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

• URL: http://arxiv.org/abs/2606.11319v1
• Date: Tue, 09 Jun 2026 18:02:09 GMT
• Title: Learning from almost nothing: How neural networks survive heavy input corruption
• Abstract summary: Learning from imperfect data is a central theme in machine learning, connecting practical questions of robustness to fundamental questions of learnability.<n>We consider two types of corruption models: additive noise and replacement noise.<n>We find that neural networks remain robust, maintaining well-above-chance accuracy even when inputs are >90% corrupted.
• Score: 1.1929558226793768
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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