Lifted Schr\"odinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions
arXiv:2605.24795v1 Announce Type: cross Abstract: We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schr\"odinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a lifted path-space construction in which each trajectory is augmented with a source--target component label. Consequently, the problem decomposes into Gaussian component-to-component Schr\"odinger bridges with explicit marginal, drift, and cost formulas, while the mixture-level assignment reduces to a finite-dime
The paper tackles a known computational challenge in optimal transport theory, which is critical for complex control problems in AI and robotics, suggesting advances in solving such problems efficiently.
This research provides a theoretical advancement in probabilistic control, enabling more sophisticated and efficient management of systems with uncertain dynamics, especially relevant for robotics and agentic AI.
The proposed 'lifted path-space construction' simplifies complex stochastic density control between Gaussian mixtures, potentially leading to more tractable large-scale AI and robotics applications.
- · AI researchers
- · Robotics developers
- · Autonomous systems sector
- · Systems relying on computationally intensive stochastic control methods
More efficient algorithms for complex probabilistic control problems, particularly in robotics and generative AI.
Accelerated development of robust autonomous agents capable of navigating high-dimensional and uncertain environments.
New classes of AI applications that were previously intractable due to computational limits in managing stochastic dynamics.
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