Nicolás García Trillos

56 papers Journal 55Unranked 1

Year	Rank	Type	Title / Venue / Authors
2025	J	`jnl`	Central limit theorems for the eigenvalues of graph Laplacians on data clouds. CoRR Chenghui Li, Nicolás García Trillos, Housen Li, Leo Suchan
2025	J	`jnl`	Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions. CoRR Camilo Andrés García-Trillos, Nicolás García Trillos
2025	J	`jnl`	Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds. CoRR Nicolás García Trillos, Chenghui Li, Raghavendra Venkatraman
2025	J	`jnl`	The Future of Artificial Intelligence and the Mathematical and Physical Sciences (AI+MPS). CoRR Andrew Ferguson, Marisa Lafleur, Lars Ruthotto, Jesse Thaler, Yuan-Sen Ting, Pratyush Tiwary, Soledad Villar, E. Paulo Alves, Jeremy Avigad, Simon Billinge, Camille L. Bilodeau, Keith Brown, Emmanuel J. Candès, Arghya Chattopadhyay, Bingqing Cheng, Jonathan Clausen, Connor W. Coley, Andrew J. Connolly, Fred Daum, Sijia S. Dong, Chrisy Xiyu Du, Cora Dvorkin, Cristiano Fanelli, Eric B. Ford, Luis Manuel Frutos, Nicolás García Trillos, Cecilia Garraffo, Robert Ghrist, Rafael Gómez-Bombarelli, Gianluca Guadagni, Sreelekha Guggilam, Sergei Gukov, Juan B. Gutierrez, Salman Habib, Johannes Hachmann, Boris Hanin, Philip C. Harris, Murray Holland, Elizabeth Holm, Hsin-Yuan Huang, Shih-Chieh Hsu, Nick Jackson, Olexandr Isayev, Heng Ji, Aggelos K. Katsaggelos, Jeremy Kepner, Yannis G. Kevrekidis, Michelle P. Kuchera, J. Nathan Kutz, Branislava Lalic, Ann Lee, Matt LeBlanc, Josiah Lim, Rebecca Lindsey, Yongmin Liu, Peter Y. Lu, Sudhir Malik, Vuk Mandic, Vidya B. Manian, Emeka P. Mazi, Pankaj Mehta, Peter Melchior, Brice Ménard, Jennifer Ngadiuba, Stella Offner, Elsa Olivetti, Shyue Ping Ong, Christopher Rackauckas, Philippe Rigollet, Chad Risko, Philip Romero, Grant M. Rotskoff, Brett Savoie, Uros Seljak, David Shih, Gary Shiu, Dima Shlyakhtenko, Eva Silverstein, Taylor Sparks, Thomas Strohmer, Christopher Stubbs, Stephen Thomas, Suriyanarayanan Vaikuntanathan, René Vidal, Francisco Villaescusa-Navarro, Gregory Voth, Benjamin Wandelt, Rachel Ward, Melanie Weber, Risa Wechsler, Stephen Whitelam, Olaf Wiest, Mike Williams, Zhuoran Yang, Yaroslava G. Yingling, Bin Yu, Shuwen Yue, Ann Zabludoff, Huimin Zhao, Tong Zhang
2025	J	`jnl`	Vector valued optimal transport: from dynamic to static formulations. CoRR Katy Craig, Nicolás García Trillos, Dorde Nikolic
2024	J	`jnl`	An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification. CoRR Nicolás García Trillos, Matt Jacobs, Jakwang Kim, Matthew Werenski
2024	J	`jnl`	An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification. J. Mach. Learn. Res. Nicolás García Trillos, Matt Jacobs, Jakwang Kim, Matthew Werenski
2024	J	`jnl`	Defending Against Diverse Attacks in Federated Learning Through Consensus-Based Bi-Level Optimization. CoRR Nicolás García Trillos, Aditya Kumar Akash, Sixu Li, Konstantin Riedl, Yuhua Zhu
2024	J	`jnl`	FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization. J. Mach. Learn. Res. José A. Carrillo, Nicolás García Trillos, Sixu Li, Yuhua Zhu
2024	J	`jnl`	Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms. J. Mach. Learn. Res. Nicolás García Trillos, Anna V. Little, Daniel McKenzie, James M. Murphy
2023	J	`jnl`	A New Perspective On Denoising Based On Optimal Transport. CoRR Nicolás García Trillos, Bodhisattva Sen
