Replace independent categorical proposals or reversible Metropolis updates for discrete latent variables with a lifted sampler carrying persistent continuous edge momenta. Neighbor transitions are biased by the momentum and use a symmetric energy factor, so momentum reversal gives the required balance relation for the target Gibbs distribution while ordinary dynamics remain non-reversible. This should reduce random-walk behavior when sampling multimodal categorical latents or token sequences.
Replace the usual parameter-plus-momentum Langevin state with a three-level chain consisting of parameters, velocity, and acceleration, while injecting Gaussian noise only into the highest auxiliary state. At a saddle, the escaping direction has a positive rate given by a cubic characteristic equation; use this rate to choose damping or adapt the temperature so that basin escape is accelerated without making the dynamics unstable.
Represent a set of neural prototypes, mixture components, or latent particles by N points in R^2, and initialize or refresh them with Langevin dynamics targeting a quadratically confined logarithmic Coulomb gas. The logarithmic repulsion prevents particle collapse, while the paper's N-uniform logarithmic Sobolev inequality predicts that mixing need not degrade as the particle bank grows.