A new arXiv preprint shows that the stochastic optimal control and path space formulations of the Schrodinger bridge problem are equivalent for the kinematic equation on compact connected Lie groups. The proof relies on geometric tools such as the horizontal lift. The result connects control-theoretic and measure-theoretic views of this class of optimal transport problems.
A new arXiv paper introduces GeoTTER, a framework that recasts optimal transport for zero-shot classification tasks. The authors argue that standard approaches are poorly calibrated and inflexible because they depend on fixed cost matrices. GeoTTER instead exploits local geometric structure to improve adaptability.
A new arXiv preprint surveys how methods for learning structure from high-dimensional data connect to ideas from control theory, statistical inference, optimal transport and thermodynamics. The author argues these shared mathematical foundations bridge physics and applied mathematics with machine learning. The paper also outlines applications of this unified perspective.
A new arXiv paper examines end-to-end supervised graph prediction, where comparing predicted graphs to targets with arbitrary node orderings requires a permutation-invariant loss. The authors analyze three optimal transport-based graph matching relaxations and propose amortization to reduce the cost of these matching steps.
A new arXiv paper proposes CyFM, a technique that applies optimal transport on a cylindrical geometry to generate complex-valued signals in few sampling steps. Rather than treating data such as MRI scans and audio spectrograms as flat two-channel Euclidean inputs, the method models amplitude and phase separately. The authors argue this representation better matches the structure of complex signals for generative modelling.
Researchers introduce the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator designed to transport densities in an amortized way. Given a new pair of source and target densities, VIOT outputs a divergence-free velocity field to carry out the transformation. The approach targets incompressible flow settings, where the velocity field must remain divergence-free.
A new arXiv paper introduces a method for learning multimodal one-step flow policies from fixed offline datasets using value-weighted optimal transport. The approach targets offline reinforcement learning, where action distributions are often multimodal and existing flow policies are slow to sample. It appears in both cs.AI and cs.LG cross-listings.
Researchers propose CyclOT, a bidirectional neural framework that recovers both forward and reverse quadratic optimal transport maps from unpaired samples in high dimensions. The learned maps induce forward and backward displacement interpolants that are synchronized during training. The work targets optimal transport estimation, a task that becomes difficult as dimensionality grows.
A revised arXiv preprint reviews how optimal transport is used to compare networks, offering both a dissimilarity measure and a plan describing how one graph maps onto another. The authors add new spectral bounds and discuss applications in machine learning. The paper is a cross-listing revision rather than a new release.
A new arXiv paper presents an anomaly detection framework built on optimal transport, aimed at spotting deviations from normal behavior in industrial time-series data. The authors position the approach as unsupervised and computationally efficient, targeting Industry 4.0 monitoring use cases. Details on datasets, baselines, and evaluation results are not available from the abstract alone.
A new arXiv paper presents a method for amortizing Branched Optimal Transport, a technique that models efficient tree-like network structures seen in rivers and biological systems. The work aims to make these network design computations faster by learning to approximate solutions rather than solving each instance from scratch. It is listed under both cs.AI and cs.LG on arXiv.
A new arXiv preprint introduces SGWIB, a method that pairs sliced Gromov-Wasserstein optimal transport with an information bottleneck to select the most informative moments in a video. The authors argue that accurate highlight prediction needs both discriminative segment features and compression of irrelevant content. The approach is positioned as a way to identify temporally important, engaging segments for automatic video highlight detection.
A new arXiv paper argues that the schedules controlling how signal and noise are mixed along diffusion and flow-matching paths can be optimized by minimizing a kinetic action borrowed from optimal transport theory. The authors show that making these schedules depend on the specific model, rather than using fixed hand-tuned coefficients, improves generation quality. The work offers a theoretical framing for why certain noise schedules perform better than others.