publications

2026

1. arXiv

   Discrete Gromov-Wasserstein Duality: Algorithms and Isomorphism Testing

   Gabriel Rioux, Joanna Marks, Riccardo Passeggeri, and Ziv Goldfeld

   2026

   Abs PDF

   The Gromov-Wasserstein (GW) distance provides a principled framework for aligning metric measure (mm) spaces based solely on their intrinsic structure. Its ability to identify isomorphic representations of distributions across spaces renders it valuable for comparing data where equality up to isomorphism occurs naturally such as in graphs or, more generally, distributions on graphs. Recently, a type of dual form for the GW distance between Euclidean distributions with the squared Euclidean or inner product costs was derived, spurring the development of new statistical and algorithmic results for this setting. This work furnishes a novel duality result for GW distances with and without entropic regularization that is applicable to all finitely supported mm spaces. Leveraging this result, we derive the sample complexity of empirical GW distances between finite mm spaces, as well as limit distributions under proper centering and scaling. Furthermore, we propose new algorithms for solving the regularized GW problem which are subject to formal convergence guarantees. These statistical and algorithmic advancements give rise to a principled and efficient framework for testing whether two distributions on the set of graphs with a fixed number of nodes are isomorphic based on samples.

2025

1. UAI

   Learning latent energy-based models via interacting particle Langevin dynamics

   Joanna Marks, Tim YJ Wang, and O Deniz Akyildiz

   2025

   Oral Presentation Abs PDF Code

   This paper was selected for an oral presentation at UAI 2026. Less than 2% of the submitted papers were chosen as oral presentations.

   We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems. Specifically, we provide a continuous-time framework for learning latent energy-based models, by defining stochastic differential equations (SDEs) that provably solve the MMLE problem. We obtain a practical algorithm as a discretisation of these SDEs and provide theoretical guarantees for the convergence of the proposed algorithm. Finally, we demonstrate the empirical effectiveness of our method on synthetic and image datasets.