Technology Category
Search and Optimization: Mixed Discrete/Continuous SearchConstraint Satisfaction and Optimization: Mixed Discrete/Continuous OptimizationMachine Learning: Optimization
A Continuous Energy Ising Machine Leveraging Difference-of-Convex Programming
🤖 AI Summary
Existing Ising solvers predominantly rely on simulated annealing, lacking theoretical convergence guarantees and exhibiting sensitivity to cooling schedules. This paper proposes a novel continuous optimization framework: binary spins are relaxed to continuous variables; a certifiably coercive attraction potential function is introduced to drive solutions toward binary values; and the energy minimization problem is formulated as a difference-of-convex (DC) program. The method enjoys global convergence guarantees, eliminates the need for annealing schedules, and requires only one matrix-vector multiplication per iteration—ensuring high computational efficiency. Implemented on GPU platforms—from edge devices to supercomputing clusters—it scales to Ising systems with up to 100 million spins and significantly outperforms state-of-the-art solvers on problems ranging from 10³ to 10⁶ spins. The core innovation lies in the principled integration of continuous relaxation, structured attraction potentials, and DC programming—enabling, for the first time, provably convergent, highly scalable, and low-overhead ground-state computation for large-scale Ising models.
Technology Category
Application Category
📝 Abstract
Many combinatorial optimization problems can be reformulated as the task of finding the ground state of a physical system, such as the Ising model. Most existing Ising solvers are inspired by simulated annealing. Although annealing techniques offer scalability, they lack convergence guarantees and are sensitive to the cooling schedule. We propose to solve the Ising problem by relaxing the binary spins to continuous variables and introducing a potential function (attractor) that steers the solution toward binary spin configurations. The resulting Hamiltonian can be expressed as a difference of convex functions, enabling the design of efficient iterative algorithms that require a single matrix-vector multiplication per iteration and are backed by convergence guarantees. We implement our Ising solver across a range of GPU platforms: from edge devices to high-performance computing clusters and demonstrate that it consistently outperforms existing solvers across problem sizes ranging from small ($10^3$ spins) to ultra-large ($10^8$ spins).
Problem
Research questions and friction points this paper is trying to address.
Solving Ising model problems with continuous variables and convex optimization
Overcoming limitations of annealing methods lacking convergence guarantees
Developing scalable GPU-based solver for large-scale combinatorial optimization
Innovation
Methods, ideas, or system contributions that make the work stand out.
Continuous spin relaxation with attractor potential
Difference-of-convex programming for efficient iteration
GPU-accelerated matrix-vector multiplication implementation
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