Random Parameter Noise Does Not Make Exact ReLU Verification Easy
We study exact verification of ReLU networks in an adversarial smoothed model. Every network weight and bias is independently perturbed by Gaussian noise, clipped to $[-2,2]$, and rounded to the exact dyadic grid determined by the input bit complexity. We show that, under the standard assumption $\mathrm{NP}\not\subseteq\mathrm{BPP}$, there is no sound and complete verifier whose expected running time is polynomial in network size, bit complexity, and inverse noise level for every base instance. The conclusion already holds at the fixed noise level $σ_\star=2^{-11}$ for one-hidden-layer networks over a unit box, with hidden fan-in at most three and base coefficients in $[-1,1]$. The proof...
| Authors | Mojtaba Soltanalian |
|---|---|
| Primary category | cs.CC |
| Published | 15 July 2026 |
| Last updated at source | 15 July 2026 |
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