Solving Max-Cut Problem Using Spiking Boltzmann Machine Based on Neuromorphic Hardware with Phase Change Memory

Efficiently solving combinatorial optimization problems (COPs) such as Max-Cut is challenging because the resources required increase exponentially with the problem size. This study proposes a hardware-friendly method for solving the Max-Cut problem by implementing a spiking neural network (SNN)-based Boltzmann machine (BM) in neuromorphic hardware systems. To implement the hardware-oriented version of the spiking Boltzmann machine (sBM), the stochastic dynamics of leaky integrate-and-fire (LIF) neurons with random walk noise are analyzed, and an innovative algorithm based on overlapping time windows is proposed. The simulation results demonstrate the effective convergence and high accuracy of the proposed method for large-scale Max-Cut problems. The proposed method is validated through successful hardware implementation on a 6-transistor/2-resistor (6T2R) neuromorphic chip with phase change memory (PCM) synapses. In addition, as an expansion of the algorithm, several annealing techniques and bias split methods are proposed to improve convergence, along with circuit design ideas for efficient evaluation of sampling convergence using cell arrays and spiking systems. Overall, the results of the proposed methods demonstrate the potential of energy-efficient and hardware-implementable approaches using SNNs to solve COPs. To the best of the author's knowledge, this is the first study to solve the Max-Cut problem using an SNN neuromorphic hardware chip.