  Probabilistic models are a critical part of the modern deep learning toolbox
- ranging from generative models (VAEs, GANs), sequence to sequence models used
in machine translation and speech processing to models over functional spaces
(conditional neural processes, neural processes). Given the size and complexity
of these models, safely deploying them in applications requires the development
of tools to analyze their behavior rigorously and provide some guarantees that
these models are consistent with a list of desirable properties or
specifications. For example, a machine translation model should produce
semantically equivalent outputs for innocuous changes in the input to the
model. A functional regression model that is learning a distribution over
monotonic functions should predict a larger value at a larger input.
Verification of these properties requires a new framework that goes beyond
notions of verification studied in deterministic feedforward networks, since
requiring worst-case guarantees in probabilistic models is likely to produce
conservative or vacuous results. We propose a novel formulation of verification
for deep probabilistic models that take in conditioning inputs and sample
latent variables in the course of producing an output: We require that the
output of the model satisfies a linear constraint with high probability over
the sampling of latent variables and for every choice of conditioning input to
the model. We show that rigorous lower bounds on the probability that the
constraint is satisfied can be obtained efficiently. Experiments with neural
processes show that several properties of interest while modeling functional
spaces can be modeled within this framework (monotonicity, convexity) and
verified efficiently using our algorithms
