Lagrange Oscillatory Neural Networks for Constraint Satisfaction and Optimization

TL;DR

This paper introduces Lagrange Oscillatory Neural Networks (LagONN), a physics-inspired approach that effectively solves constrained combinatorial optimization problems by guiding oscillatory neural systems towards feasible solutions using Lagrange multipliers.

Contribution

The paper proposes a novel LagONN model that incorporates Lagrange oscillators to handle constraints, improving upon existing Ising machines for constrained optimization tasks.

Findings

Successfully solved Max-3-SAT instances with up to 200 variables and 860 clauses.

Demonstrated deterministic solutions as an alternative to simulated annealing.

Showcased potential for applying Lagrange oscillators to other constraint types.

Abstract

Physics-inspired computing paradigms are receiving renewed attention to enhance efficiency in compute-intensive tasks such as artificial intelligence and optimization. Similar to Hopfield neural networks, oscillatory neural networks (ONNs) minimize an Ising energy function that embeds the solutions of hard combinatorial optimization problems. Despite their success in solving unconstrained optimization problems, Ising machines still face challenges with constrained problems as they can become trapped in infeasible local minima. In this paper, we introduce a Lagrange ONN (LagONN) designed to escape infeasible states based on the theory of Lagrange multipliers. Unlike existing oscillatory Ising machines, LagONN employs additional Lagrange oscillators to guide the system towards feasible states in an augmented energy landscape, settling only when constraints are met. Taking the maximum satisfiability problem with three literals as a use case (Max-3-SAT), we harness LagONN's constraint satisfaction mechanism to find optimal solutions for random SATlib instances with up to 200 variables and 860 clauses, which provides a deterministic alternative to simulated annealing for coupled oscillators. We benchmark LagONN with SAT solvers and further discuss the potential of Lagrange oscillators to address other constraints, such as phase copying, which is useful in oscillatory Ising machines with limited connectivity.