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This paper introduces IsingFormer, a Transformer-based model that enhances Parallel Tempering by generating high-quality proposal moves for Markov Chain Monte Carlo sampling. By leveraging learned proposals from finite-temperature configurations, the method achieves significantly faster convergence on complex problems like 3D spin glasses and integer factorization without inflating the time-to-solution exponent. The work demonstrates a practical pathway for integrating generative AI directly into rigorous statistical physics workflows to accelerate optimization and sampling tasks.
IsingFormer: Augmenting Parallel Tempering With Learned Proposals
arXiv:2509.23043v2 Announce Type: replace-cross Abstract: Generative models have been extensively used to accelerate MCMC mixing for sampling and optimization, but their effective integration with standard MCMC remains an open question. Here, we introduce a global proposal move in which finite-temperature configurations from an external generator are used as proposals within Parallel Tempering (PT). We examine a specific generator, IsingFormer, a Transformer trained on long-run MCMC configurations intended to approximate equilibrium distributions, and call the resulting framework Transformer-Augmented Parallel Tempering (TAPT). The IsingFormer exhibits two useful capabilities: interpolation to untrained $\beta$ values and conditional completion under clamped settings absent from training. On 3D spin-glass instances, TAPT reaches substantially lower residual energies than standard PT in fewer Monte Carlo sweeps. On integer factorization, we show how a structured problem encoding can amortize the training cost by training IsingFormer once and reusing the same model across target products that were not imposed during training. Finally, in a scaling study that uses long-run MCMC configurations as proposals, with proposal generation excluded from the timing, TAPT reduces the fitted time-to-solution exponent by approximately $33\%$ relative to PT over the tested problem sizes.
Abstract:Generative models have been extensively used to accelerate MCMC mixing for sampling and optimization, but their effective integration with standard MCMC remains an open question. Here, we introduce a global proposal move in which finite-temperature configurations from an external generator are used as proposals within Parallel Tempering (PT). We examine a specific generator, IsingFormer, a Transformer trained on long-run MCMC configurations intended to approximate equilibrium distributions, and call the resulting framework Transformer-Augmented Parallel Tempering (TAPT). The IsingFormer exhibits two useful capabilities: interpolation to untrained $\beta$ values and conditional completion under clamped settings absent from training. On 3D spin-glass instances, TAPT reaches substantially lower residual energies than standard PT in fewer Monte Carlo sweeps. On integer factorization, we show how a structured problem encoding can amortize the training cost by training IsingFormer once and reusing the same model across target products that were not imposed during training. Finally, in a scaling study that uses long-run MCMC configurations as proposals, with proposal generation excluded from the timing, TAPT reduces the fitted time-to-solution exponent by approximately $33\%$ relative to PT over the tested problem sizes.
Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech); Artificial Intelligence (cs.AI); Computational Physics (physics.comp-ph)
arXiv:2509.23043 [cs.LG]
(or arXiv:2509.23043v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2509.23043 Focus to learn more arXiv-issued DOI via DataCite
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