Search Results for author:
Found 15 papers, 3 papers with code
Depth Separation in Norm-Bounded Infinite-Width Neural Networks
We also show that a similar statement in the reverse direction is not possible: any function learnable with polynomial sample complexity by a norm-controlled depth-2 ReLU network with infinite width is also learnable with polynomial sample complexity by a norm-controlled depth-3 ReLU network.
How do Minimum-Norm Shallow Denoisers Look in Function Space?
Neural network (NN) denoisers are an essential building block in many common tasks, ranging from image reconstruction to image generation.
The Implicit Bias of Minima Stability in Multivariate Shallow ReLU Networks
Finally, we prove that if a function is sufficiently smooth (in a Sobolev sense) then it can be approximated arbitrarily well using shallow ReLU networks that correspond to stable solutions of gradient descent.
Linear Neural Network Layers Promote Learning Single- and Multiple-Index Models
This paper explores the implicit bias of overparameterized neural networks of depth greater than two layers.
The Role of Linear Layers in Nonlinear Interpolating Networks
This paper explores the implicit bias of overparameterized neural networks of depth greater than two layers.
A Function Space View of Bounded Norm Infinite Width ReLU Nets: The Multivariate Case
In this paper, we characterize the norm required to realize a function $f:\mathbb{R}^d\rightarrow\mathbb{R}$ as a single hidden-layer ReLU network with an unbounded number of units (infinite width), but where the Euclidean norm of the weights is bounded, including precisely characterizing which functions can be realized with finite norm.
Learning to Solve Linear Inverse Problems in Imaging with Neumann Networks
Recent advances have illustrated that it is often possible to learn to solve linear inverse problems in imaging using training data that can outperform more traditional regularized least squares solutions.
Neumann Networks for Inverse Problems in Imaging
We present an end-to-end, data-driven method of solving inverse problems inspired by the Neumann series, which we call a Neumann network.
Tensor Methods for Nonlinear Matrix Completion
This approach will succeed in many cases where traditional LRMC is guaranteed to fail because the data are low-rank in the tensorized representation but not in the original representation.
Algebraic Variety Models for High-Rank Matrix Completion
We consider a generalization of low-rank matrix completion to the case where the data belongs to an algebraic variety, i. e. each data point is a solution to a system of polynomial equations.
A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery
Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation and wavelet regularization.
Numerical Analysis Optimization and Control
Off-the-Grid Recovery of Piecewise Constant Images from Few Fourier Samples
In the first stage we estimate a continuous domain representation of the edge set of the image.
Recovery of Piecewise Smooth Images from Few Fourier Samples
We introduce a Prony-like method to recover a continuous domain 2-D piecewise smooth image from few of its Fourier samples.
Super-resolution MRI Using Finite Rate of Innovation Curves
We propose a two-stage algorithm for the super-resolution of MR images from their low-frequency k-space samples.
Iterative Non-Local Shrinkage Algorithm for MR Image Reconstruction
This approach is enabled by the reformulation of current non-local schemes as an alternating algorithm to minimize a global criterion.
