2024 export record
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journals/corr/abs-2401-09191 share record
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Nicolás García Trillos , Matt Jacobs , Jakwang Kim , Matthew Werenski : An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification. CoRR abs/2401.09191 (2024 )2023 export record
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journals/jmlr/Trillos0L23 share record
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Nicolás García Trillos , Pengfei He , Chenghui Li : Large sample spectral analysis of graph-based multi-manifold clustering. J. Mach. Learn. Res. 24 : 143:1-143:71 (2023 )export record
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journals/jmlr/TrillosJK23 share record
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Nicolás García Trillos , Matt Jacobs , Jakwang Kim : The multimarginal optimal transport formulation of adversarial multiclass classification. J. Mach. Learn. Res. 24 : 45:1-45:56 (2023 )export record
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journals/corr/abs-2301-03662 share record
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Camilo Garcia Trillos , Nicolás García Trillos : On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it. CoRR abs/2301.03662 (2023 )export record
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journals/corr/abs-2305-00075 share record
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Nicolás García Trillos , Matt Jacobs , Jakwang Kim : On the existence of solutions to adversarial training in multiclass classification. CoRR abs/2305.00075 (2023 )export record
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journals/corr/abs-2305-02894 share record
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Jose A. Carrillo , Nicolás García Trillos , Sixu Li , Yuhua Zhu : FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization. CoRR abs/2305.02894 (2023 )export record
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journals/corr/abs-2305-18779 share record
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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 abs/2305.18779 (2023 )export record
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journals/corr/abs-2307-02378 share record
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Nicolás García Trillos , Melanie Weber : Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower bounds. CoRR abs/2307.02378 (2023 )export record
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journals/corr/abs-2307-05750 share record
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Nicolás García Trillos , Anna Little , Daniel McKenzie , James M. Murphy : Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms. CoRR abs/2307.05750 (2023 )export record
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journals/corr/abs-2310-00729 share record
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Chenghui Li , Rishi Sonthalia , Nicolás García Trillos : Spectral Neural Networks: Approximation Theory and Optimization Landscape. CoRR abs/2310.00729 (2023 )export record
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journals/corr/abs-2312-08135 share record
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Nicolás García Trillos , Bodhisattva Sen : A New Perspective On Denoising Based On Optimal Transport. CoRR abs/2312.08135 (2023 )2022 share record
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Nicolás García Trillos , Ryan Murray : Adversarial Classification: Necessary Conditions and Geometric Flows. J. Mach. Learn. Res. 23 : 187:1-187:38 (2022 )share record
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Nicolás García Trillos , Javier Morales : Semi-discrete Optimization Through Semi-discrete Optimal Transport: A Framework for Neural Architecture Search. J. Nonlinear Sci. 32 (3 ) : 27 (2022 )export record
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journals/siamma/CalderTL22 share record
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Jeff Calder , Nicolás García Trillos , Marta Lewicka : Lipschitz Regularity of Graph Laplacians on Random Data Clouds. SIAM J. Math. Anal. 54 (1 ) : 1169-1222 (2022 )export record
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journals/corr/abs-2204-12676 share record
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Nicolás García Trillos , Matt Jacobs , Jakwang Kim : The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification. CoRR abs/2204.12676 (2022 )export record
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journals/corr/abs-2207-01093 share record
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Nicolás García Trillos , Daniel Sanz-Alonso , Ruiyi Yang : Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning. CoRR abs/2207.01093 (2022 )export record
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journals/corr/abs-2209-02305 share record
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Nicolás García Trillos , Ryan Murray , Matthew Thorpe : Rates of Convergence for Regression with the Graph Poly-Laplacian. CoRR abs/2209.02305 (2022 )export record
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journals/corr/abs-2209-15130 share record
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Yuetian Luo , Nicolás García Trillos : Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective. CoRR abs/2209.15130 (2022 )export record
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journals/corr/abs-2210-06671 share record
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Aditya Kumar Akash , Sixu Li , Nicolás García Trillos : Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks. CoRR abs/2210.06671 (2022 )2021 export record
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journals/jmlr/TrillosHH21 share record
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Nicolás García Trillos , Franca Hoffmann , Bamdad Hosseini : Geometric structure of graph Laplacian embeddings. J. Mach. Learn. Res. 22 : 63:1-63:55 (2021 )share record
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Nicolás García Trillos , Félix Morales , Javier Morales : Traditional and Accelerated Gradient Descent for Neural Architecture Search. GSI 2021 : 507-514 export record
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journals/corr/abs-2107-13610 share record
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Nicolás García Trillos , Pengfei He , Chenghui Li : Large sample spectral analysis of graph-based multi-manifold clustering. CoRR abs/2107.13610 (2021 )export record
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journals/corr/abs-2108-08687 share record
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Katy Craig , Nicolás García Trillos , Dejan Slepcev : Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation. CoRR abs/2108.08687 (2021 )export record
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journals/corr/abs-2109-06294 share record
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Camilo Garcia Trillos , Nicolás García Trillos : On the regularized risk of distributionally robust learning over deep neural networks. CoRR abs/2109.06294 (2021 )export record
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journals/corr/abs-2111-13613 share record
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Leon Bungert , Nicolás García Trillos , Ryan Murray : The Geometry of Adversarial Training in Binary Classification. CoRR abs/2111.13613 (2021 )2020 export record
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journals/focm/TrillosGHS20 share record
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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 ) : 827-887 (2020 )export record
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journals/jmlr/TrillosKSS20 share record
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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 : 28:1-28:47 (2020 )export record
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journals/simods/TrillosM20 share record
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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 ) : 705-739 (2020 )export record
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journals/corr/abs-2003-07991 share record
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Daniele Bigoni , Yuming Chen , Nicolás García Trillos , Youssef M. Marzouk , Daniel Sanz-Alonso : Data-Driven Forward Discretizations for Bayesian Inversion. CoRR abs/2003.07991 (2020 )export record
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journals/corr/abs-2004-09304 share record
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Nicolás García Trillos , Ryan Murray , Matthew Thorpe : From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds. CoRR abs/2004.09304 (2020 )