Homogenization of 2-Adversarial Training in High-Dimensions: Exact Dynamics under Stochastic Gradient Descent
Fabrizzio Sabelli
math.OC, cs.LG, math.PR, stat.ML
Submitted: 2026-06-30
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- From high-dimensional & mean-field dynamics to dimensionless ODEs: A unifying approach to SGD in two-layers networks
- Escaping mediocrity: how two-layer networks learn hard generalized linear models with SGD
- High-dimensional limit theorems for SGD: Effective dynamics and critical scaling
- High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance
- Lower Bounds on Adversarial Robustness from Optimal Transport
- Learning Curves for SGD on Structured Features
- The high-dimensional asymptotics of first order methods with random data
- Why adversarial training can hurt robust accuracy
- Exact Dynamics of Multi-class Stochastic Gradient Descent
- Revisiting Outer Optimization in Adversarial Training
- Smoothing the Landscape Boosts the Signal for SGD: Optimal Sample Complexity for Learning Single Index Models
- Sharp Statistical Guarantees for Adversarially Robust Gaussian Classification
- The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponents
- Provable tradeoffs in adversarially robust classification
- High-dimensional learning dynamics of multi-pass Stochastic Gradient Descent in multi-index models
- Adversarial Training for Gradient Descent: Analysis Through its Continuous-time Approximation
- The curse of overparametrization in adversarial training: Precise analysis of robust generalization for random features regression
- Precise Statistical Analysis of Classification Accuracies for Adversarial Training
- Precise Tradeoffs in Adversarial Training for Linear Regression
- Trajectory of Mini-Batch Momentum: Batch Size Saturation and Convergence in High Dimensions
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