Higher-Order Neuromorphic Ising Machines -- Autoencoders and Fowler-Nordheim Annealers are all you need for Scalability

TL;DR

This paper introduces a higher-order neuromorphic Ising machine that leverages autoencoders and Fowler-Nordheim annealing to improve scalability, solution quality, and speed in solving complex combinatorial optimization problems.

Contribution

It proposes a novel higher-order Ising machine architecture that directly manipulates Ising clauses, maintaining resource efficiency and demonstrating superior performance over second-order models.

Findings

Achieves higher solution quality than second-order Ising machines.

Provides faster solution times across multiple benchmark problems.

Demonstrates effective use of sparsity techniques and FPGA hardware co-design.

Abstract

We report a higher-order neuromorphic Ising machine that exhibits superior scalability compared to architectures based on quadratization, while also achieving state-of-the-art quality and reliability in solutions with competitive time-to-solution metrics. At the core of the proposed machine is an asynchronous autoencoder architecture that captures higher-order interactions by directly manipulating Ising clauses instead of Ising spins, thereby maintaining resource complexity independent of interaction order. Asymptotic convergence to the Ising ground state is ensured by sampling the autoencoder latent space defined by the spins, based on the annealing dynamics of the Fowler-Nordheim quantum mechanical tunneling. 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. Our findings indicate that the proposed architecture consistently provides higher quality solutions in shorter time frames compared to the second-order model across multiple runs. Additionally, we show that the techniques based on the sparsity of the interconnection matrix, such as graph coloring, can be effectively applied to higher-order neuromorphic Ising machines, enhancing the solution quality and the time-to-solution. The time-to-solution can be further improved through hardware co-design, as demonstrated in this paper using a field-programmable gate array (FPGA). The results presented in this paper provide further evidence that autoencoders and Fowler-Nordheim annealers are sufficient to achieve reliability and scaling of any-order neuromorphic Ising machines.