arXiv:2605. 10931v2 Announce Type: replace-cross Abstract: Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models.
By Albert Alcalde, Leon Bungert, Konstantin Riedl, Tim Roith
The paper introduces a new optimal transport framework that uses the Barron energy—an intrinsic neural network complexity measure—instead of the traditional kinetic energy. By modeling transport as deep residual networks that map a reference distribution to a target distribution, the authors define a new metric on probability measures and analyze its properties for generative modeling. They demonstrate that diffusion generative models are suboptimal in this Barron geometry and explore how adaptivity can improve alternative generative approaches.
By Evan Dogariu, Joan Bruna
arXiv:2501. 18322v2 Announce Type: replace Abstract: Transformers, which are state-of-the-art in most machine learning tasks, represent the data as sequences of vectors called tokens.
By Val\'erie Castin, Pierre Ablin, Jos\'e Antonio Carrillo, Gabriel Peyr\'e
arXiv:2609.25659v1 Announce Type: new
Abstract: Many scientific datasets, such as molecular conformational ensembles or single-cell tissue measurements, are naturally modeled as meta-distributions: d...
By Doron Haviv, Edward De Brouwer, Rishabh Anand, Rex Ying, A\"icha Bentaieb, Gabriele Scalia, Hector Corrada Bravo
arXiv:2604. 09560v2 Announce Type: replace Abstract: Softmax attention is the row-normalized operator of a diffusion map: both normalize a learned score into a Markov operator, and differ only in what the score is allowed to contain.
By Julio Candanedo
RW-Flow presents a new one‑step generative framework for data on compact manifolds, leveraging Wasserstein gradient flows. The authors derive a necessary and sufficient identifiability condition for velocity fields on compact, connected Riemannian manifolds, showing that a symmetric, Lipschitz‑continuous cost function yields identifiability iff its Gibbs kernel is nondegenerate. Experiments on geospatial events, protein and RNA torsion angles, and discretized manifolds demonstrate that RW‑Flow surpasses existing one‑step methods across most benchmark settings.
By Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn, Minhyuk Sung