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

TL;DR

This paper analyzes the dynamics of feature unlearning in neural networks trained with stochastic gradient descent, revealing how different time scales influence the loss of learned features and providing theoretical and numerical insights.

Contribution

It introduces a fast-slow differential equation framework for understanding feature unlearning in infinite-width neural networks, with new scaling laws and conditions identified.

Findings

Feature unlearning is driven by the strength of the primary nonlinear data term.

Initial scale of second-layer weights affects the likelihood of feature unlearning.

The analysis provides theoretical grounding and validation through numerical experiments.

Abstract

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, a 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 updated 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 a 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 of the feature unlearning. Our results yield the following insights: (i) the strength of the primary nonlinear term in data induces the feature unlearning, and (ii) an initial scale of the second-layer weights mitigates the feature unlearning. Technically, our analysis utilizes Tensor Programs and the singular perturbation theory.