用振荡网络实现计算，靠同步学习，无需复杂训练。
Harnessing omnipresent oscillator networks as computational resource
- 用相位锁定的库朗托模型构建振荡网络，通过反馈环模仿目标系统。
- 网络在节点数线性时间内完成全连接同步，参数丰富且泛化性强。
- 利用序参量解释集体智能，适合研究自然计算与新型神经形态系统。
自然界中普遍存在振荡动力学。在耦合振荡器网络中，当系统同步于外部输入时，会涌现出模式，从而具备处理与记忆输入的能力。本文提出一个通用框架，将振荡器网络作为计算资源加以利用。该框架基于描述相位锁定的普遍模型——库朗托模型（Kuramoto model）。通过施加非线性目标系统对库朗托模型进行驱动，再以训练好的反馈回路替代目标系统，使网络可有效模拟原系统。结果表明：其一，训练后的网络继承了库朗托模型的性能优势，全连接同步可在与节点数成线性的时间内完成，且同步参数丰富，因此系统具有普遍成功性，学习依赖于同步机制；其二，振荡网络的学习能力——一种集体智能现象——可通过库朗托模型的序参量（order parameter）进行解释。综上，本工作为利用自然界中的振荡器网络构建新型信息处理系统奠定了基础。
原文摘要 · Abstract (English)
Nature is pervaded with oscillatory dynamics. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal framework for harnessing oscillator networks as computational resource. This computing framework is introduced by the ubiquitous model for phase-locking, the Kuramoto model. We force the Kuramoto model by a nonlinear target-system, then after substituting the target-system with a trained feedback-loop it emulates the target-system. Our results are two-fold. Firstly, the trained network inherits performance properties of the Kuramoto model, where all-to-all coupling is performed in linear time with respect to the number of nodes and parameters for synchronization are abundant. The latter implies that the network is generically successful since the system learns via sychronization. Secondly, the learning capabilities of the oscillator network, which describe a type of collective intelligence, can be explained using Kuramoto model's order parameter. In summary, this work provides the foundation for utilizing nature's oscillator networks as a new class of information processing systems.
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