Nicolás García Trillos

Publication Activity (10 Years)

Years Active: 2014-2024
Publications (10 Years): 43

Top Topics

Convergence Rate

Neural Architecture

Multiclass Classification

Graph Laplacian

Top Venues

J. Mach. Learn. Res.

SIAM J. Math. Data Sci.

SIAM J. Math. Anal.

Publications

Nicolás García Trillos, Matt Jacobs, Jakwang Kim, Matthew Werenski
An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification. CoRR (2024)
Nicolás García Trillos, Melanie Weber
Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower bounds. CoRR (2023)
Nicolás García Trillos, Pengfei He, Chenghui Li
Large sample spectral analysis of graph-based multi-manifold clustering. J. Mach. Learn. Res. 24 (2023)
Nicolás García Trillos, Anna Little, Daniel McKenzie, James M. Murphy
Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms. CoRR (2023)
Chenghui Li, Rishi Sonthalia, Nicolás García Trillos
Spectral Neural Networks: Approximation Theory and Optimization Landscape. CoRR (2023)
Nicolás García Trillos, Matt Jacobs, Jakwang Kim
On the existence of solutions to adversarial training in multiclass classification. CoRR (2023)
Jose A. Carrillo, Nicolás García Trillos, Sixu Li, Yuhua Zhu
FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization. CoRR (2023)
Nicolás García Trillos, Matt Jacobs, Jakwang Kim
The multimarginal optimal transport formulation of adversarial multiclass classification. J. Mach. Learn. Res. 24 (2023)
Camilo Garcia Trillos, Nicolás García Trillos
On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it. CoRR (2023)
Leon Bungert, Nicolás García Trillos, Matt Jacobs, Daniel McKenzie, Dorde Nikolic, Qingsong Wang
It begins with a boundary: A geometric view on probabilistically robust learning. CoRR (2023)
Nicolás García Trillos, Bodhisattva Sen
A New Perspective On Denoising Based On Optimal Transport. CoRR (2023)
Nicolás García Trillos, Daniel Sanz-Alonso, Ruiyi Yang
Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning. CoRR (2022)
Nicolás García Trillos, Javier Morales
Semi-discrete Optimization Through Semi-discrete Optimal Transport: A Framework for Neural Architecture Search. J. Nonlinear Sci. 32 (3) (2022)
Jeff Calder, Nicolás García Trillos, Marta Lewicka
Lipschitz Regularity of Graph Laplacians on Random Data Clouds. SIAM J. Math. Anal. 54 (1) (2022)
Nicolás García Trillos, Ryan Murray
Adversarial Classification: Necessary Conditions and Geometric Flows. J. Mach. Learn. Res. 23 (2022)
Nicolás García Trillos, Ryan Murray, Matthew Thorpe
Rates of Convergence for Regression with the Graph Poly-Laplacian. CoRR (2022)
Aditya Kumar Akash, Sixu Li, Nicolás García Trillos
Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks. CoRR (2022)
Camilo Garcia Trillos, Nicolás García Trillos
On the regularized risk of distributionally robust learning over deep neural networks. CoRR (2021)
Leon Bungert, Nicolás García Trillos, Ryan Murray
The Geometry of Adversarial Training in Binary Classification. CoRR (2021)
Nicolás García Trillos, Félix Morales, Javier Morales
Traditional and Accelerated Gradient Descent for Neural Architecture Search. GSI (2021)
Nicolás García Trillos, Pengfei He, Chenghui Li
Large sample spectral analysis of graph-based multi-manifold clustering. CoRR (2021)
Katy Craig, Nicolás García Trillos, Dejan Slepcev
Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation. CoRR (2021)
Nicolás García Trillos, Franca Hoffmann, Bamdad Hosseini
Geometric structure of graph Laplacian embeddings. J. Mach. Learn. Res. 22 (2021)
Nicolás García Trillos, Zachary Kaplan, Thabo Samakhoana, Daniel Sanz-Alonso
On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms. J. Mach. Learn. Res. 21 (2020)
Nicolás García Trillos, Ryan Murray, Matthew Thorpe
From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds. CoRR (2020)
Nicolás García Trillos, Ryan Murray
Adversarial Classification: Necessary conditions and geometric flows. CoRR (2020)
Nicolás García Trillos, Moritz Gerlach, Matthias Hein, Dejan Slepcev
Error Estimates for Spectral Convergence of the Graph Laplacian on Random Geometric Graphs Toward the Laplace-Beltrami Operator. Found. Comput. Math. 20 (4) (2020)
Nicolás García Trillos, Javier Morales
Semi-discrete optimization through semi-discrete optimal transport: a framework for neural architecture search. CoRR (2020)
Jeff Calder, Nicolás García Trillos, Marta Lewicka
Lipschitz regularity of graph Laplacians on random data clouds. CoRR (2020)
Nicolás García Trillos, Félix Morales, Javier Morales
Traditional and accelerated gradient descent for neural architecture search. CoRR (2020)
Nicolás García Trillos, Ryan W. Murray
A Maximum Principle Argument for the Uniform Convergence of Graph Laplacian Regressors. SIAM J. Math. Data Sci. 2 (3) (2020)
Daniele Bigoni, Yuming Chen, Nicolás García Trillos, Youssef M. Marzouk, Daniel Sanz-Alonso
Data-Driven Forward Discretizations for Bayesian Inversion. CoRR (2020)
Nicolás García Trillos, Zachary Kaplan, Daniel Sanz-Alonso
Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning. CoRR (2019)
Nicolás García Trillos, Daniel Sanz-Alonso, Ruiyi Yang
Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis. J. Mach. Learn. Res. 20 (2019)
Nicolás García Trillos, Ryan Murray
A maximum principle argument for the uniform convergence of graph Laplacian regressors. CoRR (2019)
Nicolás García Trillos
Variational Limits of k-NN Graph-Based Functionals on Data Clouds. SIAM J. Math. Data Sci. 1 (1) (2019)
Nicolás García Trillos, Daniel Sanz-Alonso, Ruiyi Yang
Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis. CoRR (2019)
Jeff Calder, Nicolás García Trillos
Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs. CoRR (2019)
Nicolás García Trillos, Zachary Kaplan, Daniel Sanz-Alonso
Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning. Entropy 21 (5) (2019)
Nicolás García Trillos, Daniel Sanz-Alonso
Continuum Limits of Posteriors in Graph Bayesian Inverse Problems. SIAM J. Math. Anal. 50 (4) (2018)
Nicolás García Trillos, Zachary Kaplan, Thabo Samakhoana, Daniel Sanz-Alonso
On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithms. CoRR (2017)
Aaditya Ramdas, Nicolás García Trillos, Marco Cuturi
On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests. Entropy 19 (2) (2017)
Nicolás García Trillos, Dejan Slepcev, James H. von Brecht, Thomas Laurent, Xavier Bresson
Consistency of Cheeger and Ratio Graph Cuts. J. Mach. Learn. Res. 17 (2016)
Nicolás García Trillos, Dejan Slepcev
A variational approach to the consistency of spectral clustering. CoRR (2015)
Nicolás García Trillos, Dejan Slepcev, James H. von Brecht, Thomas Laurent, Xavier Bresson
Consistency of Cheeger and Ratio Graph Cuts. CoRR (2014)