Franck Gabriel

Work in Progress/New Preprints

• Kernel-Smoothed Scores for Denoising Diffusion: A Bias-Variance Study; with François G. Ged, Maria Han Veiga, Emmanuel Schertzer. 

• Liquid Staking: When does it help? with Sylvain Carré.

• Security and Efficiency in DeFi Lending; Non-Technical Summary; a previous version of the paper was circulated under the title "Security and Credit in Proof-of-Stake DeFi Protocols", S. Carré, F. Gabriel. Presented at NEOMA (2022),  ISFA Lyon 1 (2022), SKMA Business School (2023), Apéro DeFi @ Palais Brongniart, Paris (2023), 2nd International Fintech Conference at Cardiff Business School (2023).

Publications

Machine Learning 

• Feature Learning in L2-regularized DNNs: Attraction/Repulsion and Sparsity, A. Jacot, E. Golikov, C. Hongler, F. Gabriel, 36th Conference on Neural Information Processing Systems (NeurIPS 2022). 

• Freeze and Chaos: NTK views on DNN Normalization, Checkerboard and Boundary Artifacts.  Arthur Jacot, Franck Gabriel, François Ged, Clément Hongler, Proceedings of Machine Learning Research vol 145:1–39, 2022, Mathematical and Scientific Machine Learning 2022. 

• Neural Tangent Kernel: Convergence and Generalization in Neural Networks. invited paper, A. Jacot, F. Gabriel, C. Hongler,  STOC 2021: Proceedings of the 53rd Annual ACM SIGACT, Symposium on Theory of Computing, June 2021. 

• Kernel Alignment Risk Estimator: Risk Prediction from Training Data. A. Jacot, B. Simsek, F. Spadaro, C. Hongler, F. Gabriel, arXiv:2006.09796, Advances in Neural Information Processing Systems 33, 2020. 

• Implicit Regularization of Random Feature Models. A. Jacot, B. Simsek, F. Spadaro, C. Hongler, F. Gabriel, arXiv:2002.08404, ICML 2020 Conference, 2020. 

• Scaling description of generalization with number of parameters in deep learning. M. Geiger, A. Jacot, S. Spigler, F. Gabriel, L. Sagun, S. d'Ascoli, G. Biroli, C. Hongler, M. Wyart, arXiv:1901.01608, JSTAT (Journal of Statistical Mechanics: Theory and Experiment), 2020.

•  The asymptotic spectrum of the Hessian of DNN throughout training. A. Jacot, F. Gabriel, C. Hongler, arXiv:1910.02875, ICLR 2020 Conference, 2020.

• Neural Tangent Kernel: Convergence and Generalization in Neural Networks. A. Jacot, F. Gabriel, C. Hongler, arXiv:1806.07572, Advances in Neural Information Processing Systems 31, 2018.

Economics 

• Insider Trading with Penalties, S. Carré, P. Collin-Dufresne, F. Gabriel. Journal of  Economic Theory, 2022. 

• Smart Proofs via Recursive Information Gathering: Decentralized Refereeing by Smart Contracts, S. Carré, F. Gabriel, C. Hongler, G. Lacerda, G. Capano, Distributed Ledger Technologies: Research and Practice, ACM, 2023. 

Mathematics

• Lattice Models and Conformal Field Theory, F. Gabriel, C. Hongler, F. Spadaro, Courant Lecture Notes; Volume: 32; 2024, 205 pp. 

• Freeness of type B and conditional freeness for random matrices, G. Cébron, A. Dahlqvist, F. Gabriel. To Indiana University Mathematics Journal, 2024.

• Random matrices and random graphs, (Mireille Capitaine, Simon Coste, Franck Gabriel, Pascal Maillard, and Cécile Mailler), ESAIM: PROCEEDINGS AND SURVEYS, November 2023, Vol. 74, p. 137-157

• Geometric Stochastic Heat Equations. Y. Bruned, F. Gabriel, M. Hairer, L. Zambotti, arXiv:1902.02884, Journal of the American Mathematical Society, 35, 1-80, 2022.

