Annealed correlation and quenched noise sensitivity in biased deep neural networks
In earlier work by Jonasson, Steif and Zetterqvist (2023), fully connected deep neural networks with layers of width $n$, i.i.d.\ standard Gaussian weights, sign activations and no bias terms were shown to be annealed and quenched noise sensitive with respect to any joint probability distribution $\mathbb{Q}^{(n)}$ on the input $\boldsymbolω$ and its perturbation $\boldsymbolη$ satisfying a mild positive-correlation condition and $\mathbb{Q}^{(n)}(\boldsymbolη \in \{\boldsymbolω,-\boldsymbolω\}) \to 0$. Here we add independent Gaussian biases of the natural order and show that quenched noise sensitivity is retained over a broad range of depths, indeed under the slightly weaker assumption ...
| Authors | Johan Jonasson |
|---|---|
| Primary category | stat.ML |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
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