Title: Springs and a stopwatch: neural units with time-dependent multifunctionality

Abstract: Several branches of computing use a system's physical dynamics to do computation. We show that the dynamics of an underdamped harmonic oscillator can perform multifunctional computation, solving distinct problems at distinct times within a single dynamical trajectory. Oscillator computing usually focuses on the oscillator's phase as the information-carrying component. Here we focus on the time-resolved amplitude of an oscillator whose inputs influence its frequency, which has a natural parallel as the activity of a time-dependent neural unit. Because the activity of the unit at fixed time is a nonmonotonic function of the input, the unit can solve nonlinearly-separable problems such as XOR. Because the activity of the unit at fixed input is a nonmonotonic function of time, the unit is multifunctional in a temporal sense, able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. Time-resolved computing of this nature can be done in or out of equilibrium, with the natural time evolution of the system giving us multiple computations for the price of one.