This paper presents a novel hardware architecture for adaptive systems whose exact specification is unknown. The architecture is suitable for linear and nonlinear systems whose inputs are real or complex signals (variables), and that have an acceptable representation as low order polynomials in these variables. The implementation is based on using an a priori selected subset of Walsh spectral coefficients. The proposed architecture can acquire its target functionality and adapt itself to changing environments even if the number of variables, their order and precision are unknown in advance. This is in contrast to conventional multiply-and-accumulate (MAC) based architectures where this information must be determined before the design and implementation of the system. In this context (of systems whose functionality is unknown), the delay and the implementation cost of the proposed architecture is significantly lower than MAC-based solutions.