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.
Exact solution for on-line learning in multilayer neural networks.Physical Review Letters, 74(21):4337
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Derives α^{-1/3} scaling for generalization error in online softmax classification from boundary layers in a teacher-student model.
Gradient flow in energy-based models for strictly positive binary distributions produces stable data-consistent fixed points and a learning hierarchy that favors lower-order interactions first, mechanistically explaining distributional simplicity bias.
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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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A Boundary-Layer Mechanism for One-Third Scaling in Online Softmax Classification
Derives α^{-1/3} scaling for generalization error in online softmax classification from boundary layers in a teacher-student model.
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Distributional simplicity bias and effective convexity in Energy Based Models
Gradient flow in energy-based models for strictly positive binary distributions produces stable data-consistent fixed points and a learning hierarchy that favors lower-order interactions first, mechanistically explaining distributional simplicity bias.