2023	J	`jnl`	Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower bounds. CoRR Nicolás García Trillos, Melanie Weber
2023	J	`jnl`	FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization. CoRR José A. Carrillo, Nicolás García Trillos, Sixu Li, Yuhua Zhu
2023	J	`jnl`	Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms. CoRR Nicolás García Trillos, Anna V. Little, Daniel McKenzie, James M. Murphy
2023	J	`jnl`	It begins with a boundary: A geometric view on probabilistically robust learning. CoRR Leon Bungert, Nicolás García Trillos, Matt Jacobs, Daniel McKenzie, Dorde Nikolic, Qingsong Wang
2023	J	`jnl`	Large sample spectral analysis of graph-based multi-manifold clustering. J. Mach. Learn. Res. Nicolás García Trillos, Pengfei He, Chenghui Li
2023	J	`jnl`	On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it. CoRR Camilo Garcia Trillos, Nicolás García Trillos
2023	J	`jnl`	On the existence of solutions to adversarial training in multiclass classification. CoRR Nicolás García Trillos, Matt Jacobs, Jakwang Kim
2023	J	`jnl`	Spectral Neural Networks: Approximation Theory and Optimization Landscape. CoRR Chenghui Li, Rishi Sonthalia, Nicolás García Trillos
2023	J	`jnl`	The multimarginal optimal transport formulation of adversarial multiclass classification. J. Mach. Learn. Res. Nicolás García Trillos, Matt Jacobs, Jakwang Kim
2022	J	`jnl`	Adversarial Classification: Necessary Conditions and Geometric Flows. J. Mach. Learn. Res. Nicolás García Trillos, Ryan Murray
2022	J	`jnl`	Lipschitz Regularity of Graph Laplacians on Random Data Clouds. SIAM J. Math. Anal. Jeff Calder, Nicolás García Trillos, Marta Lewicka
2022	J	`jnl`	Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning. CoRR Nicolás García Trillos, Daniel Sanz-Alonso, Ruiyi Yang
2022	J	`jnl`	Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective. CoRR Yuetian Luo, Nicolás García Trillos
2022	J	`jnl`	Rates of Convergence for Regression with the Graph Poly-Laplacian. CoRR Nicolás García Trillos, Ryan Murray, Matthew Thorpe
2022	J	`jnl`	Semi-discrete Optimization Through Semi-discrete Optimal Transport: A Framework for Neural Architecture Search. J. Nonlinear Sci. Nicolás García Trillos, Javier Morales
2022	J	`jnl`	The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification. CoRR Nicolás García Trillos, Matt Jacobs, Jakwang Kim
2022	J	`jnl`	Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks. CoRR Aditya Kumar Akash, Sixu Li, Nicolás García Trillos
2021	J	`jnl`	Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation. CoRR Katy Craig, Nicolás García Trillos, Dejan Slepcev
2021	J	`jnl`	Geometric structure of graph Laplacian embeddings. J. Mach. Learn. Res. Nicolás García Trillos, Franca Hoffmann, Bamdad Hosseini
2021	J	`jnl`	Large sample spectral analysis of graph-based multi-manifold clustering. CoRR Nicolás García Trillos, Pengfei He, Chenghui Li
2021	J	`jnl`	On the regularized risk of distributionally robust learning over deep neural networks. CoRR Camilo Garcia Trillos, Nicolás García Trillos
2021	J	`jnl`	The Geometry of Adversarial Training in Binary Classification. CoRR Leon Bungert, Nicolás García Trillos, Ryan Murray
2021	—	`conf`	Traditional and Accelerated Gradient Descent for Neural Architecture Search. GSI Nicolás García Trillos, Félix Morales, Javier Morales
