79 citations · 172 across the 20 of their papers we have counts for
10 papers · 1 filter
Operator learning regularization for macroscopic permeability prediction in dual-scale flow problem
Christina Runkel, Sinan Xiao, Nicolas Boullé +1
Liquid composites moulding is an important manufacturing technology for fibre reinforced composites, due to its cost-effectiveness. Challenges lie in the optimisation of the proces…
Density estimation with LLMs: a geometric investigation of in-context learning trajectories
Toni J. B. Liu, Nicolas Boullé, Raphaël Sarfati +1
Large language models (LLMs) demonstrate remarkable emergent abilities to perform in-context learning across various tasks, including time series forecasting. This work investigate…
Large Language Models as Markov Chains
Oussama Zekri, Ambroise Odonnat, Abdelhakim Benechehab +3
Large language models (LLMs) are remarkably efficient across a wide range of natural language processing tasks and well beyond them. However, a comprehensive theoretical analysis o…
Lines of Thought in Large Language Models
Raphaël Sarfati, Toni J. B. Liu, Nicolas Boullé +1
Large Language Models achieve next-token prediction by transporting a vectorized piece of text (prompt) across an accompanying embedding space under the action of successive transf…
Structure-Preserving Operator Learning
Nacime Bouziani, Nicolas Boullé
Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cas…
Multiplicative Dynamic Mode Decomposition
Nicolas Boullé, Matthew J. Colbrook
Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of…
Randomized Nyström approximation of non-negative self-adjoint operators
David Persson, Nicolas Boullé, Daniel Kressner
The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and stro…
LLMs learn governing principles of dynamical systems, revealing an in-context neural scaling law
Toni J. B. Liu, Nicolas Boullé, Raphaël Sarfati +1
Pretrained large language models (LLMs) are surprisingly effective at performing zero-shot tasks, including time-series forecasting. However, understanding the mechanisms behind su…
Operator learning without the adjoint
Nicolas Boullé, Diana Halikias, Samuel E. Otto +1
There is a mystery at the heart of operator learning: how can one recover a non-self-adjoint operator from data without probing the adjoint? Current practical approaches suggest th…
On the Convergence of Hermitian Dynamic Mode Decomposition
Nicolas Boullé, Matthew J. Colbrook
We study the convergence of Hermitian Dynamic Mode Decomposition (DMD) to the spectral properties of self-adjoint Koopman operators. Hermitian DMD is a data-driven method that appr…