Derives explicit step-size conditions ensuring the metastability behavior of discrete SGD under heavy-tailed noise approximates its continuous SDE limit.
Kramers' law: Validity, derivations and generalisations
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abstract
Kramers' law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. We review different approaches that have been followed to obtain a mathematically rigorous proof of this formula. We also discuss some generalisations, and a case in which Kramers' law is not valid. This review is written for both mathematicians and theoretical physicists, and endeavours to link concepts and terminology from both fields.
verdicts
UNVERDICTED 2representative citing papers
A stochastic gradient flow on particle swarms driven by a softmin energy approximation converges to global minima for strongly convex functions and exhibits faster hitting times between wells than overdamped Langevin dynamics.
citing papers explorer
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First Exit Time Analysis of Stochastic Gradient Descent Under Heavy-Tailed Gradient Noise
Derives explicit step-size conditions ensuring the metastability behavior of discrete SGD under heavy-tailed noise approximates its continuous SDE limit.
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Global Optimization via Softmin Energy Minimization
A stochastic gradient flow on particle swarms driven by a softmin energy approximation converges to global minima for strongly convex functions and exhibits faster hitting times between wells than overdamped Langevin dynamics.