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Trainable threshold logic elements have been used in the adaptive pattern recognition field to design linear classifiers for patterns of binary variables. This paper shows how one of these trainable linear devices can be used to implement a trainable non-linear function generator. A trainable function generator is similar in function to the spatial function generators found in analog computers except that the coefficients of its function are set in an iterative "training" procedure instead of being predetermined in the design stage. The primary application of the trainable function generator, to date, has been in the real-time design of nonlinear pattern classification devices, therefore, the use of the trainable function generator as a nonlinear discriminant function in pattern classification is emphasized. It is demonstrated that in the implementation of the trainable function generator it is highly advantageous to use what has been defined as a linearly independent code to represent the analog pattern parameters as binary patterns for the threshold element. When a linearly independent code is used, a linear threshold element in a trainable function generator can be used to "learn" nonlinear discriminant functions just as it is used to learn linear discriminant functions.