Thomas Laurent

Loyola Marymount University
Mathematics Department
e-mail: tlaurent [AT] lmu.edu

[Google Scholar Profile]









About me


I am an associate professor of Mathematics at Loyola Marymount University. My research interests are in Deep Learning, Machine Learning and Partial Differential equations.

I did my PhD at Duke University with Prof. Michael Reed, and my postdoc at UCLA with Prof. Andrea Bertozzi. Before joining LMU I was an assistant professor at UCR.



Machine Learning and Deep Learning Publications



C. K. Joshi, T. Laurent and X. Bresson
On Learning Paradigms for the Travelling Salesman Problem
NeurIPS 2019 workshop on Graph Representation Learning [paper]

X. Bresson and T. Laurent
A Two-Step Graph Convolutional Decoder for Molecule Generation
NeurIPS 2019 workshop on Machine Learning and the Physical Sciences [paper]

T. Laurent and J. von Brecht
The Multilinear Structure of ReLU Networks
ICML 2018 [paper] [video]

T. Laurent and J. von Brecht
Deep linear neural networks with arbitrary loss: All local minima are global
ICML 2018 [paper] [video]

X. Bresson and T. Laurent
An Experimental Study of Neural Networks for Variable Graphs
ICLR 2018 (workshop track) [paper]

X. Bresson, H. Hu, T. Laurent, A. Szlam and J. von Brecht
An incremental reseeding strategy for clustering
Mathematics and Visualization, 2018 [paper]

T. Laurent and J. von Brecht
A recurrent neural network without chaos
ICLR 2017 [paper]

X. Bresson, T. Laurent, A. Szlam and J. von Brecht
The product cut
NIPS 2016 [paper]

N. Garcia, D. Slepcev, J. von Brecht, T. Laurent, and X. Bresson
Consistency of Cheeger and ratio graph cuts
JMLR, volume 17, 2016 [paper]

X. Bresson, T. Laurent and J. von Brecht
Enhanced lasso recovery on graph
European Signal Processing Conference (EUSIPCO), 2015 [paper]

X. Bresson, T. Laurent, D. Uminsky and J. von Brecht
Multiclass total variation clustering
NIPS 2013 [paper]

H. Hu, T. Laurent, M. A. Porter and A. L. Bertozzi
A method based on total variation for network modularity optimization using the MBO scheme
SIAM J. Appl. Math., 73(6), pp. 2224-2246, 2013 [paper]

X. Bresson, T. Laurent, D. Uminsky and J. von Brecht
Convergence and energy landscape for Cheeger cut clustering
NIPS 2012 [paper]



Partial Differential Equations Publications



A. Bertozzi, J. Garnett, T. Laurent and J. Verdera
The regularity of the boundary of a multidimensional aggregation patch
SIAM J. Math. Anal., 48(6), 3789-3819, 2016 [paper]

S. Ramakrishnan, T. Laurent, M. Kumar, and A. Bertozzi
A spatiotemporal chemotactic model for ant foraging
Modern Physics Letters B, Vol. 28, No. 30, 2014

D. Balague, J. A. Carrillo, T. Laurent and G. Raoul
Dimensionality of Local Minimizers of the Interaction Energy
Archive for Rational Mechanics and Analysis, Volume 209, Issue 3, pp 1055-1088, 2013 [paper]

D. Balague, J. A. Carrillo, T. Laurent and G. Raoul
Nonlocal interactions by repulsive-attractive potentials: radial in/stability
Physica D: Nonlinear Phenomena, 2012 [paper]

A. Bertozzi, T. Laurent and F. LeĢger
Aggregation and spreading via the Newtonian potential: the dynamics of patch solutions
Mathematical Models and Methods in Applied Sciences, 22, (2012)

A. Bertozzi, J. Garnett and T. Laurent
Characterization of radially symmetric finite time blowup in multidimensional aggregation equations
SIAM J. Math. Anal., 44, No 2 (2012), pp. 651-681

J. A. Carrillo, M. DiFrancesco, A. Figalli, T. Laurent and D. Slepcev
Confinement in nonlocal interaction equations
Nonlinear Analysis, 75 (2012), pp. 550-558

J. A. Carrillo, M. DiFrancesco, A. Figalli, T. Laurent and D. Slepcev
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
Duke Math. J., 156, No 2 (2011), pp. 229-271 [paper]

A. Bertozzi, T. Laurent and J. Rosado
Lp Theory for the Multidimensional Aggregation Equation
Communications on Pure and Applied Mathematics, 64, No 1 (2011), pp. 45-83

A. Bertozzi and T. Laurent
The Behavior of Solutions of Multidimensional Aggregation Equations with Mildly Singular interaction Kernels
Chinese Annals of Mathematics, Special Majda issue, 30, No 5 (2009), pp. 463-482

A. Bertozzi, J. A. Carrillo and T. Laurent
Blowup in multidimensional aggregation equations with mildly singular interaction kernels
Nonlinearity, 22, No 3 (2009), pp. 683-710

A. Bertozzi and T. Laurent
Finite-time Blow-up of Solutions of an Aggregation Equation in Rn
Comm. Math. Phys., 274, No 3 (2007), pp. 717-735

T. Laurent
Local and Global Existence for an Aggregation Equation
Communications in Partial Differential Equations, 32, No 12 (2007), pp. 1941-1964

T. Laurent, B. Rider and M. Reed
Parabolic Behavior of a Hyperbolic Delay Equation
SIAM J. Math. Anal. 38, No 1 (2006), pp. 1-15