arXiv:2602. 14885v2 Announce Type: replace-cross Abstract: Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows.
By Ram\'on Nartallo-Kaluarachchi, Renaud Lambiotte, Alain Goriely
arXiv:2605. 15806v2 Announce Type: replace Abstract: Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends.
By Kai Hidajat
arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.
By Gabriel Peyr\'e
arXiv:2607. 14361v1 Announce Type: cross Abstract: We address fundamental challenges in representing and computing $\mathbb{R}^{d}$-valued predictable square-integrable processes over $[0,T]$, collected in the space $\mathcal{H}^2_T(\mathbb{R}^{d})$.
By Anastasis Kratsios, Giulia Livieri, Philipp Schmocker
arXiv:2607. 03347v1 Announce Type: new Abstract: We consider the Multiscale Single-Index Model (MSIM), first introduced in \cite{oymak2021learning}, as a stylized model for hierarchical learning with \emph{scale separation}.
By Joan Bruna
arXiv:2606. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.
By Kelan Gray, Finlay Brown, Nicolas Boull\'e, Matthew J. Colbrook