Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning.

Tothisend,weshowthat parameter gradients and forces of such inverses can be computed from forward evaluations viatheinversefunction theorem.

All GEMINIsaresummarisedin Table 1, (see Appendix Dforderivations). Figure 2: Clusteringofamixtureof 3 Gaussiandistributionswith MI (left) anda GEMINI (right) usingcategoricaldistributions.