• Freeness over the diagonal for large random matrices. B. Au, G. Cébron, A. Dahlqvist, F. Gabriel, C. Male, arXiv:1805.07045, Annals of Probability, Volume 49, Number 1, 157-179, 2021.

• The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces. B. K. Driver, F. Gabriel, B. C. Hall, T. Kemp, arXiv:1602.03905, Communications in Mathematical Physics, Volume 352, Issue 3, pp 967-978, 2017.

• The Generalized Master Fields. G. Cébron, A. Dahlqvist, F. Gabriel, arXiv:1601.00214, Journal of Geometry and Physics, Volume 119, pp 34-53, 2017.

Preprints

• Saddle-to-Saddle Dynamics in Deep Linear Networks: Small Initialization Training, Symmetry, and Sparsity. A. Jacot, F. Ged, B. Simsek, C. Hongler, F.Gabriel, arXiv:2106.159 33, 2021.

• Combinatorial theory of random matrices III: random walks on S(N), ramified coverings and the S(\infty) Yang-Mills measure. F. Gabriel, arXiv:1510.01046, 2015.

• Combinatorial theory of permutation-invariant random matrices II: cumulants, freeness and Levy processes. F. Gabriel, arXiv:1507.02465, 2015. 

• Combinatorial theory of permutation-invariant random matrices I: partitions, geometry and renormalization. F. Gabriel, arXiv:1503.02792, 2015. 

• Planar Markovian Holonomy Fields. F. Gabriel, arXiv:1501.05077, 2015. 

Discussions

• Discussion / Article : The interaction between variable annuity providers and their customers under a dynamic approach, Anna Rita Bacinello, Rosario Maggistro and Ivan Zoccolan. 76e Journée de séminaires actuariels (CNAM Paris, ISFA Lyon et DSA-HEC Lausanne), UNIL, 2024. 

Thesis 

For an introduction to my early research work, you can refer to the thesis introduction. My thesis, "Holonomy fields and random matrices: symmetries under braiding and permutation" (under the direction of Pr. Thierry Lévy, in Paris 6 at the LPMA laboratory) is about 

1. two-dimensional Markovian holonomy fields, Yang-Mills measure and random ramified coverings,

2. random matrices invariant in law by conjugation by the symmetric group, with applications to random walks on the symmetric group. 

Selected Talks (Slides) 

• Permutation Invariant Matrix-Valued Levy Processes and Partition Algebra. Non-Commutative Stochastic Analysis Workshop, NTNU, Trondheim. 

• Random Features and Kernel Ridge Regression: Effective Ridge and Kernel Alignment Risk Estimator. Non-commutative algebra, probability and analysis in action, Greifswald. 

• Tweaking Algorithms in Finite-Size Random Matrix Approximations. Journées Modélisation Aléatoire et Statistique de la SMAI, Session Matrices et Graphes Aléatoires. 

• Two Dimensional Yang-Mills Measure as Planar Markovian Holonomy Fields. Stochastic Differential Geometry and Mathematical Physics, Rennes. 

• Random Walks on the Symmetric Group as Permutation Invariant Matrix-Valued Lévy Processes. Random Matrices Meet Random Permutations Workshop, 7-8 April 2022, Lille. 

Collaborators: 

        G. Cébron, A. Dahlqvist , B. K. Driver, E. Golikov, B. C. Hall, T. Kemp, C. Male, B. Au, M. Hairer, L. Zambotti, Y. Bruned, C. Hongler, A. Jacot, F. Spadaro, B. Simsek, F. Ged, J. Fageot, S. Carré, P. Collin-Dufresne, M. Geiger, S. Spigler, L. Sagun, S. d'Ascoli, G. Biroli, M. Wyart, M. Han Veiga, E. Schertzer, G. Lacerda, G. Capano, 

Organizing the ISFA seminar. Interested in speaking on topics such as insurance, economics, probabilities, informatics, finance, or machine learning? Don't hesitate to contact me!