Variational Neural Annealing

TL;DR

This paper introduces a variational annealing method using neural autoregressive models to efficiently find ground states in complex optimization landscapes, outperforming traditional simulated annealing especially in rough or glassy problems.

Contribution

It proposes a novel variational annealing framework leveraging neural autoregressive models for efficient optimization in complex landscapes, extending annealing techniques to modern neural network parameterizations.

Findings

Outperforms traditional simulated annealing on spin glass Hamiltonians

Efficiently searches for ground states in rough energy landscapes

Demonstrates potential of neural models in optimization tasks

Abstract

Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for groundstate solutions of a target Hamiltonian. While powerful, simulated annealing is known to have prohibitively slow sampling dynamics when the optimization landscape is rough or glassy. Here we show that by generalizing the target distribution with a parameterized model, an analogous annealing framework based on the variational principle can be used to search for groundstate solutions. Modern autoregressive models such as recurrent neural networks provide ideal parameterizations since they can be exactly sampled without slow dynamics even when the model encodes a rough landscape. We implement this procedure in the classical and quantum settings on several prototypical spin glass Hamiltonians, and find that it significantly outperforms traditional simulated annealing in the asymptotic limit, illustrating the potential power of this yet unexplored route to optimization.