Kinetic traps in Latent MCMC

[franknoe]

Current Boltzmann Generators: In nontrivial systems, the transformation can contain what I will call "trap states". In reweighting (as used in the Boltzmann Generator paper) these trap states will also have an effect because they get a lot of weight, but in this approach they are just producing "outliers" in expectations computed from the sampling, such as peaks in the free energy profile. By doing model averaging (as done in the paper), this problem seems to disappear on average because the mean free energy is correct within uncertainties. But for MCMC this is a problem, because the system gets trapped there for a long time.

See Figure 3 here:
https://github.com/noegroup/project_boltzmann_generators/blob/master/latent_mcmc/manuscript.pdf

I am not actually sure if these states cause the statistics to be wrong, but in practice they cause a sampling problem. Trap states are stabilized by something, for example an exceptionally large latent vector or an exceptionally large value of the log determinant. My feeling is that they need to be avoided by some form of regularization that makes the Boltzmann Generator transformation more "smooth" or less "peaky". Perhaps NICE networks alone do not have this problem (I used to have similar problems when using NICE networks alone, but many things got changed since then, so I can't put the finger on that), but NICE alone is not expressive enough.

Note that this particle system is especially hard because of the permutation invariance of solvent particles, so I would not recommend to use that system for addressing this problem, but to find a simpler system where the problem also arises and study it there.