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Found 10 papers, 1 papers with code
Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares
We prove locally quadratic convergence of the iterates to a simultaneously structured data matrix in a regime of minimal sample complexity (up to constants and a logarithmic factor), which is known to be impossible for a combination of convex surrogates.
A simple approach for quantizing neural networks
In this short note, we propose a new method for quantizing the weights of a fully trained neural network.
More is Less: Inducing Sparsity via Overparameterization
In deep learning it is common to overparameterize neural networks, that is, to use more parameters than training samples.
Robust Sensing of Low-Rank Matrices with Non-Orthogonal Sparse Decomposition
We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process A.
Information Theory Information Theory
Gradient Descent for Deep Matrix Factorization: Dynamics and Implicit Bias towards Low Rank
This suggests that deep learning prefers trajectories whose complexity (measuredin terms of effective rank) is monotonically increasing, which we believe is a fundamental concept for thetheoretical understanding of deep learning.
Quantized Compressed Sensing by Rectified Linear Units
This work is concerned with the problem of recovering high-dimensional signals $\mathbf{x} \in \mathbb{R}^n$ which belong to a convex set of low-complexity from a small number of quantized measurements.
Information Theory Information Theory Probability 62B10 G.3
Computational approaches to non-convex, sparsity-inducing multi-penalty regularization
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements.
Information Theory Information Theory
On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds
This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension.
Information Theory Information Theory
Analysis of Hard-Thresholding for Distributed Compressed Sensing with One-Bit Measurements
A simple hard-thresholding operation is shown to be able to recover $L$ signals $\mathbf{x}_1,...,\mathbf{x}_L \in \mathbb{R}^n$ that share a common support of size $s$ from $m = \mathcal{O}(s)$ one-bit measurements per signal if $L \ge \log(en/s)$.
Information Theory Information Theory
Robust Recovery of Low-Rank Matrices with Non-Orthogonal Sparse Decomposition from Incomplete Measurements
By adapting the concept of restricted isometry property from compressed sensing to our novel model class, we prove error bounds between global minimizers and ground truth, up to noise level, from a number of subgaussian measurements scaling as $R(s_1+s_2)$, up to log-factors in the dimension, and relative-to-diameter distortion.
Numerical Analysis Numerical Analysis
