arXiv:2611.05626 · v1

Exact signal recovery from generative priors with sigmoid output activation

首次提交 2026-11-04 05:15

版本更新 2026-11-04 05:15

雷达观测 2026-11-05 10:08

摘要

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 $m \gtrsim k(d \log(K/k) + \log(1+\log(1/δ)))$ measurements.

作者备注：9 pages