Benign Overfitting of Long-Tailed Data Classification in Two-layer Neural Networks
Keywords: two-layer neural networks, benign overfitting, long-tailed data distribution
TL;DR: We re-examine benign overfitting in two-layer neural networks and prove that while short-tailed data is classified by explicit features, long-tailed data is classified through covariance-realted implicit features.
Abstract: Recent theoretical studies (Kou et al., 2023; Cao et al., 2022) have revealed a sharp phase transition from benign to harmful overfitting when the noise-to-feature ratio exceeds a threshold—a situation common in long-tailed data distributions where atypical data is prevalent. However, harmful overfitting rarely happens in overparameterized neural networks. Experimental results further suggested that memorization is necessary for achieving near-optimal generalization error in long-tailed data distributions (Feldman & Zhang, 2020). We argue that this discrepancy between theoretical predictions and empirical observations arises because previous feature-noise data models overlook the heterogeneous nature of noise across different data classes. In this paper, we refine the feature-noise data model by incorporating class-dependent heterogeneous noise and re-examine the overfitting phenomenon in neural networks. Through a comprehensive analysis of the training dynamics, we establish test loss bounds for the refined model. Our findings show that neural networks can benefit from "data noise", previously deemed harmful, and learn implicit features to enhance classification accuracy for long-tailed data. Experiments on both synthetic and real-world data validate our theory.
Primary Area: learning theory
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Submission Number: 10542
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