# Logarithmic Width Suffices for Robust Memorization

arXiv: https://arxiv.org/abs/2502.11162 · HTML: https://mlsanity.com/paper/2502.11162/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2025.

## Built on by (most cited first, 1 of 1)

- [Geometric Factual Recall in Transformers](https://mlsanity.com/paper/2605.12426/) (2026)

## Abstract (arXiv)

The memorization capacity of neural networks with a given architecture has been thoroughly studied in many works. Specifically, it is well-known that memorizing N samples can be done using a network of constant width, independent of N. However, the required constructions are often quite delicate. In this paper, we consider the natural question of how well feedforward ReLU neural networks can memorize robustly, namely while being able to withstand adversarial perturbations of a given radius. We establish both upper and lower bounds on the possible radius for general lp norms, implying (among other things) that width logarithmic in the number of input samples is necessary and sufficient to achieve robust memorization (with robustness radius independent of N).