IsingFormer: Augmenting Parallel Tempering With Learned Proposals

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.