Localized Schr\"odinger Bridge Sampler
Georg A. Gottwald, Sebastian Reich

TL;DR
This paper introduces a localized Schr"odinger bridge sampling method that reduces high-dimensional sampling problems into multiple low-dimensional problems, improving efficiency and extending to conditional and Bayesian sampling.
Contribution
It proposes a novel localization strategy for Schr"odinger bridge samplers that exploits conditional independence, enabling scalable high-dimensional sampling and connections to transformer architectures.
Findings
Effective in high-dimensional Gaussian sampling
Demonstrates success on stochastic process data
Extends to conditional and Bayesian inference
Abstract
We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. In this paper, we build on previous work combining Schr\"odinger bridges and plug & play Langevin samplers. A key bottleneck of these approaches is the exponential dependence of the required training samples on the dimension, , of the ambient state space. We propose a localization strategy which exploits conditional independence of conditional expectation values. Localization thus replaces a single high-dimensional Schr\"odinger bridge problem by low-dimensional Schr\"odinger bridge problems over the available training samples. In this context, a connection to multi-head self attention transformer architectures is established. As for the original Schr\"odinger bridge sampling approach, the localized sampler is stable and geometric ergodic.…
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Taxonomy
TopicsTerahertz technology and applications
MethodsSoftmax · Attention Is All You Need
