Dichotomy of Feature Learning and Unlearning: Fast-Slow Analysis on Neural Networks with Stochastic Gradient Descent

The dynamics of gradient-based training in neural networks often exhibit nontrivial structures; hence, understanding them remains a central challenge in theoretical machine learning. In particular, the concept of feature unlearning, in which a neural network progressively loses previously learned features over long training, has gained attention. In this study, we consider the infinite-width limit of a two-layer neural network trained with a large-batch stochastic gradient, then derive differential equations with different time scales, revealing the mechanism and conditions for feature unlearning to occur. Specifically, we utilize the fast-slow dynamics: while an alignment of first-layer weights develops rapidly, the second-layer weights develop slowly. The direction of the flow on a critical manifold, determined by the slow dynamics, decides whether feature unlearning occurs. We give numerical validation of the result and derive theoretical grounding and scaling laws for the feature unlearning. Our results yield the following insights: (i) the strength of the primary nonlinear term in the data induces the feature unlearning, and (ii) an initial scale of the second-layer weights mitigates the feature unlearning. Our result should be understood as a population loss of alignment rather than finite-sample overfitting. Technically, our analysis utilizes Tensor Programs and singular perturbation theory.