Derives joint asymptotic jump-diffusion limit for global parameters and latent variables in SGLD-Gibbs under space-time rescaling, yielding explicit hyperparameter tuning guidance for calibrated uncertainty quantification.
Hitting the high-dimensional notes: An ode for sgd learning dynamics on glms and multi-index models, 2023
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At the critical step-size scaling for SGD in high-dimensional single-layer networks, effective dynamics gain a diffusive correction term that changes the phase diagram and reduces to an Ornstein-Uhlenbeck process near fixed points, with the information exponent governing sample complexity.
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Large-scale Uncertainty Quantification for Latent Variable Models Using Subsampling Markov Chain Monte Carlo
Derives joint asymptotic jump-diffusion limit for global parameters and latent variables in SGLD-Gibbs under space-time rescaling, yielding explicit hyperparameter tuning guidance for calibrated uncertainty quantification.
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Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks
At the critical step-size scaling for SGD in high-dimensional single-layer networks, effective dynamics gain a diffusive correction term that changes the phase diagram and reduces to an Ornstein-Uhlenbeck process near fixed points, with the information exponent governing sample complexity.