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.
On the geometry of regularization in adversarial training: High-dimensional asymptotics and generalization bounds, 2024
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Thesis uses statistical mechanics to study DAM and RBM models for understanding memorization, low-dimensional learning, and adversarial robustness in neural networks.
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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.