Computational capabilities of nonlinear oscillator networks
Mikhail Erementchouk, Aditya Shukla, Pinaki Mazumder · arXiv (Cornell University) · 2021
The ability of nonlinear oscillator networks to provide good heuristics for NP-hard optimization problems attracts significant attention to oscillator-based computing devices. Besides the case when such devices reproduce boolean logic, however, the origin of their computational capabilities remains largely unknown. We show that the dynamics of oscillator networks can be related to continuous relaxations of combinatorial optimization problems. This establishes a framework for classifying and evaluating the networks, outlining difficulties and further development perspectives. This also emphasizes the problem of rounding (reconstructing a binary Ising state). This problem remains underexplored, as the implemented dynamics force the network to collapse to a close-to-Ising state. We demonstrate, however, that such forcing may diminish the computational capabilities. This suggests that a consistent treatment of rounding may significantly improve various metrics of operation of already existing and upcoming dynamical Ising machines.