End-to-end learnable discrete-continuous models are compositional, tend togeneralize better,and are more interpretable.

We develop a method for generating causal post-hoc explanations of black-box classifiers based on a learned low-dimensional representation of the data. The explanation is causal in the sense that changing learned latent factors produces a change in the classifier output statistics.

Popular models for predicting the output (or label, response, outcome)yfrom theinput (orcovariate)xhavebeenfound erroneous when confronted with a distribution change, even from an essentially irrelevant perturbation like a position shift or background change forimages [91,6,102,41,2,27].

Givenasignature , a (possiblyinfinite) set Z andrelation-decoders ,a soft-structureisatuple Z =( Z, ). Inordertoground andevaluate architecture 3. Figure 1 outlines S and DCretains embeddings show regions, DC, increasing appears performance.

Randomized smoothing has been shown to provide good certified-robustness guarantees for high-dimensional classification problems.

Experimental results on both synthetic and real data demonstrate theefficacyoftheproposed frameworkfordomain adaptation.

The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs.