In the high-dimensional regime, SGD on diagonal linear networks is approximated by an SDE and a deterministic PDE that together give an explicit non-asymptotic description of convergence to zero risk.
Ethier and Thomas G
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Derives novel scaling limit and explicit consensus probabilities for mean-field voter model with heavy-tailed waiting times, governed by extreme-value landscape of the tail index.
General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.
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High-dimensional Limit of SGD for Diagonal Linear Networks
In the high-dimensional regime, SGD on diagonal linear networks is approximated by an SDE and a deterministic PDE that together give an explicit non-asymptotic description of convergence to zero risk.
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The mean field stubborn voter model
Derives novel scaling limit and explicit consensus probabilities for mean-field voter model with heavy-tailed waiting times, governed by extreme-value landscape of the tail index.
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Convergence rate of the occupation measure of classes of ergodic processes toward their invariant distribution in mean Wasserstein distance
General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.