English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Generative neural networks have been empirically found very promising inproviding effective structural priors for compressed sensing, since they can betrained to span low-dimensional data manifolds in high-dimensional signalspaces. Despite the non-convexity of the resulting optimization problem, it hasalso been shown theoretically that, for neural networks with random Gaussianweights, a signal in the range of the network can be efficiently, approximatelyrecovered from a few noisy measurements. However, a major bottleneck of thesetheoretical guarantees is a network expansivity condition: that each layer ofthe neural network must be larger than the previous by a logarithmic factor.Our main contribution is to break this strong expansivity assumption, showingthat constant expansivity suffices to get efficient recovery algorithms,besides it also being information-theoretically necessary. To overcome thetheoretical bottleneck in existing approaches we prove a novel uniformconcentration theorem for random functions that might not be Lipschitz butsatisfy a relaxed notion which we call "pseudo-Lipschitzness." Using thistheorem we can show that a matrix concentration inequality known as the WeightDistribution Condition (WDC), which was previously only known to hold forGaussian matrices with logarithmic aspect ratio, in fact holds for constantaspect ratios too. Since the WDC is a fundamental matrix concentrationinequality in the heart of all existing theoretical guarantees on this problem,our tighter bound immediately yields improvements in all known results in theliterature on compressed sensing with deep generative priors, including one-bitrecovery, phase retrieval, low-rank matrix recovery, and more.

Constant-Expansion Suffices for Compressed Sensing with Generative Priors