239 citations · 1.1k across the 35 of their papers we have counts for
6 papers · 1 filter
Finite Depth and Width Corrections to the Neural Tangent Kernel
Boris Hanin, Mihai Nica
We prove the precise scaling, at finite depth and width, for the mean and variance of the neural tangent kernel (NTK) in a randomly initialized ReLU network. The standard deviation…
Deep ReLU Networks Have Surprisingly Few Activation Patterns
Boris Hanin, David Rolnick
The success of deep networks has been attributed in part to their expressivity: per parameter, deep networks can approximate a richer class of functions than shallow networks. In R…
Nonlinear Approximation and (Deep) ReLU Networks
I. Daubechies, R. DeVore, S. Foucart +2
This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers. The res…
Interface Asymptotics of Wigner-Weyl Distributions for the Harmonic Oscillator
Boris Hanin, Steve Zelditch
We prove several types of scaling results for Wigner distributions of spectral projections of the isotropic Harmonic oscillator on . In prior work, we studied Wigner d…
Interface Asymptotics of Eigenspace Wigner distributions for the Harmonic Oscillator
Boris Hanin, Steve Zelditch
Eigenspaces of the quantum isotropic Harmonic Oscillator on have extremally high multiplicites and the…
Complexity of Linear Regions in Deep Networks
Boris Hanin, David Rolnick
It is well-known that the expressivity of a neural network depends on its architecture, with deeper networks expressing more complex functions. In the case of networks that compute…