# Light Schr\\"odinger Bridge

Source: [Light Schr\\"odinger Bridge](<https://www.sota2.com/research/paper/68fa728e1e209131cea57068>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T02:28:52.799Z

Authors: Alexander Korotin, Nikita Gushchin, Evgeny Burnaev

Published: 2023-10-02T13:06:45.000Z

## Abstract

Despite the recent advances in the field of computational Schr\\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., $k$-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Intermediate distribution restoration on Single-cell data (intermediate time points ti for i in {1, 2, 3})](<https://www.sota2.com/research/sota/intermediate-distribution-restoration-on-single-cell-data-intermediate-time-points-ti-for-i-in-1-2-3.md>): Intermediate distribution restoration; Single-cell data (intermediate time points ti for i in {1, 2, 3}); W1 Score: 0.823.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2310.01174>)

[PDF](<https://arxiv.org/pdf/2310.01174.pdf>)