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I've been working on using the RTBM as the integration driver for VegasFlow (i.e., instead of using the Vegas algorithm for sampling, using the RTBM). For that I needed several changes, some of them 100% needed (like the transformation to the sampling) although they could be if needed in the VegasFlow side.
Some are really needed inside the RTBM but are there just to facilitate the optimization (the gaussian initialization and forcing positivity through the cholesky decomposition).
The PR that implements the RTBM can be seen in: N3PDF/vegasflow#68

The main changes that this PR introduces are:

  • The possibility to save (and thus train) the parameters of the RTBM as the cholesky decomposition of the matrices (to ensure positivity).
  • Gaussian initialization (a bit modified but mainly @scarrazza version)
  • Transformation to the sampling (and the corresponding jacobian) to ensure the sampling is fixed between 0 and 1.
  • Inverse transformation (could be useful for training, still not sure)

There are, however, many points that need to be improved. The main that comes to mind is the fact that the boundaries don't really mean much now as I haven't really transformed then that much.

Note: There are many changes in this PR (and not all of them useful) so I don't think this should be merge as is, but since @scarrazza is thinking on maybe having a student work on this, it's better if they have all changes available.

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