A variational approach to the consistency of spectral clustering. - Nicolás García Trillos; Dejan Slepcev (CoRR, 2015)

Consistency of Cheeger and Ratio Graph Cuts. - Nicolás García Trillos; Dejan Slepcev; James H. von Brecht; Thomas Laurent 001; Xavier Bresson (J. Mach. Learn. Res., 2016)

On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithms. - Nicolás García Trillos; Zachary Kaplan; Thabo Samakhoana; Daniel Sanz-Alonso (CoRR, 2017)

On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests. - Aaditya Ramdas; Nicolás García Trillos; Marco Cuturi (Entropy, 2017)

Continuum Limits of Posteriors in Graph Bayesian Inverse Problems. - Nicolás García Trillos; Daniel Sanz-Alonso (SIAM J. Math. Anal., 2018)

Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs. - Jeff Calder; Nicolás García Trillos (CoRR, 2019)

Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning. - Nicolás García Trillos; Zachary Kaplan; Daniel Sanz-Alonso (Entropy, 2019)

Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis. - Nicolás García Trillos; Daniel Sanz-Alonso; Ruiyi Yang (J. Mach. Learn. Res., 2019)

Variational Limits of k-NN Graph-Based Functionals on Data Clouds. - Nicolás García Trillos (SIAM J. Math. Data Sci., 2019)

Data-Driven Forward Discretizations for Bayesian Inversion. - Daniele Bigoni; Yuming Chen; Nicolás García Trillos; Youssef M. Marzouk; Daniel Sanz-Alonso (CoRR, 2020)

From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds. - Nicolás García Trillos; Ryan Murray 001; Matthew Thorpe (CoRR, 2020)

Error Estimates for Spectral Convergence of the Graph Laplacian on Random Geometric Graphs Toward the Laplace-Beltrami Operator. - Nicolás García Trillos; Moritz Gerlach; Matthias Hein 001; Dejan Slepcev (Found. Comput. Math., 2020)

On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms. - Nicolás García Trillos; Zachary Kaplan; Thabo Samakhoana; Daniel Sanz-Alonso (J. Mach. Learn. Res., 2020)

A Maximum Principle Argument for the Uniform Convergence of Graph Laplacian Regressors. - Nicolás García Trillos; Ryan W. Murray (SIAM J. Math. Data Sci., 2020)

Traditional and Accelerated Gradient Descent for Neural Architecture Search. - Nicolás García Trillos; Félix Morales; Javier Morales (GSI, 2021)

Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation. - Katy Craig; Nicolás García Trillos; Dejan Slepcev (CoRR, 2021)

On the regularized risk of distributionally robust learning over deep neural networks. - Camilo Garcia Trillos; Nicolás García Trillos (CoRR, 2021)

The Geometry of Adversarial Training in Binary Classification. - Leon Bungert; Nicolás García Trillos; Ryan Murray 001 (CoRR, 2021)

Geometric structure of graph Laplacian embeddings. - Nicolás García Trillos; Franca Hoffmann; Bamdad Hosseini (J. Mach. Learn. Res., 2021)

Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning. - Nicolás García Trillos; Daniel Sanz-Alonso; Ruiyi Yang (CoRR, 2022)

Rates of Convergence for Regression with the Graph Poly-Laplacian. - Nicolás García Trillos; Ryan Murray 001; Matthew Thorpe (CoRR, 2022)

Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective. - Yuetian Luo; Nicolás García Trillos (CoRR, 2022)

Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks. - Aditya Kumar Akash; Sixu Li; Nicolás García Trillos (CoRR, 2022)

Adversarial Classification: Necessary Conditions and Geometric Flows. - Nicolás García Trillos; Ryan Murray 001 (J. Mach. Learn. Res., 2022)

Semi-discrete Optimization Through Semi-discrete Optimal Transport: A Framework for Neural Architecture Search. - Nicolás García Trillos; Javier Morales (J. Nonlinear Sci., 2022)

Lipschitz Regularity of Graph Laplacians on Random Data Clouds. - Jeff Calder; Nicolás García Trillos; Marta Lewicka (SIAM J. Math. Anal., 2022)

On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it. - Camilo Garcia Trillos; Nicolás García Trillos (CoRR, 2023)

On the existence of solutions to adversarial training in multiclass classification. - Nicolás García Trillos; Matt Jacobs; Jakwang Kim (CoRR, 2023)

It begins with a boundary: A geometric view on probabilistically robust learning. - Leon Bungert; Nicolás García Trillos; Matt Jacobs; Daniel McKenzie; Dorde Nikolic; Qingsong Wang (CoRR, 2023)

Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower bounds. - Nicolás García Trillos; Melanie Weber 001 (CoRR, 2023)

Spectral Neural Networks: Approximation Theory and Optimization Landscape. - Chenghui Li; Rishi Sonthalia; Nicolás García Trillos (CoRR, 2023)

A New Perspective On Denoising Based On Optimal Transport. - Nicolás García Trillos; Bodhisattva Sen (CoRR, 2023)

Large sample spectral analysis of graph-based multi-manifold clustering. - Nicolás García Trillos; Pengfei He 002; Chenghui Li (J. Mach. Learn. Res., 2023)

The multimarginal optimal transport formulation of adversarial multiclass classification. - Nicolás García Trillos; Matt Jacobs; Jakwang Kim (J. Mach. Learn. Res., 2023)

An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification. - Nicolás García Trillos; Matt Jacobs; Jakwang Kim; Matthew Werenski (CoRR, 2024)

Defending Against Diverse Attacks in Federated Learning Through Consensus-Based Bi-Level Optimization. - Nicolás García Trillos; Aditya Kumar Akash; Sixu Li; Konstantin Riedl; Yuhua Zhu (CoRR, 2024)

FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization. - José A. Carrillo 001; Nicolás García Trillos; Sixu Li; Yuhua Zhu (J. Mach. Learn. Res., 2024)

Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms. - Nicolás García Trillos; Anna V. Little; Daniel McKenzie; James M. Murphy (J. Mach. Learn. Res., 2024)

Vector valued optimal transport: from dynamic to static formulations. - Katy Craig; Nicolás García Trillos; Dorde Nikolic (CoRR, 2025)

Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds. - Nicolás García Trillos; Chenghui Li; Raghavendra Venkatraman (CoRR, 2025)

Central limit theorems for the eigenvalues of graph Laplacians on data clouds. - Chenghui Li; Nicolás García Trillos; Housen Li; Leo Suchan (CoRR, 2025)