arXiv:2609.13758v1 Announce Type: cross Abstract: We establish the equivalence between the stochastic optimal control and path space formulations of the Schr\"odinger bridge problem (SBP) for the kin...
arXiv:2605. 24795v2 Announce Type: replace-cross Abstract: We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics.
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:2605. 27478v3 Announce Type: replace-cross Abstract: Schr\"odinger bridges for time series (SBTS) generate synthetic paths by projecting, in relative entropy, a Brownian reference onto the path laws that match the joint distribution of the data on the observation grid.
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. 07851v1 Announce Type: cross Abstract: We give mathematically self-contained formulations, in the complex-time (kime) representation, of three open problems from the foundations of classical mechanics: (I) the extension of the classical entropic uncertainty principle to non-canonical variables and to multiple degrees of freedom; (II) the characterization of coordinate-invariant measures and entropies, i.
The paper introduces a probabilistic generative framework called Schr"odinger Bridges on Lie Group Manifolds, enabling direct modeling of non‑Euclidean data without flattening or coordinate inconsistencies. It develops two computational realizations—Wrapped‑Kernel Bridge Calibration for compact Abelian groups and Reciprocal Conditional‑Control Bridge Matching for compact non‑Abelian groups—while providing a modular error bound that separates various sources of approximation error. Experiments on protein, RNA torsions, SO(3), U(n), and protein conformational pathways demonstrate the method’s feasibility and consistency.
arXiv:2607. 23642v1 Announce Type: cross Abstract: Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm.
arXiv:2608. 01658v1 Announce Type: cross Abstract: For mirror descent generated by a Legendre kernel, perhaps one of the most basic question in optimization is this: must every accumulation point of a bounded mirror descent sequence be Karush--Kuhn--Tucker (KKT) stationary under proper stepsizes?
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.
arXiv:2601. 16041v2 Announce Type: replace-cross Abstract: In constrained stochastic optimization, one expects that restricting the feasible set, provided it still contains the true parameter, should not increase the statistical risk of the corresponding projection estimator.
The paper introduces a Bethe Lagrangian formulation of expected free energy (EFE) that preserves a Kullback–Leibler structure, enabling message‑passing inference. By imposing an information constraint—requiring the mutual information between future observations, states, and parameters given actions to be at least the entropy of the goal prior—the authors recover the standard EFE solution at a specific Karush‑Kuhn‑Tucker multiplier. They analyze how varying this multiplier transitions the agent’s epistemic drive through inactive, interior, and saturated regimes, and benchmark the constrained Bethe agent against EFE and Q‑MDP on three tasks.