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This work concerns the development of deep networks that are certifiably robust to adversarial attacks. Joint robust classification-detection was recently introduced as a certified defense mechanism, where adversarial examples are either correctly classified or assigned to the “abstain” class. In this work, we show that such a provable framework can benefit by extension to networks with multiple explicit abstain classes, where the adversarial examples are adaptively assigned to those. We show that naïvely adding multiple abstain classes can lead to “model degeneracy”, then we propose a regularization approach and a training method to counter this degeneracy by promoting full use of the multiple abstain classes. Our experiments demonstrate that the proposed approach consistently achieves favorable standard vs. robust verified accuracy tradeoffs, outperforming state-of-the-art algorithms for various choices of number of abstain classes 

Despite the success of large-scale empirical risk minimization (ERM) at achieving high accuracy across a variety of machine learning tasks, fair ERM is hindered by the incompatibility of fairness constraints with stochastic optimization. We consider the problem of fair classification with discrete sensitive attributes and potentially large models and data sets, requiring stochastic solvers. Existing in-processing fairness algorithms are either impractical in the large-scale setting because they require large batches of data at each iteration or they are not guaranteed to converge. In this paper, we develop the first stochastic in-processing fairness algorithm with guaranteed convergence. For demographic parity, equalized odds, and equal opportunity notions of fairness, we provide slight variations of our algorithm–called FERMI–and prove that each of these variations converges in stochastic optimization with any batch size. Empirically, we show that FERMI is amenable to stochastic solvers with multiple (non-binary) sensitive attributes and non-binary targets, performing well even with minibatch size as small as one. Extensive experiments show that FERMI achieves the most favorable tradeoffs between fairness violation and test accuracy across all tested setups compared with state-of-the-art baselines for demographic parity, equalized odds, equal opportunity. These benefits are especially significant with small batch sizes and for non-binary classification with large number of sensitive attributes, making FERMI a practical, scalable fairness algorithm. The code for all of the experiments in this paper is available at: https://github.com/optimization-for-data-driven-science/FERMI.