Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorization

TL;DR

This paper reveals that large learning rates in denoising score matching induce an implicit regularization effect, preventing neural networks from memorizing training data and improving generative model robustness.

Contribution

It uncovers an implicit regularization mechanism driven by large learning rates that mitigates memorization in denoising score matching models.

Findings

Large learning rates lead to high irregularity in the empirical optimal score.

Neural networks trained with large learning rates cannot converge to overly memorizing solutions.

Experiments confirm the regularization effect of large learning rates beyond one-dimensional data.

Abstract

Denoising score matching plays a pivotal role in the performance of diffusion-based generative models. However, the empirical optimal score--the exact solution to the denoising score matching--leads to memorization, where generated samples replicate the training data. Yet, in practice, only a moderate degree of memorization is observed, even without explicit regularization. In this paper, we investigate this phenomenon by uncovering an implicit regularization mechanism driven by large learning rates. Specifically, we show that in the small-noise regime, the empirical optimal score exhibits high irregularity. We then prove that, when trained by stochastic gradient descent with a large enough learning rate, neural networks cannot stably converge to a local minimum with arbitrarily small excess risk. Consequently, the learned score cannot be arbitrarily close to the empirical optimal score, thereby mitigating memorization. To make the analysis tractable, we consider one-dimensional data and two-layer neural networks. Experiments validate the crucial role of the learning rate in preventing memorization, even beyond the one-dimensional setting.