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Abstract The increasing utility of specialized circuits and growing applications of optimization call for the development of efficient hardware accelerator for solving optimization problems. Hopfield neural network is a promising approach for solving combinatorial optimization problems due to the recent demonstrations of efficient mixed-signal implementation based on emerging non-volatile memory devices. Such mixed-signal accelerators also enable very efficient implementation of various annealing techniques, which are essential for finding optimal solutions. Here we propose a “weight annealing” approach, whose main idea is to ease convergence to the global minima by keeping the network close to its ground state. This is achieved by initially setting all synaptic weights to zero, thus ensuring a quick transition of the Hopfield network to its trivial global minima state and then gradually introducing weights during the annealing process. The extensive numerical simulations show that our approach leads to a better, on average, solutions for several representative combinatorial problems compared to prior Hopfield neural network solvers with chaotic or stochastic annealing. As a proof of concept, a 13-node graph partitioning problem and a 7-node maximum-weight independent set problem are solved experimentally using mixed-signal circuits based on, correspondingly, a 20 × 20 analog-grade TiO 2 memristive crossbar and a 12 × 10 eFlash memory array. 

The superior density of passive analog-grade memristive crossbar circuits enables storing large neural network models directly on specialized neuromorphic chips to avoid costly off-chip communication. To ensure efficient use of such circuits in neuromorphic systems, memristor variations must be substantially lower than those of active memory devices. Here we report a 64 × 64 passive crossbar circuit with ~99% functional nonvolatile metal-oxide memristors. The fabrication technology is based on a foundry-compatible process with etch-down patterning and a low-temperature budget. The achieved <26% coefficient of variance in memristor switching voltages is sufficient for programming a 4K-pixel gray-scale pattern with a <4% relative tuning error on average. Analog properties are also successfully verified via experimental demonstration of a 64 × 10 vector-by-matrix multiplication with an average 1% relative conductance import accuracy to model the MNIST image classification by ex-situ trained single-layer perceptron, and modeling of a large-scale multilayer perceptron classifier based on more advanced conductance tuning algorithm.