Computing with dynamical systems in the post-CMOS era

In the pursuit for building hardware accelerators to compute optimization problems researchers realize that the challenges in achieving this objective lie not only in implementing the hardware but also in the formulating the computing fundamentals of such designs. Neural network algorithms are considered most suited for this task, as there is usually a direct description of distributed computing entities, called “neurons”, and their interactions which can be mapped to both electronic and non-electronic hardware. In this regard, coupled oscillator systems have been studied where individual oscillators correspond to neurons and the information is encoded in either phase or frequency. But as is the case with neural networks, the computational power of the network depends on complexity of interactions among oscillators, and it is a challenge to implement oscillator networks with complex simultaneous interactions among multiple oscillators. Sinusoidal oscillators with assumption of weak linear phase coupling, akin to Kumamoto models, have been studied in theory but implementing such oscillators with weak couplings and encoding information in phase or frequency have been a challenge. Examples of using novel devices for making neural network hardware include memristor based neuromorphic synapses [1] and spin-torque oscillator (STO) based systems [2]. In our work, we use relaxation oscillators coupled using passive elements - capacitances or resistances - without the assumption of weak linear phase couplings. Our theoretical models are derived from circuit implementations, instead of the other way round, which means there are only engineering challenges in implementing the hardware, and no modeling discrepancies. We have explored two kinds of implementations - (a) simple pairwise coupling scheme with information encoded as frequency for pattern matching and associative computing, and (b) complex global coupling with information encoded in phase for the NP-hard graph coloring problem. We have been demonstrated in theory, using simulations and experimental implementations using VO
₂
devices, the working of such coupled relaxation oscillator networks.