Derives ODE deterministic equivalents and an adversarial homogenized SDE for SGD iterates in high-dim ℓ2-adversarial training, showing no constant learning rate ensures monotone descent for single-class adversarial least squares and equivalence to adaptive regularized standard SGD.
arXiv preprint arXiv:2010.00467 , year=
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Homogenization of $\ell_2$-Adversarial Training in High-Dimensions: Exact Dynamics under Stochastic Gradient Descent
Derives ODE deterministic equivalents and an adversarial homogenized SDE for SGD iterates in high-dim ℓ2-adversarial training, showing no constant learning rate ensures monotone descent for single-class adversarial least squares and equivalence to adaptive regularized standard SGD.