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 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. We call this unit an oscillatron. The activity of an oscillatron at fixed time is a nonmonotonic function of the input, and so it can solve nonlinearly-separable problems such as XOR. The activity of the oscillatron at fixed input is a nonmonotonic function of time, and so it 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.

翻译：计算领域的多个分支利用系统的物理动力学进行计算。我们证明，欠阻尼谐振子的动力学能够实现多功能计算，在单一动力学轨迹的不同时间点解决不同的问题。基于振子的计算通常关注振子相位作为信息载体。本文聚焦于振子受输入影响频率后的时间分辨振幅，该特性自然地类比于具有时间依赖性神经单元的活性。我们将该单元命名为振荡子。固定时间下振荡子的活性是输入的非单调函数，因此能够解决异或（XOR）等非线性可分问题；固定输入下振荡子的活性是时间的非单调函数，因此在时间意义上具有多功能性——能在同一动力学轨迹的不同时间点执行不同的非线性计算。此类时间分辨计算可在平衡态或非平衡态下进行，系统的自然时间演化能以单一计算成本实现多重计算。