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[2502.08834] Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers
Summary
The paper introduces Rex, a family of reversible exponential (stochastic) Runge-Kutta solvers designed to enhance the inversion accuracy of generative models based on neural differential equations, addressing limitations in existing solvers.
Why It Matters
As deep generative models gain traction in various applications, the ability to accurately invert these models is crucial for stability and performance. Rex offers a novel solution to overcome discretization errors, making it significant for researchers and practitioners in machine learning and AI.
Key Takeaways
- Rex solvers improve the inversion accuracy of generative models.
- They address issues with existing solvers that accumulate discretization errors.
- Theoretical and empirical analyses demonstrate their effectiveness.
- Rex enhances sampling of Boltzmann distributions and image generation.
- The approach is applicable to both ODE and SDE domains.
Computer Science > Machine Learning arXiv:2502.08834 (cs) [Submitted on 12 Feb 2025 (v1), last revised 19 Feb 2026 (this version, v3)] Title:Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers Authors:Zander W. Blasingame, Chen Liu View a PDF of the paper titled Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers, by Zander W. Blasingame and Chen Liu View PDF Abstract:Deep generative models based on neural differential equations have quickly become the state-of-the-art for numerous generation tasks across many different applications. These models rely on ODE/SDE solvers which integrate from a prior distribution to the data distribution. In many applications it is highly desirable to then integrate in the other direction. The standard solvers, however, accumulate discretization errors which don't align with the forward trajectory, thereby prohibiting an exact inversion. In applications where the precision of the generative model is paramount this inaccuracy in inversion is often unacceptable. Current approaches to solving the inversion of these models results in significant downstream issues with poor stability and low-order of convergence; moreover, they are strictly limited to the ODE domain. In this work, we propose a new family of reversible exponential (stochastic) Runge-Kutta solvers which we refer to as Rex developed by an application of Lawson methods to convert any explicit (stochastic) Runge-Kutta scheme into a reversible ...
