On the Optimal Memorization Power of ReLU Neural Networks
Abstract
We study the memorization power of feedforward ReLU neural networks. We show that such networks can memorize any $N$ points that satisfy a mild separability assumption using $\tilde{O}\left(\sqrt{N}\right)$ parameters. Known VC-dimension upper bounds imply that memorizing $N$ samples requires $\Omega(\sqrt{N})$ parameters, and hence our construction is optimal up to logarithmic factors. We also give a generalized construction for networks with depth bounded by $1 \leq L \leq \sqrt{N}$, for memorizing $N$ samples using $\tilde{O}(N/L)$ parameters. This bound is also optimal up to logarithmic factors. Our construction uses weights with large bit complexity. We prove that having such a large bit complexity is both necessary and sufficient for memorization with a sub-linear number of parameters.
Cite
Text
Vardi et al. "On the Optimal Memorization Power of ReLU Neural Networks." International Conference on Learning Representations, 2022.Markdown
[Vardi et al. "On the Optimal Memorization Power of ReLU Neural Networks." International Conference on Learning Representations, 2022.](https://mlanthology.org/iclr/2022/vardi2022iclr-optimal/)BibTeX
@inproceedings{vardi2022iclr-optimal,
title = {{On the Optimal Memorization Power of ReLU Neural Networks}},
author = {Vardi, Gal and Yehudai, Gilad and Shamir, Ohad},
booktitle = {International Conference on Learning Representations},
year = {2022},
url = {https://mlanthology.org/iclr/2022/vardi2022iclr-optimal/}
}