[eli_gottlieb]

In more strictly mathematical terms, having a "normative" update rule (Bayes' rule) doesn't tell you what topology of latent variables the generative model "ought" to have, only how to link new information into a preexisting generative model.

Using the KL divergence of the posterior predictive distribution as a target to optimize does a bit better, but still isn't a "solution".

[thanatropism]

Seriously, what doeos "topology of latent variables" even mean?

A topology on U is a system of subsets of U that's closed under union and finite intersections and containing the empty set and U itself. Go!

[eli_gottlieb]

>Seriously, what doeos "topology of latent variables" even mean?

The simple answer is: the graph topology of the resulting program traces, equivalent to the topology of a graphical model sampled from a distribution over graphical models. The complicated answer is: the Scott topology of the program-trace space.