Higher-order neuromorphic Ising machines—autoencoders and Fowler-Nordheim annealers are all you need for scalability
Faiek Ahsan, Saptarshi Maiti, Zihao Chen, Jakob Kaiser, Ankita Nandi, Madhuvanthi Srivatsav, Johannes Schemmel, Andreas G. Andreou, Jason K. Eshraghian, Chetan Singh Thakur, Shantanu Chakrabartty · Nature Communications · 2026
We report that an autoencoder-based neuromorphic architecture, combined with Fowler-Nordheim annealing, is sufficient to implement scalable higher-order Ising machines. We show that these machines can consistently produce state-of-the-art solutions with high reliability and with competitive time-to-solution metrics. The autoencoder captures higher-order interactions by decomposing Ising clauses and Ising spins into encoder-decoder layers of spiking neurons, thereby keeping the resource complexity independent of the interaction order for sparse problems. An annealing process based on the dynamics of Fowler-Nordheim quantum mechanical tunneling extrapolates between an $${{\mathcal{O}}}(1/t)$$ annealing schedule and an $${{\mathcal{O}}}(1/\log (t))$$ annealing schedule. This not only ensures fast convergence towards high-quality solutions but also guarantees asymptotic convergence to the Ising ground state. To demonstrate the advantages of the proposed higher-order neuromorphic Ising machine, we systematically solved benchmark combinatorial optimization problems such as MAX-CUT and MAX-SAT, comparing the results to those obtained using a second-order Ising machine employing the same annealing process. The authors demonstrate that an autoencoder-based neuromorphic architecture combined with Fowler-Nordheim annealing, is sufficient to implement scalable higher-order Ising machines. They show that these machines can consistently produce state-of-the-art solutions with high reliability and competitive time-to-solution metrics.