"Deep lifts": Neural networks can generalize even with the dumbest optimizer
Given a labeled dataset $\{(x_i, y_i)\}_{i = 1}^n$, consider drawing a parameter vector $\hatθ$ uniformly at random from those that interpolate the data within a width-$W$ depth-$D$ ReLU architecture with continuous weights bounded within $[-M, M]$. We study the generalization properties of $\hatθ$ in the case where the dataset can, in fact, be explained by a smaller $w$-by-$d$ ReLU network. Despite the obliviousness of the selection rule for $\hatθ$, it adaptively generalizes at the rate $\tilde O\left(\frac{wdWD}{n}\right)$, rather than being governed by the VC dimension of the full $W$-by-$D$ hypothesis class. The reason is due to a particular inductive bias in ReLU networks: the $w$-b...
| Authors | Sunil Madhow, Yu-Xiang Wang |
|---|---|
| Primary category | cs.LG |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
Popularity, last 5 days
0 now. Counts as reported by the source, snapshotted daily by Silytics.
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 23 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.