Franck Raymond Gabriel

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At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit [12, 9], thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: ...

Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF model with P feat ...

This book introduces the mathematical ideas connecting Statistical Mechanics and Conformal Field Theory (CFT). Building advanced structures on top of more elementary ones, the authors map out a well-posed road from simple lattice models to CFTs. Structure ...

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 ...

We consider a Kyle (1985) one-period model where insider trading may be subject to a penalty that is increasing in trade size. We characterize the solution - the equilibrium price and optimal trading strategy explicitly and establish existence and uniquene ...

Franck Raymond Gabriel

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Neural Tanget Kernel: Convergence and Generalization in Neural Networks

Implicit Regularization of Random Feature Models

Lattice Models and Conformal Field Theory

Geometric Stochastic Heat Equations

Scaling description of generalization with number of parameters in deep learning

Insider trading with penalties