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.
High-dimensional learning dynamics of multi-pass stochastic gradient descent in multi-index models, 2026
2 Pith papers cite this work. Polarity classification is still indexing.
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Proves uniform CLT for gradient flows in ERM and constructs an algorithm-aware, inversion-free covariance estimator for asymptotically valid time-uniform confidence intervals.
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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.
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Statistical Inference on Gradient Flows
Proves uniform CLT for gradient flows in ERM and constructs an algorithm-aware, inversion-free covariance estimator for asymptotically valid time-uniform confidence intervals.