Higher-order neuromorphic Ising machines-autoencoders and Fowler-Nordheim annealers are all you need for scalability.

Abstract

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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>/</mo><mi>t</mi></mrow><mo>)</mo></mrow></math> annealing schedule and an <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>/</mo><mi>log</mi><mrow><mo>(</mo><mrow><mi>t</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow></math> 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.