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The asymptotic spectrum of the Hessian of DNN throughout training
Arthur Jacot, Franck Gabriel, Clément Hongler
The dynamics of DNNs during gradient descent is described by the so-called Neural Tangent Kernel (NTK). In this article, we show that the NTK allows one to gain precise insight int…
Order and Chaos: NTK views on DNN Normalization, Checkerboard and Boundary Artifacts
Arthur Jacot, Franck Gabriel, François Ged +1
We analyze architectural features of Deep Neural Networks (DNNs) using the so-called Neural Tangent Kernel (NTK), which describes the training and generalization of DNNs in the inf…
Geometric stochastic heat equations
Yvain Bruned, Franck Gabriel, Martin Hairer +1
We consider a natural class of -valued one-dimensional stochastic PDEs driven by space-time white noise that is formally invariant under the action of the diffeomorph…
Scaling description of generalization with number of parameters in deep learning
Mario Geiger, Arthur Jacot, Stefano Spigler +6
Supervised deep learning involves the training of neural networks with a large number of parameters. For large enough , in the so-called over-parametrized regime, one can es…