This paper discusses pattern recognition using a learning system which can learn an arbitrary function of the input and which has built-in generalization with the characteristic that similar inputs lead to similar outputs even for untrained inputs. The amount of similarity is controlled by a parameter of the program at compile time. Inputs and/or outputs may be vectors. The system is trained in a way similar to other pattern recognition systems using an LMS rule. Patterns in the input space are not separated by hyperplanes in the way they normally are using adaptive linear elements. As a result, linear separability is not the problem it is when using Perceptron or Adaline type elements. In fact, almost any shape category region is possible, and a region need not be simply connected nor convex. An example is given of geometric shape recognition using as features autoregressive model parameters representing the shape boundaries. These features are approximately independent of translation, rotation, and size of the shape. Results in the form of percent correct on test sets are given for eight different combinations of training and test sets derived from two groups of shapes.