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Through 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.
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10/14/2026
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Related Claims
UnverifiedA 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.80% 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.76% 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% similarUnverifiedThe threshold for switching between the fast and slow paths is not a constant set once and for all, but a parameter that requires continuous calibration as the input distribution changes, and it should be written as an observable, adjustable configuration.73% similarUnverifiedPrevious generalization analyses of flow matching/diffusion models often required strong restrictive assumptions on the estimated velocity field, such as global Lipschitz continuity, bounded norm, or specific regularity conditions.71% similar
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