A canonical ensemble approach to graded-response perceptrons
  Perceptrons with graded input-output relations and a limited output precision are studied within the Gardner-Derrida canonical ensemble approach. Soft non- negative error measures are introduced allowing for extended retrieval properties. In particular, the performance of these systems for a linear and quadratic error measure, corresponding to the perceptron respectively the adaline learning algorithm, is compared with the performance for a rigid error measure, simply counting the number of errors. Replica-symmetry-breaking effects are evaluated. 
D. Bolle and R. Erichsen Jr