Steady-state analysis of a single-layer perceptron based on a system identification model with bias terms

A stochastic analysis is presented of the steady-state convergence properties of a single-layer perceptron for Gaussian input signals. A system identification formulation is presented whereby the desired response signal (+or-1) is modeled by an unknown linear FIR system F plus an unknown bias, followed by a signum function nonlinearity. The perceptron nonlinearity is based on the error function, which implements the signum function as a special case, and it also includes a bias adjustment. It is demonstrated that the converged adaptive weights of the perceptron are proportional to F, and the proportionality constant is infinite when the bias terms are set to zero. If the bias terms are both nonzero, the converged perceptron weights have a unique finite solution determined by the bias factor magnitudes.<>