Neural networks become centroid classifiers when trained on heavily corrupted inputs
Abstract
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 multilayer 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.
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BibTeX
@article{tahmassebpur2026neural,
title = {{Neural networks become centroid classifiers when trained on heavily corrupted inputs}},
author = {Justin Tahmassebpur and Asadullah Bhuiyan and Hyejin Kim and Omri Lesser},
journal = {Physical Review Research},
year = {2026},
month = oct,
doi = {10.1103/qkrg-wbbj},
url = {http://link.aps.org/doi/10.1103/qkrg-wbbj},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Neural networks become centroid classifiers when trained on heavily corrupted inputs
AU - Justin Tahmassebpur
AU - Asadullah Bhuiyan
AU - Hyejin Kim
AU - Omri Lesser
PY - 2026
DA - 2026/10/23
JO - Physical Review Research
DO - 10.1103/qkrg-wbbj
UR - http://link.aps.org/doi/10.1103/qkrg-wbbj
AB - 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 multilayer 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.
SN - 2643-1564
ER -