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

2025-06-24

AI Summary

To address the poor scalability and limited solution quality of conventional quadratic Ising machines for high-order combinatorial optimization, this paper proposes a quadratic-free neuromorphic higher-order Ising machine. The architecture directly encodes arbitrary-order Ising clauses without quadratization, achieving interaction-order-independent resource complexity. It integrates asynchronous autoencoders with Fowler–Nordheim quantum tunneling annealing dynamics, with theoretical proof of asymptotic convergence. Hardware-aware optimizations—including latent-space sampling and graph-coloring-driven sparse interconnectivity—are introduced to enhance efficiency and physical feasibility. Evaluated on MAX-CUT and MAX-SAT benchmarks, the proposed machine achieves significantly higher solution quality and reduced solving time compared to equivalent second-order models operating under the same mechanism, thereby demonstrating superior performance, scalability, and hardware implementability.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

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.

Problem

• Develop scalable higher-order neuromorphic Ising machine
• Ensure asymptotic convergence to Ising ground state
• Solve combinatorial optimization problems efficiently

Innovation

• Asynchronous autoencoder captures higher-order interactions
• Fowler-Nordheim tunneling ensures asymptotic convergence
• Hardware co-design improves time-to-solution