New arXiv paper shows unconstrained MLIPs face exponentially ill-conditioned sampling limits
CatAstro_Piyush · x · 2026-10-15
arXiv paper 2610.15078 challenges the assumption that energy-and-force matching alone ensures accurate molecular dynamics sampling. For unconstrained hypothesis classes, the relationship between prediction error and sampling accuracy is exponentially ill-conditioned in dimension. The authors identify two failure mechanisms — kinetic trapping (relaxation to accurate equilibrium takes exponentially long even from perfectly matched training configurations) and equilibrium mismatch (the learned stationary distribution stays far from target, even in local symmetry-preserving models). They also establish global energy-control conditions guaranteeing equilibrium accuracy.
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