30 citations · 180 across the 40 of their papers we have counts for
14 papers · 1 filter
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…
Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions
Camilo Andrés García Trillos, Nicolás García 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…
Defending Against Diverse Attacks in Federated Learning Through Consensus-Based Bi-Level Optimization
Nicolás García 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…
An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification
Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim +1
Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial traini…
Spectral Neural Networks: Approximation Theory and Optimization Landscape
Chenghui Li, Rishi Sonthalia, Nicolas Garcia Trillos
There is a large variety of machine learning methodologies that are based on the extraction of spectral geometric information from data. However, the implementations of many of the…
FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization
Jose A. Carrillo, Nicolas Garcia Trillos, Sixu Li +1
Federated learning is an important framework in modern machine learning that seeks to integrate the training of learning models from multiple users, each user having their own loca…
It begins with a boundary: A geometric view on probabilistically robust learning
Leon Bungert, Nicolás García Trillos, Matt Jacobs +3
Although deep neural networks have achieved super-human performance on many classification tasks, they often exhibit a worrying lack of robustness towards adversarially generated e…
On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it
Camilo Garcia Trillos, Nicolas Garcia Trillos
We propose iterative algorithms to solve adversarial problems in a variety of supervised learning settings of interest. Our algorithms, which can be interpreted as suitable ascent-…
Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks
Aditya Kumar Akash, Sixu Li, Nicolás García Trillos
Based on the concepts of Wasserstein barycenter (WB) and Gromov-Wasserstein barycenter (GWB), we propose a unified mathematical framework for neural network (NN) model fusion and u…
The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification
Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim
We study a family of adversarial multiclass classification problems and provide equivalent reformulations in terms of: 1) a family of generalized barycenter problems introduced in…
The Geometry of Adversarial Training in Binary Classification
Leon Bungert, Nicolás García Trillos, Ryan Murray
We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where…
Large sample spectral analysis of graph-based multi-manifold clustering
Nicolas Garcia Trillos, Pengfei He, Chenghui Li
In this work we study statistical properties of graph-based algorithms for multi-manifold clustering (MMC). In MMC the goal is to retrieve the multi-manifold structure underlying a…
Adversarial Classification: Necessary conditions and geometric flows
Nicolas Garcia Trillos, Ryan Murray
We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance , using tools from variational analysis. In…
Traditional and accelerated gradient descent for neural architecture search
Nicolas Garcia Trillos, Felix Morales, Javier Morales
In this paper we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [5] which used the geometric struct…