Publications

Lattice Models and Field Theories

• Complex Analysis meets Statistical Mechanics: Applications to Kernel Methods and Conformal Field Theory (Francesco Spadaro), PhD Thesis, EPFL, November 2021.
• Ising Model and Field Theory : Lattice Local Fields and Massive Scaling Limit, (Sung Chul Park), PhD Thesis, EPFL, September 2019.
• Magnetization in the zig-zag layered Ising model and orthogonal polynomials (Dmitry Chelkak, Clément Hongler, Rémy Mahfouf), [arXiv preprint arXiv:1904.09168].
• The scaling limit of critical Ising interfaces is CLE(3) (Stéphane Benoist, Clément Hongler),  Annals of Prob., September 2019.
• Ising model: Local spin correlations and conformal invariance (Reza Gheissari, Clément Hongler, Sungchul Park), Comm. Math. Phys., February 2019.
• Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure (Clément Hongler, Fredrik Johansson Viklund and Kalle Kytölä), [arXiv:1307.4104v2].
• Conformal invariance of crossing probabilities for the Ising model with free boundary conditions (Stéphane Benoist, Hugo Duminil-Copin, Clément Hongler), Ann. of IHP, October 2016.
• Crossing probabilities in topological rectangles for the critical planar FK-Ising model (Dmitry Chelkak, Hugo  Duminil-Copin, Clément Hongler), Elec. J. of Prob., January 2016.
• Discrete holomorphicity and Ising model operator formalism (Kalle  Kytölä, Clément Hongler, Ali Zahabi),  Contemporary Mathematics Series of the AMS, 2015.
• Conformal Invariance of Spin Correlations in the Planar Ising Model (Dmitry Chelkak, Clément Hongler, Konstantin Izyurov), Annals of Math., May 2015.
• Convergence of Ising interfaces to Schramm’s SLE curves (Dmitry Chelkak, Hugo Duminil-Copin, Clément Hongler, Antti Kemppainen, Stanislav Smirnov), C. R. Acad. Sci. Paris, January 2014.
• Conformal Invariance of Ising Model Correlations (Clément Hongler), ICMP 2012 proceedings, World Scientific, October 2013.
• Ising interfaces and free boundary conditions (Clément Hongler, Kalle Kytölä), J. of the Amer. Math. Soc., October 2013.
• The energy density in the planar Ising model (Clément Hongler, Stanislav Smirnov), Acta Math., December 2013.
• Hardy Spaces and Boundary Conditions from the Ising Model (Clément Hongler, Duong H. Phong), Math. Zeit., June 2013.
• Connection probabilities and RSW-type bounds for the FK Ising model (Hugo Duminil-Copin, Clément Hongler, Pierre Nolin), Comm. Pure and Appl. Math., September 2011.
• Critical percolation: the expected number of clusters in a rectangle (Clément Hongler, Stanislav Smirnov), Prob. Th. and Rel. Fields, November 2011.
• Conformal invariance of Ising model correlations (Clément Hongler), Ph.D. thesis, Université de Genève, July 2010.

Machine Learning Theory

• Arrows of Time for Large Language Models, Vassilis Papadopoulos, Jérémie Wenger, Clément Hongler, 2024, [arXiv link].
• A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape (Berfin Simsek), PhD Thesis, EPFL, July 2023.
• Theory of Deep Learning: Neural Tangent Kernel and Beyond (Arthur Jacot), PhD Thesis, EPFL, August 2022.
• Feature Learning in L2-regularized DNNs: Attraction/Repulsion and Sparsity, Arthur Jacot, Eugene Golikov, Clément Hongler, Franck Gabriel. Proceedings of Neural Information Processing Systems 2022. [Conference paper page] [arXiv link]
• Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances, Berfin Simsek, François Ged,  Arthur Jacot, Francesco Spadaro, Clément Hongler, Wulfram Gerstner, Johanni Brea, International Conference on Machine Learning 2021. [arXiv link].
• Kernel Alignment Risk Estimator: Risk Prediction from Training Data (Arthur Jacot, Berfin Simsek, Francesco Spadaro, Clément Hongler, Franck Gabriel), NeurIPS 2020, [arXiv link].
• Implicit regularization of Random Feature Models (Arthur Jacot, Berfin Simsek, Francesco Spadaro, Clément Hongler, Franck Gabriel), ICML 2020. [arXiv link].
• The asymptotic spectrum of the Hessian of DNN throughout training  (Arthur Jacot, Franck Gabriel, Clément Hongler), [arXiv:1910.02875]. ICLR 2020.
• Order and Chaos: NTK views on DNN Normalization, Checkerboard and Boundary Artifacts,
  (Arthur Jacot, Franck Gabriel, François Ged, Clément Hongler), [arXiv:1907.05715].
• Scaling description of generalization with number of parameters in deep learning (Mario Geiger, Arthur Jacot, Stefano Spigler, Franck Gabriel, Levent Sagun, Stéphane d’Ascoli, Giulio Biroli, Clément Hongler, Matthieu Wyart), [arXiv:1901.01608]. J. of Stat. Mech.: Theory and Experiment, Volume 2020, February 2020.
• Neural Tangent Kernel: Convergence and Generalization in Neural Networks (Arthur Jacot, Franck Gabriel, Clément Hongler), [arXiv:1806.07572]. NeurIPS 2018 (Spotlight Talk–Poster).

Decentralized Systems

• Smart Proofs via Smart Contracts: Succinct and Informative Mathematical Derivations via Decentralized Markets. (Sylvain Carré, Franck Gabriel, Gustavo Lacerda, Gloria Capano), [https://arxiv.org/abs/2102.03044]