# Explicit and Effectively Symmetric Schemes for Neural SDEs

**Authors:** Daniil Shmelev, Cristopher Salvi  
**arXiv:** [2509.20599](https://arxiv.org/abs/2509.20599)  
**Date:** 2025-09-24  
**Summary page:** https://www.summarizepaper.com/en/paper/2509.20599v1/

## Key points

- Authors Daniil Shmelev and Cristopher Salvi address challenges of backpropagation through neural stochastic differential equation (SDE) solvers.
- They propose a novel class of stable, near-reversible Runge-Kutta schemes called Explicit and Effectively Symmetric (EES) schemes for neural SDEs.
- EES schemes offer superior stability and reliability compared to traditional methods.
- Numerical experiments show that EES schemes enable scalable and accurate training of neural SDEs without severe restrictions on step size or model complexity.
- This contribution advances the field of neural SDE solvers and enhances training strategies in deep learning applications.

## Summary

In their paper titled "Explicit and Effectively Symmetric Schemes for Neural SDEs," authors Daniil Shmelev and Cristopher Salvi address the challenges of backpropagation through (neural) stochastic differential equation (SDE) solvers. They propose a novel class of stable, near-reversible Runge-Kutta schemes specifically designed for neural SDEs to overcome limitations of existing methods. These Explicit and Effectively Symmetric (EES) schemes offer superior stability and reliability compared to traditional approaches. Through numerical experiments, the authors demonstrate that their EES schemes provide a practical foundation for scalable and accurate training of neural SDEs without imposing severe restrictions on step size or model complexity. This contribution significantly advances the field of neural SDE solvers and paves the way for more effective training strategies in deep learning applications.