  Generative neural networks can be used to specify continuous transformations
between images via latent-space interpolation. However, certifying that all
images captured by the resulting path in the image manifold satisfy a given
property can be very challenging. This is because this set is highly
non-convex, thwarting existing scalable robustness analysis methods, which are
often based on convex relaxations. We present ApproxLine, a scalable
certification method that successfully verifies non-trivial specifications
involving generative models and classifiers. ApproxLine can provide both sound
deterministic and probabilistic guarantees, by capturing either infinite
non-convex sets of neural network activation vectors or distributions over such
sets. We show that ApproxLine is practically useful and can verify interesting
interpolations in the networks latent space.
