Apologies, for the late reply. By deep functions I simply meant small deep networks embedded in probabilistic models as a drop-in replacement for probability d

Apologies, for the late reply. By deep functions I simply meant small deep networks embedded in probabilistic models as a drop-in replacement for probability distributions, like e.g. a neuralHMM: https://pyro.ai/examples/hmm_funsor.html https://pyro.ai/examples/hmm_funsor.html Aside from looking into Pyro docs and all references, another good entry point is this publication: https://arxiv.org/pdf/1610.05735.pdf https://arxiv.org/pdf/1610.05735.pdf. Here the authors show how to use deep networks to aid sampling of complex probabilistic models.