FrOGS: Discrete Neural Sampler for Independent Alloy Configurations Across Chemical Conditions

What the math gives to ML

The paper contains a transferable discrete-sampling construction: an autoregressive generator is augmented with a continuous-time Markov chain whose moves are local single-site species substitutions. This is useful for neural samplers over combinatorial objects because the autoregressive component can make global proposals while the CTMC supplies local stochastic refinement, potentially reducing mode collapse. The explicit effective sample size formula provides a practical, scale-invariant signal for detecting weight degeneracy and adapting the sampler during training. The most immediately testable transfer is an ESS-controlled autoregressive-plus-CTMC sampler for discrete sequences, molecular graphs, or constrained categorical assignments.