# A Rate Transfer Method: Convergence Rates in Stochastic Gradient Descent via Stochastic Calculus

arXiv: https://arxiv.org/abs/2610.18739 · HTML: https://mlsanity.com/paper/2610.18739/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 5 of 5)

- [Stochastic modified equations and adaptive stochastic gradient algorithms](https://mlsanity.com/paper/1511.06251/) (2015)
- [Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations](https://mlsanity.com/paper/1811.01558/) (2018)
- [Continuous-time Models for Stochastic Optimization Algorithms](https://mlsanity.com/paper/1810.02565/) (2018)
- [Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation](https://mlsanity.com/paper/1902.00635/) (2019)
- [On uniform-in-time diffusion approximation for stochastic gradient descent](https://mlsanity.com/paper/2207.04922/) (2022)

## Abstract (arXiv)

We develop a rate-transfer method that converts finite-time Lyapunov estimates for an associated stochastic differential equation (SDE) into finite-time convergence bounds for stochastic gradient algorithms. Under generic moment and smoothness conditions, the convergence analysis of the stochastic gradient method reduces to a calculus argument verifying a Lyapunov generator inequality for the SDE. The method recovers established rates for classical stochastic gradient methods and provides a way to establish convergence rates for new optimization algorithms through calculus arguments applied to their associated SDEs.