Appendix A Probabilistic Specifications: Examples

Below we provide further examples of specifications that can be captured by our framework. Another desirable specification towards ensuring reliable uncertainty calibration for NNs is that the expected uncertainty in the predictions increases monotonically with an increase in the variance of the input-noise distribution. We can capture this specification within the formulation described by equation 1, by letting: 1. P A natural generalization of this specification is one where low reconstruction error is guaranteed in expectation, since in practice the latent-representations that are fed into the decoder are drawn from a normal distribution whose mean and variance are predicted by the encoder. A more general specification is one where we wish to verify that for a set of norm-bounded points around a given input, the expected reconstruction error from the VAE is small. Writing this in terms of expected values, we obtain g (λ).