Unveiling Memorization-Generalization Coexistence: A Case Study on Arithmetic Tasks with Label Noise
Provides mechanistic understanding of memorization-generalization coexistence in over-parameterized models, relevant for improving robustness to label noise.
The paper investigates how over-parameterized neural networks simultaneously memorize noisy labels and generalize, using modular arithmetic tasks. It shows that with 80% label noise, near-perfect test accuracy can be achieved by extracting internal generalization structure via frequency-based methods.
Highly over-parameterized models can simultaneously memorize noisy labels and generalize well, yet how these behaviors coexist remains poorly understood. In this work, we investigate the underlying mechanisms of this coexistence using modular arithmetic tasks under heavy label noise. Through extensive experiments on two-layer neural networks, we find that larger models tend to generalize better under appropriate optimization and model configurations, while noisy labels are memorized faster than clean data. Over-parameterized models internally form a generalization structure, but its expression in the output is suppressed by the need to fit noisy labels. Remarkably, even with 80\% label noise, near-perfect test accuracy can be achieved by extracting this internal structure using frequency-based methods. We further propose a task-agnostic method to partition networks into generalization and memorization components. Although this subnetwork improves generalization, it is limited compared with frequency-based extraction, indicating that the generalization structure is distributed across neurons and motivating the development of new tools to retrieve generalizable knowledge from over-parameterized networks.