Rethinking Benign Overfitting in Two-Layer Neural Networks
This work addresses the problem of understanding overfitting in neural networks for researchers and practitioners dealing with long-tailed data distributions, though it is incremental as it builds on existing models.
The paper tackles the discrepancy between theoretical predictions of harmful overfitting and empirical observations of benign overfitting in neural networks by refining a feature-noise data model to include class-dependent heterogeneous noise, revealing that networks can use data noise to learn implicit features that improve classification accuracy for long-tailed data.
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. Further experimental results 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 reveal that neural networks can leverage "data noise" to learn implicit features that improve the classification accuracy for long-tailed data. Our analysis also provides a training-free metric for evaluating data influence on test performance. Experimental validation on both synthetic and real-world datasets supports our theoretical results.