3 problems

The square-root condition-number conjecture. Although existing sampling algorithms require a number of iterations scaling at least linearly in $\kappa$, underdamped dynamics might…

The underdamped Langevin condition-number acceleration conjecture. Underdamped algorithms should have better dependence on the condition number $\kappa$ than existing sampling algo…

The underdamped Langevin acceleration conjecture. Underdamped Langevin dynamics has long been conjectured to be the natural candidate for acceleration in log-concave sampling.