Publications

A (hopefully) up to date list of my publications, in reverse chronological order.

  • Large Data Limits and Scaling Laws for tSNE. Submitted 2024. preprint
  • On Probabilistic Embeddings in Optimal Dimension Reduction, R. Murray, A. Pickarski. Submitted 2024. preprint
  • Uniform Convergence of Adversarially Robust Classifiers, R. Morris, R. Murray. Submitted 2024. preprint
  • Wellposedness and singularity formation beyond the Yudovich class, T. Elgindi, R. Murray, A. Said, Submitted 2023. preprint
  • Dirichlet Active Learning, K. Miller, R. Murray, Submitted 2023. preprint
  • Using Higher-Order Moments to Assess the Quality of GAN-generated Image Features, L. Luzi, H. Jenne, R. Murray, C. Ortiz Marrero, Accepted to Transactions on Machine Learning Research 2024. preprint
  • Non-Linear Singularity Formation for Circular Vortex Sheets, R. Murray, G. Wilcox. Accepted to Quarterly for Applied Mathematics, 2023.  preprint
  • On the long-time behavior of scale-invariant solutions to the 2d Euler equation and applications, T. Elgindi, R. Murray, A. Said. Accepted in Annales scientifiques de l’École normale supérieure, 2024. preprint
  • Eikonal depth: an optimal control approach to statistical depths, M. Molina-Fructuoso, R. Murray. To Appear in Foundations of Data Science, 2024. preprint
  • Rates of Convergence for Regression with the Graph Poly-Laplacian, N. Garcia Trillos, R. Murray, M. Thorpe. Accepted to Sampling Theory, Signal Processing, and Data Analysis 2022. preprint
  • The geometry of adversarial training in binary classification, L. Bungert, N. Garcia Trillos, R. Murray. Accepted to Information and Inference, 2022. preprint
  • Tukey depths and Hamilton-Jacobi Equations. M. Molina-Fructuoso, R. Murray. Accepted to SIAM Mathematics of Data Science, 2022. preprint
  • Adversarial classification: Necessary conditions and geometric flows. R. Murray, N. Garcia Trillos. JMLR 2022. preprint
  • Dropout Regularization for Nonparametric Learning. R. Murray, E. Fokoue. Accepted to JSTP special issue on deep learning, 2020.
  • Regular Potential Games. B. Swenson, R. Murray, S. Kar. Accepted to Games and Economic Behavior, 2020. Preprint,
  • Distributed gradient flow: nonsmoothness, nonconvexity, and saddle point evasion. B. Swenson, R. Murray, V. Poor, S. Kar. Accepted to IEEE TAC, to appear 2022, preprint
  • Distributed stochastic gradient descent: nonconvexity, nonsmoothness, and convergence to local minima. B. Swenson, R. Murray, V. Poor, S. Kar. Accepted to JMLR, preprint
  • On self-similar solutions to the incompressible Euler equations. A. Bressan, R. Murray. JDE 2020.
  • From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds. N. Garcia Trillos, R. Murray, M. Thorpe. ARMA, 2022. preprint
  • A maximum principle argument for the uniform convergence of graph Laplacian regressors. N. Garcia Trillos, R. Murray. SIAM Mathematics of Data Science, 2020. preprint
  • Modelling uncertainty in reinforcement learning. R. Murray, M. Palladino. CDC 2019.
  • Neutral competition in a deterministically changing environment: revisiting continuum approaches. R. Murray, G. Young. JTB 2019.
  • Local minimizers and slow motion for the mass preserving Allen–Cahn equation in higher dimensions. G. Leoni, R. Murray. Proceedings of the AMS, 2019. Preprint
  • A model for system uncertainty in reinforcement learning. R. Murray, M. Palladino. Systems and Control Letters, 2018. Preprint.
  • Revisiting Normalized Gradient Descent: Evasion of Saddle Points. R. Murray, B. Swenson, S. Kar. IEEE TAC, 2018. Preprint.
  • On Best-Response Dynamics in Potential Games. B. Swenson, R. Murray, S. Kar. SIAM Control, 2018. Published. Preprint.
  • A new analytical approach to consistency and overfitting in regularized empirical risk minimization. N. Garcia Trillos, R. Murray. EJAM, 2017. Published Preprint
  • Cutoff Estimates for the Linearized Becker-Doring Equations. R. Murray, B. Pego. Comm. Math. Sci. 2017. Published, Preprint.
  • Slow Motion for the Nonlocal Allen Cahn Equation in n-dimensions. R. Murray, M. Rinaldi. Calc Var PDE 2016. Published, Preprint
  • Algebraic Decay to Equilibrium for the Becker-Doring Equations. R. Murray, B. Pego. SIMA. 2016. Published, Preprint.
  • Second Order Γ-Limit for the Cahn-Hilliard Functional. G. Leoni, R. Murray. ARMA. 2016. Published, Preprint