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Both transduction and rejection have emerged as important techniques fordefending against adversarial perturbations. A recent work by Tram\`er showedthat, in the rejection-only case (no transduction), a strong rejection-solutioncan be turned into a strong (but computationally inefficient) non-rejectionsolution. This detector-to-classifier reduction has been mostly applied to giveevidence that certain claims of strong selective-model solutions aresusceptible, leaving the benefits of rejection unclear. On the other hand, arecent work by Goldwasser et al. showed that rejection combined withtransduction can give provable guarantees (for certain problems) that cannot beachieved otherwise. Nevertheless, under recent strong adversarial attacks(GMSA, which has been shown to be much more effective than AutoAttack againsttransduction), Goldwasser et al.'s work was shown to have low performance in apractical deep-learning setting. In this paper, we take a step towardsrealizing the promise of transduction+rejection in more realistic scenarios.Theoretically, we show that a novel application of Tram\`er'sclassifier-to-detector technique in the transductive setting can givesignificantly improved sample-complexity for robust generalization. While ourtheoretical construction is computationally inefficient, it guides us toidentify an efficient transductive algorithm to learn a selective model.Extensive experiments using state of the art attacks (AutoAttack, GMSA) showthat our solutions provide significantly better robust accuracy.

Two Heads are Better than One: Towards Better Adversarial Robustness by Combining Transduction and Rejection