563 citations · 891 across the 25 of their papers we have counts for
5 papers · 1 filter
Density estimation for shift-invariant multidimensional distributions
Anindya De, Philip M. Long, Rocco A. Servedio
We study density estimation for classes of shift-invariant distributions over . A multidimensional distribution is "shift-invariant" if, roughly speaking, it is close…
Learning Sums of Independent Random Variables with Sparse Collective Support
Anindya De, Philip M. Long, Rocco A. Servedio
We study the learnability of sums of independent integer random variables given a bound on the size of the union of their supports. For , a sum…
The Singular Values of Convolutional Layers
Hanie Sedghi, Vineet Gupta, Philip M. Long
We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation. This charact…
Representing smooth functions as compositions of near-identity functions with implications for deep network optimization
Peter L. Bartlett, Steven N. Evans, Philip M. Long
We show that any smooth bi-Lipschitz can be represented exactly as a composition of functions that are close to the identity in the sens…
Gradient descent with identity initialization efficiently learns positive definite linear transformations by deep residual networks
Peter L. Bartlett, David P. Helmbold, Philip M. Long
We analyze algorithms for approximating a function mapping to using deep linear neural networks, i.e. that learn a function parameterized by matrice…