---
title: "A law of robustness for two-layer neural networks with arbitrary weights — Stuff That Spins"
description: "arXiv:2607.07778v1 Announce Type: new Abstract: Bubeck, Li and Nagaraj conjectured that, for generic data, any two-layer neural network with $m$ neurons that f…"
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date: "2026-07-10T04:00:00+00:00"
modified: "2026-07-10T06:05:07.698281+00:00"
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# A law of robustness for two-layer neural networks with arbitrary weights

**Source:** Unknown  
**Published:** July 10, 2026  
**Original:** https://arxiv.org/abs/2607.07778  

## On this page

- [Overview](#overview)

<a id="overview"></a>

## Overview

arXiv:2607.07778v1 Announce Type: new Abstract: Bubeck, Li and Nagaraj conjectured that, for generic data, any two-layer neural network with $m$ neurons that fits $n$ noisy labels must have Lipschitz constant at least of order $\sqrt{n/m}$, with no restriction on the size of the weights. Bubeck and Sellke proved a universal version of this law for Lipschitz-parameterized classes, but under a polynomial bound on the parameters; at depth three that boundedness hypothesis is genuinely necessary. Th

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