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:2604. 06531v3 Announce Type: replace-cross Abstract: The mean-field Schr\"odinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline.
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.
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.
The paper introduces a mesh‑free, self‑supervised neural operator—called the Normalizing Flow Invertible Solution Transformer (NFIST)—for stochastic mean‑field control (MFC). By reformulating the controlled Fokker–Planck dynamics as a deterministic continuity equation via a probability‑flow ODE and an invertible normalizing‑flow transformer, the authors enable closed‑form score evaluation with linear cost per particle. The resulting operator learns from task prompts (distribution parameters or particle clouds) and can solve unseen MFC tasks in a single forward pass, achieving zero‑shot generalization across applications such as stochastic optimal control, Schrödinger bridges, systemic‑risk control, and obstacle‑avoiding path planning.
arXiv:2606. 15871v1 Announce Type: cross Abstract: Bayesian inference for inverse problems is run to evaluate integrals -- posterior expectations, tail probabilities, and risks -- across a stream of observations.
arXiv:2605.29371v2 Announce Type: replace-cross Abstract: We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed thr...
The paper proposes a mean‑field reinforcement learning framework that models rewards and transitions as functions of an unknown low‑dimensional aggregate statistic of a large agent population. By learning this low‑dimensional representation in an offline setting, the authors demonstrate a provable method for obtaining near‑optimal policies. Experiments on a one‑step routing game inspired by supply‑chain problems show that, with a fixed neural‑network size and optimization budget, the learned representation improves reward prediction and the quality of Nash equilibria compared to baselines that ignore population structure.
arXiv:2608. 02844v1 Announce Type: cross Abstract: We develop a class of diffusion-based stochastic particle optimisation methods for loss functions with intractable gradients.
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.
DeepSPoC is a neural particle method that replaces direct particle-particle interactions in sequential propagation of chaos (SPoC) with particle‑network interactions, using a neural density representation (KRnet) to approximate the empirical measure. By simulating particles in batches and embedding a neural network into the mean‑field SDE coefficients, DeepSPoC reduces memory usage and computational cost compared to traditional particle methods. The approach is demonstrated on various mean‑field equations, showing improved scalability for high‑dimensional problems.
arXiv:2509.26364v3 Announce Type: replace Abstract: The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certa...
arXiv:2602. 03670v2 Announce Type: replace-cross Abstract: Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning.