We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed time is a nonmonotonic function of its inputs, and so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator 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. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and can perform binary addition, the latter usually implemented in hardware using 5 logic gates. We show that a set of $n$ oscillators, observed at different times, can perform an arbitrary number of analog-to-$n$-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations.

翻译：我们证明，欠阻尼谐振子的时间分辨动力学可用于实现多功能计算，在单个动力学轨迹内的不同时间执行不同的计算。我们考虑一个输入影响其频率的谐振子振幅。谐振子在固定时间的活动是其输入的非单调函数，因此可以解决诸如异或（XOR）这类线性不可分问题。谐振子在固定输入下的活动是时间的非单调函数，因此在时间意义上具有多功能性，能够在同一动力学轨迹内的不同时间执行不同的非线性计算。我们证明，单个谐振子在不同时间观测下可以充当所有基本逻辑门，并能执行二进制加法（后者在硬件中通常需要5个逻辑门实现）。我们证明，一组$n$个谐振子在不同时间观测下可以执行任意数量的模拟到$n$位数字转换。我们还证明，谐振子可以通过梯度下降训练以在不同时间执行不同的分类任务。具有时变功能的计算可在平衡或非平衡状态下实现，这为减少非线性计算所需参数或设备数量提供了一种途径。