Adaptive-learning neuron circuits are proposed, in which a pulse frequency modulation (PFM) system is used and the interval of output pulses is continuously changed through the learning process. Kdy components of the circuits are MISFETs in which the gate insulator film is composed of a ferroelectric material and the source-drain resistance of the FETs is gradually changed by applying input pulses to the gates. Then, the curent status of the basic research for realizing these circuits are reviewed. In order to fabricate FETs with a ferroelectirc gate insulator, BaMg$F_4$ films are formed on Si and GaAs substrates using a molecular beam epitaxy method. It has been shown that BaMg$F_4$ films grow epitaxially on both substrates and the polarization vs. electric field characteristics of the capactiors formed on Si(III) and GaAs(100) subsrates show ferroelectric hystersis loops.