9 papers
On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers
Sixu Li, Thomas Jacob Maranzatto, Jan Peszek +5
We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems. In this perspective, tokens are modeled as particles…
The Future of Artificial Intelligence and the Mathematical and Physical Sciences (AI+MPS)
Andrew Ferguson, Marisa LaFleur, Lars Ruthotto +97
This community paper developed out of the NSF Workshop on the Future of Artificial Intelligence (AI) and the Mathematical and Physics Sciences (MPS), which was held in March 2025 w…
Wasserstein-Cramér-Rao Theory of Unbiased Estimation
Nicolás GarcÃa Trillos, Adam Quinn Jaffe, Bodhisattva Sen
The quantity of interest in the classical Cramér-Rao theory of unbiased estimation (e.g., the Cramér-Rao lower bound, its exact attainment for exponential families, and asymptoti…
Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions
Camilo Andrés GarcÃa Trillos, Nicolás GarcÃa Trillos
We consider adversarially robust classification in a multiclass setting under arbitrary loss functions and derive dual and barycentric reformulations of the corresponding learner-a…
Central limit theorems for the eigenvalues of graph Laplacians on data clouds
Chenghui Li, Nicolás GarcÃa Trillos, Housen Li +1
Given i.i.d.\ samples from a distribution supported on a low dimensional manifold embedded in Eucliden space, we consider the graph Laplacian ope…
Defending Against Diverse Attacks in Federated Learning Through Consensus-Based Bi-Level Optimization
Nicolás GarcÃa Trillos, Aditya Kumar Akash, Sixu Li +2
Adversarial attacks pose significant challenges in many machine learning applications, particularly in the setting of distributed training and federated learning, where malicious a…