Computing combinatorial optimization problems with low-power VO2 neuromorphic oscillators

Abstract

A wide range of computing tasks, including modelling chemical reactions for drug synthesis, designing layout for very large scale integrated-circuits (VLSI), and performing speech detection and object visualization in real-world environments for Computer Vision, belong to a class of problems extremely costly to solve for modern computers operating under the von Neumann architecture.[1] As these problems grow in complexity, the associated challenges related to an exponentially increasing number of interconnected devices, energy consumption, and high latency limit the development of computing systems capable of solving such problems.[2] This performance bottleneck has motivated novel research areas focusing on new algorithms and circuit designs [3], integrating unconventional ‘neuromorphic’ materials inspired by the brain, where memory and computation are co-integrated on the same platform for power efficiency.[4] Such innovative materials, with programmable resistive states, show immense potential to power the next generation computers, where artificial intelligence applications require faster and more energy-demanding operation. They exhibit high performance and ultrafast switching properties at low energy costs that can operate in the analog domain.[1], [5] While hafnium oxide (HfO2) holds promise for several nonvolatile memory applications and matrix multiplication[5], vanadium dioxide (VO2) has received increasing research interest due to its nanoscale phase transition at 68 °C, which can be quickly activated electrically from room temperature.[6] VO2 also features low-power and high frequency operation, scalability, and compatibility with CMOS technology.[1] At IBM Research Zurich, we have developed a fabrication process on a Si/SiO2/HfO2 substrate that enables precise control over the formation of VO2 grains to produce crossbar devices scalable to nanometric dimensions and mitigated device-to-device variability.[7] Our VO2 devices serve as the main building blocks for both linear relaxation oscillators and nonlinear self-coupled FitzHugh-Nagumo neurons to build oscillating neural networks (ONNs). With these networks, we demonstrate how simple yet efficient Ising machines can be realized to map and minimize Hamiltonian equations due to the natural tendency of coupled oscillators to converge in phase to a stable solution.[8] Specifically, we solve complex optimization problems such as Graph Coloring and nondeterministic polynomial time (NP) problems such as Max-cut and Max-3SAT, while also establishing the groundwork for nonlinear VO2-based oscillating computing through self-coupled FitzHugh-Nagumo neurons.[9], [10] Our research extends from material fabrication to circuit integration for targeted applications in unconventional computing. Our VO2 ONNs excel in processing data locally, thereby avoiding the energy costs associated with data transfer from memory to processor, positioning them as an attractive and scalable computing unit for hardware accelerators. [1] G. Csaba et al., 2018 IEEE International Symposium on Circuits and Systems (ISCAS), IEEE, 2018, pp. 1–5. [2] J. Backus, Commun ACM, vol. 21, no. 8, pp. 613–641, Aug. 1978, doi: 10.1145/359576.359579. [3] E. Chicca et al., Proceedings of the IEEE, vol. 102, no. 9, pp. 1367–1388, Sep. 2014. [4] G. Indiveri and S.-C. Liu, Proceedings of the IEEE, vol. 103, no. 8, pp. 1379–1397, Aug. 2015. [5] T. Stecconi et al., Adv Electron Mater, vol. 8, no. 10, Oct. 2022, doi: 10.1002/aelm.202200448. [6] E. Corti et al., Solid State Electron, vol. 168, p. 107729, Jun. 2020, doi: 10.1016/j.sse.2019.107729. [7] O. Maher et al., ‘Highly Reproducible and CMOS-compatible VO2-based Oscillators for Brain-inspired Computing’. Sci Rep, 2024 [8] S. Dutta et al., Nat Electron, vol. 4, no. 7, pp. 502–512, Jul. 2021, doi: 10.1038/s41928-021-00616-7. [9] O. Maher et al., ‘A CMOS-compatible oscillation-based VO2 Ising machine solver’, Nature Communications, 15, 3334, 2024 [10] M. Desroches et al., Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 18, no. 1, Mar. 2008