4 problems

Weight-sensitive complexity conjecture. The true complexity of sequential Monte Carlo should depend not on the minimum weight, but either on a bottleneck coefficient or on the tota…

Low-density Jacobian conjecture. Separatrices in the pushforward density follow from the intrinsic difficulty of capturing the correct slope, or Jacobian determinant, of $S$ in reg…

Multimodal Langevin-sampling conjecture. The observed separatrices further demonstrate the difficulty of sampling from multimodal distributions with Langevin dynamics.

Let $\pi_{\sigma}$ be a mixture distribution of the form … where $f_{1},\ldots,f_{k}$ are probability densities, $\mu_{1},\ldots,\mu_{k}\geq 0$ are fixed weights satisfying…