Person
Clément Hongler
Related publications (19)
Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure
Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin et al. (Nucl Phys B 241(2):333-380, 1984). Both exhibit exactly solvable structures in two dimensions. A long-standing question ( ...
SPRINGER2022Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances
Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot
We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with layers of minimal widths reaches a zero-loss minimum at $ r_1^*! \c ...
2021Neural Tangent Kernel: Convergence and Generalization in Neural Networks (Invited Paper)
Clément Hongler, Franck Raymond Gabriel, Arthur Jacot
The Neural Tangent Kernel is a new way to understand the gradient descent in deep neural networks, connecting them with kernel methods. In this talk, I'll introduce this formalism and give a number of results on the Neural Tangent Kernel and explain how th ...
ASSOC COMPUTING MACHINERY2021Scaling description of generalization with number of parameters in deep learning
Matthieu Wyart, Clément Hongler, Mario Geiger, Stefano Spigler, Levent Dogus Sagun, Franck Raymond Gabriel, Arthur Jacot
Supervised deep learning involves the training of neural networks with a large number N of parameters. For large enough N, in the so-called over-parametrized regime, one can essentially fit the training data points. Sparsitybased arguments would suggest th ...
IOP PUBLISHING LTD2020Ising Model: Local Spin Correlations and Conformal Invariance
Clément Hongler, Sung Chul Park
We study the 2-dimensional Ising model at critical temperature on a simply connected subset of the square grid Z2. The scaling limit of the critical Ising model is conjectured to be described by Conformal Field Theory; in particular, there is expected to b ...
Springer2019The Scaling Limit Of Critical Ising Interfaces Is Cle3
In this paper, we consider the set of interfaces between + and - spins arising for the critical planar Ising model on a domain with + boundary conditions, and show that it converges to nested CLE3. Our proof relies on the study of the coupling between the ...
INST MATHEMATICAL STATISTICS2019Conformal invariance of crossing probabilities for the Ising model with free boundary conditions
We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin (J. Stat. Phys. 98 (2000) ...
Inst Mathematical Statistics2016Crossing Probabilities in Topological Rectangles for the Critical Planar FK-Ising model
We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundary conditions, generalizing results of [DCHN11] and [CS12]. Our result relies ...
Institute of Mathematical Statistics2016Conformal Invariance of Spin Pattern Probabilities in the Planar Ising Model
Clément Hongler, Sung Chul Park
We study the 2-dimensional Ising model at critical temperature on a smooth simply-connected graph Ω.We rigorously prove the conformal invariance of arbitrary spin-pattern probabilities centered at a point a and derive formulas to compute the probabilities ...
2015Conformal Invariance of Spin Correlations in the Planar Ising Model
We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming fro ...
2015