The paper presents a new formulation of the Schr"odinger bridge problem on graphs that incorporates state costs via a Feynman‑Kac tilt, eliminating the need for learned control or temporal‑difference penalties. The resulting cost‑augmented bridge is solved exactly by alternating two endpoint rescalings, each requiring only a sparse matrix‑exponential application, and the method scales linearly with network size. Experiments on a protein‑folding model and a large road‑network demonstrate that the exact bridge reduces expected energy barriers and matches target distributions within sampling error.
arXiv:2606. 04265v1 Announce Type: cross Abstract: The Schr\"odinger Bridge Problem constructs a stochastic process that connects an initial distribution to a terminal distribution with minimum energy.
arXiv:2607. 16987v1 Announce Type: cross Abstract: Over the past few years, diffusion-based Schr\"odinger bridge models have been proposed to approximate optimal transport dynamics between two prescribed boundary distributions, with successful applications to generative modeling.
arXiv:2609.27250v1 Announce Type: cross Abstract: The Schr\"odinger bridge owes its computational power to a single structural fact: by Girsanov's theorem the controlled problem is a Kullback--Leible...
arXiv:2605. 02961v2 Announce Type: replace-cross Abstract: Most modern bridge-diffusion methods achieve finite-time transport by specifying an interpolation, Schrodinger-bridge, or stochastic-control objective and then learning the associated score or drift field with a neural network.
Long-range learning is hard for recurrent networks trained with stochastic gradient descent, because the influence of a past input fades with the lag $\ell$, and if it fades too fast the dependence cannot be learned from finite data. This fade is captured by an envelope $f(\ell)$.
arXiv:2606. 29519v1 Announce Type: new Abstract: Long-range learning is hard for recurrent networks trained with stochastic gradient descent, because the influence of a past input fades with the lag $\ell$, and if it fades too fast the dependence cannot be learned from finite data.
arXiv:2608. 09366v1 Announce Type: new Abstract: Large-scale learning systems often face the challenge of balancing multiple, potentially competing objectives, such as fairness, accuracy, and latency.
Spectral Prioritized Sweeping (SPS) extends traditional Prioritized Sweeping by incorporating graph topology through the resolvent and Laplacian diffusion, creating a smoother priority score that propagates reward changes more effectively in nonstationary reinforcement learning. The method, called Graph Topology Augmentation for Prioritized Sweeping (GTA-PS), uses a mixing of regularized Laplacian inverses and an adaptive scheduler based on the Second Largest Eigenvalue Modulus to adjust the influence of topology during replanning. Experiments on FourRooms and GARNET domains show that GTA-PS improves replanning efficiency compared to standard PS under both exact dynamic programming and Dyna-style planners.
The paper studies finite‑horizon minimum‑energy steering of inertial swarms under stochastic disturbances, focusing on mean‑field models with Cucker–Smale alignment or Morse attraction–repulsion interactions. It formulates the problem as a Schr"odinger bridge, deriving nonlinear, time‑symmetric optimality systems and proposing nested fixed‑point schemes for numerical solution. Numerical experiments demonstrate that the optimal corrective drift can either exploit or counteract the natural interaction forces, depending on their alignment with the steering objective.
arXiv:2608. 06893v1 Announce Type: new Abstract: Schr\"odinger bridge models restore a clean signal from a degraded observation by following the conditional bridges of a reference process, yet this reference is chosen heuristically, typically white noise with a hand-tuned schedule.
arXiv:2607. 04978v1 Announce Type: new Abstract: Joint-Embedding Predictive Architectures (JEPAs) underpin a growing family of latent world models for control from raw pixels, but every existing JEPA world model commits at training time to a single inference paradigm: either trajectory optimisation in a learned dynamics model, or direct behaviour cloning.
arXiv:2507.20088v4 Announce Type: replace Abstract: We study neural architectures in which each hidden layer is defined by the stationary state of a dissipative Schr\"odinger-type dynamics on a learn...