprint of page proofs of Chapter 12 of Perceptrons, M. Minsky and S. Papert, MIT Press 1968, (we hope). It replaces A.I. Memo No. 156 dated March 1968. The perceptron and convergence theorems of Chapter 11 are related to many other procedures that are studied in an extensive and disorderly literature under such titles as LEARNING MACHINES, MODELS OF LEARNING, INFORMATION RETRIEVAL, STATISTICAL DECISION THEORY, PATTERN RECOGNITION and many more. In this chapter we will study a few of these to indicate points of contact with the perception and to revel deep differences. We can give neither a fully rigorous account not a unifying theory of these topics: this would go as far beyond our knowledge as beyond the scope of this book. The chapter is written more in the spirit of inciting students to research than to offering solutions to problems.