2020	J	`jnl`	A Maximum Principle Argument for the Uniform Convergence of Graph Laplacian Regressors. SIAM J. Math. Data Sci. Nicolás García Trillos, Ryan W. Murray
2020	J	`jnl`	Adversarial Classification: Necessary conditions and geometric flows. CoRR Nicolás García Trillos, Ryan Murray
2020	J	`jnl`	Data-Driven Forward Discretizations for Bayesian Inversion. CoRR Daniele Bigoni, Yuming Chen, Nicolás García Trillos, Youssef M. Marzouk, Daniel Sanz-Alonso
2020	J	`jnl`	Error Estimates for Spectral Convergence of the Graph Laplacian on Random Geometric Graphs Toward the Laplace-Beltrami Operator. Found. Comput. Math. Nicolás García Trillos, Moritz Gerlach, Matthias Hein, Dejan Slepcev
2020	J	`jnl`	From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds. CoRR Nicolás García Trillos, Ryan Murray, Matthew Thorpe
2020	J	`jnl`	Lipschitz regularity of graph Laplacians on random data clouds. CoRR Jeff Calder, Nicolás García Trillos, Marta Lewicka
2020	J	`jnl`	On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms. J. Mach. Learn. Res. Nicolás García Trillos, Zachary Kaplan, Thabo Samakhoana, Daniel Sanz-Alonso
2020	J	`jnl`	Semi-discrete optimization through semi-discrete optimal transport: a framework for neural architecture search. CoRR Nicolás García Trillos, Javier Morales
2020	J	`jnl`	Traditional and accelerated gradient descent for neural architecture search. CoRR Nicolás García Trillos, Félix Morales, Javier Morales
2019	J	`jnl`	A maximum principle argument for the uniform convergence of graph Laplacian regressors. CoRR Nicolás García Trillos, Ryan Murray
2019	J	`jnl`	Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs. CoRR Jeff Calder, Nicolás García Trillos
2019	J	`jnl`	Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis. CoRR Nicolás García Trillos, Daniel Sanz-Alonso, Ruiyi Yang
2019	J	`jnl`	Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis. J. Mach. Learn. Res. Nicolás García Trillos, Daniel Sanz-Alonso, Ruiyi Yang
2019	J	`jnl`	Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning. CoRR Nicolás García Trillos, Zachary Kaplan, Daniel Sanz-Alonso
2019	J	`jnl`	Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning. Entropy Nicolás García Trillos, Zachary Kaplan, Daniel Sanz-Alonso
2019	J	`jnl`	Variational Limits of k-NN Graph-Based Functionals on Data Clouds. SIAM J. Math. Data Sci. Nicolás García Trillos
2018	J	`jnl`	Continuum Limits of Posteriors in Graph Bayesian Inverse Problems. SIAM J. Math. Anal. Nicolás García Trillos, Daniel Sanz-Alonso
2017	J	`jnl`	On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests. Entropy Aaditya Ramdas, Nicolás García Trillos, Marco Cuturi
2017	J	`jnl`	On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithms. CoRR Nicolás García Trillos, Zachary Kaplan, Thabo Samakhoana, Daniel Sanz-Alonso
2016	J	`jnl`	Consistency of Cheeger and Ratio Graph Cuts. J. Mach. Learn. Res. Nicolás García Trillos, Dejan Slepcev, James H. von Brecht, Thomas Laurent, Xavier Bresson
2015	J	`jnl`	A variational approach to the consistency of spectral clustering. CoRR Nicolás García Trillos, Dejan Slepcev
2014	J	`jnl`	Consistency of Cheeger and Ratio Graph Cuts. CoRR Nicolás García Trillos, Dejan Slepcev, James H. von Brecht, Thomas Laurent, Xavier Bresson