Add a replay buffer to KLXX training

Develop and analyze a replay-buffer extension of the KLXX normalizing-flow Boltzmann generator that reuses QT samples and target-surrogate samples from earlier training steps, with the purpose of reducing repeated sampling and exploration costs.

Background

The KLXX training procedure constructs a QT sample set and rebuilds target-surrogate samples during training. The paper notes that FAB reuses annealed samples through a prioritized replay buffer, whereas KLXX does not. Reusing samples from earlier iterations could reduce the cost of repeatedly constructing QT and sequential Monte Carlo batches, but the effects on bias, sample staleness, gradient variance, mode coverage, and theoretical guarantees remain unresolved.

References

A replay buffer would let the QT set and the target surrogate of earlier steps be reused, as FAB reuses its annealed samples \citep{midgley2022flow}, and adding one to KLXX is left to future work.

Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variation  (2609.09473 - Feng et al., 8 Sep 2026) in Section 7, Conclusions