# Learning from almost nothing: How neural networks survive heavy input corruption

arXiv: https://arxiv.org/abs/2606.11319 · HTML: https://mlsanity.com/paper/2606.11319/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 10 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [The Principles of Deep Learning Theory](https://mlsanity.com/paper/2106.10165/) (2021)
- [Deep Learning is Robust to Massive Label Noise](https://mlsanity.com/paper/1705.10694/) (2017)
- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)

## Abstract (arXiv)

Learning from imperfect data is a central theme in machine learning, connecting practical questions of robustness to fundamental questions of learnability. Here we examine attribute noise: learning from corrupted inputs while keeping the labels intact, a setting that has received considerably less analytical attention than its label-noise counterpart. We consider two types of corruption models: additive noise and replacement noise. Through experiments with multi-layer perceptrons (MLPs) on corrupted classification datasets, we find that neural networks remain robust, maintaining well-above-chance accuracy even when inputs are >90% corrupted -- far beyond human recognition. To understand this robustness, we analyze infinite-width networks in the heavy-corruption regime using a mean-field-inspired approach and derive a leading-order decision rule for the classification outcome: the network implements a prototype rule, the nearest-class-mean, assigning each test point to the class whose training-set average it most closely resembles. This leading-order decision rule is universal across a broad range of MLP architectures, holding for any depth, as well as a wide class of activation functions and noise distributions. The same centroid mechanism closely matches finite-width network behavior in our experiments and provides an interpretable and analytically tractable account of why learning can succeed even when individual training examples carry almost no signal.