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

Neural networks maintain well-above-chance accuracy on classification tasks even when over 90% of input data is corrupted, far exceeding human recognition capabilities. Researchers analyzing multi-layer perceptrons under heavy attribute noise found that networks implement a nearest-class-mean prototype rule, assigning test points to the class whose training-set average they most closely resemble. This universal centroid mechanism, derived using a mean-field-inspired approach, explains why learning succeeds even when individual training examples carry almost no signal.

arXiv:2606.11319v1 Announce Type: new 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 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.