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Exact signal recovery from generative priors with sigmoid output activation
Abstract
We show exact signal recovery in generative compressed sensing for feedforward neural networks with piecewise-linear activations and a final sigmoid activation, with no assumption of expansivity. Consider a ReLU network of depth d with a sigmoid final activation, whose input layer, of dimension k, is the narrowest, and let K be the geometric mean of the widths of its layers. We show that, with high probability, all signals of the range whose entries lie in $[δ, 1 - δ]$ are uniformly recovered from m ≳ k(d log(K/k) + log(1+log(1/δ))) measurements.
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BibTeX
@misc{scott2026exact,
title = {{Exact signal recovery from generative priors with sigmoid output activation}},
author = {Matthew S. Scott and Yaniv Plan and Özgür Yılmaz},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05626},
eprint = {2611.05626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05626},
}
RIS
TY - UNPB
TI - Exact signal recovery from generative priors with sigmoid output activation
AU - Matthew S. Scott
AU - Yaniv Plan
AU - Özgür Yılmaz
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05626
UR - https://arxiv.org/abs/2611.05626
AB - We show exact signal recovery in generative compressed sensing for feedforward neural networks with piecewise-linear activations and a final sigmoid activation, with no assumption of expansivity. Consider a ReLU network of depth d with a sigmoid final activation, whose input layer, of dimension k, is the narrowest, and let K be the geometric mean of the widths of its layers. We show that, with high probability, all signals of the range whose entries lie in $[δ, 1 - δ]$ are uniformly recovered from m ≳ k(d log(K/k) + log(1+log(1/δ))) measurements.
ER -