Coupled oscillators are being increasingly used as the basis of machine learning (ML) architectures, for instance in sequence modeling, graph representation learning and in physical neural networks that are used in analog ML devices. We introduce an abstract class of neural oscillators that encompasses these architectures and prove that neural oscillators are universal, i.e, they can approximate any continuous and casual operator mapping between time-varying functions, to desired accuracy. This universality result provides theoretical justification for the use of oscillator based ML systems. The proof builds on a fundamental result of independent interest, which shows that a combination of forced harmonic oscillators with a nonlinear read-out suffices to approximate the underlying operators.

翻译：耦合振荡器日益被用作机器学习架构的基础，例如在序列建模、图表示学习以及模拟机器学习设备中使用的物理神经网络中。我们引入了一类涵盖这些架构的抽象神经振荡器，并证明神经振荡器具有普适性，即它们能够以所需精度近似任意连续且具有因果性的时变函数映射算子。这一普适性结果为基于振荡器的机器学习系统提供了理论依据。证明基于一个独立且有意义的根本性结果，该结果表明，将受迫谐振子与非线性读出相结合足以近似底层算子。