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A recent study proposed a 'rate transfer' method that, through Lyapunov analysis of stochastic differential equations (SDEs), directly converts continuous-time stability estimates into finite-time convergence bounds for discrete algorithms.
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10/14/2026
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UnverifiedThrough refined moment conditions (such as bounded variance or sub-Gaussianity of the gradient noise) and smoothness assumptions on the drift term (such as Lipschitz continuity), the rate transfer theorem proves that the deviation between the discrete trajectory and the SDE trajectory can be bounded within a finite time by a power of the step size.80% similarUnverifiedThe rate transfer theorem states that if the Lyapunov generator inequality holds for the coefficients $(b,\sigma)$, and the SGD update operator and the SDE coefficients satisfy certain moment and smoothness matching conditions, then the expected Lyapunov function of the discrete iteration also decays at a similar rate, and an explicit finite-time bound is given.75% similarUnverifiedExperiments show that the lightweight variant consistently and stably improves transfer performance compared to random sampling.72% similarUnverifiedThe rate transfer proposed in the paper does not require an extremely small step size, but instead quantifies the deviation between the SDE and SGD at a finite step size, thereby obtaining non-asymptotic convergence bounds.71% similarUnverifiedMPE targets discrete-time, finite-state stochastic processes and measures the average improvement in prediction accuracy when using the complete history compared to using only the static marginal distribution.70% similar
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