A Mixed-Signal Oscillatory Neural Network for Scalable Analog Computations in Phase Domain

Digital electronics based on von Neumann's architecture are reaching their limits to solve large scale problems essentially due to the memory fetching. Instead, recent efforts to bring the memory near the computation have enabled highly parallel computations at low energy cost. Oscillatory Neural Network (ONN) is one example of in-memory analog computing paradigm consisting of coupled oscillating neurons. When implemented in hardware, ONNs naturally perform gradient descent of an energy landscape that makes them particularly suited for solving optimization problems. Although the ONN computational capability and its link with the Ising model are known for decades, implementing a large-scale ONN remains difficult. Beyond the oscillators' variations, there are still design challenges such as having compact, programmable synapses and a modular architecture for solving large problem instances. In this paper, we propose a mixed-signal architecture named Saturated Kuramoto ONN (SKONN) that leverages both analog and digital domains for efficient ONN hardware implementation. SKONN computes in the analog phase domain while propagating the information digitally to facilitate scaling up the ONN size. SKONN's separation between computation and propagation enhances the robustness and enables a feed-forward phase propagation that is showcased for the first time. Moreover, the SKONN architecture leads to unique binarizing dynamics that are particularly suitable for solving NP-hard combinatorial optimization problems such as finding the Weighted Max-cut of a graph. We find that SKONN's accuracy is as good as the Goemans-Williamson 0.878-approximation algorithm for Max-cut; whereas SKONN's computation time only grows logarithmically. We report on Weighted Max-cut experiments using a 9-neuron SKONN proof-of-concept on PCB. Finally, we present a low-power 16-neuron SKONN integrated circuit and illustrate SKONN's feed-forward ability while computing the XOR function

Computing With Hybrid Material Oscillators

The evolution of computers is driven by advances not only in computer science, but also in materials science. As the post-CMOS era approaches, research is increasingly focusing on flexible and unconventional computing systems, including the study of systems that incorporate new computational paradigms into the materials, enabling the computer and the material to be the same entity. In this dissertation, we design a coupled oscillator system based on a new hybrid material that can autonomously transduce chemical, mechanical, and electrical energy. Each material unit in this system integrates a self-oscillating gel, which undergoes the Belousov-Zhabotinsky (BZ) reaction, with an overlaying piezoelectric (PZ) cantilever. The chemo-mechanical oscillations of the BZ gels deflect the piezoelectric layer, which consequently generates a voltage across the material. When these BZ-PZ units are connected in series by electrical wires, the oscillations of these coupled units become synchronized across the network, with the mode of synchronization depending on the polarity of the piezoelectric. Taking advantage of this synchronization behavior, we demonstrate that the network of coupled BZ-PZ oscillators can perform specific computational tasks such as pattern matching in a self-organized manner, without external electrical power sources. The results of the computational modeling show that the convergence time for stable synchronization gives a distance measure between the “stored” and “input” patterns, which are encoded by the connection and phases of BZ-PZ oscillators. In addition, we demonstrate two methods to enrich the information representation in our system. One is to employ multiple BZ-PZ oscillator networks in parallel and to process information encoded in different channels. The other is to introduce capacitors into a BZ-PZ network that modify the dynamical behavior of the systems and increase the information storage. We analyze and simulate the proposed coupled oscillator systems by using linear stability analysis and phase models and explore their potential computational capabilities. Through these studies, we establish experimentally realizable design rules for creating “materials that compute”