迈出一大步:去噪得分匹配中的大学习率防止记忆化
Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorization
AI总结:
本文揭示大学习率在去噪得分匹配中作为隐式正则化机制,通过阻止神经网络收敛到经验最优得分来防止扩散模型记忆化训练数据,并在一维及更广泛设置中验证了该作用。
摘要:
去噪得分匹配在基于扩散的生成模型性能中起着关键作用。然而,经验最优得分——去噪得分匹配的精确解——会导致记忆化,即生成的样本复制训练数据。但在实践中,即使没有显式正则化,也只观察到中等程度的记忆化。本文通过揭示一种由大学习率驱动的隐式正则化机制来研究这一现象。具体而言,我们表明在小噪声机制下,经验最优得分表现出高度不规则性。然后我们证明,当使用足够大的学习率通过随机梯度下降训练时,神经网络无法稳定地收敛到具有任意小超额风险的局部最小值。因此,学习到的得分不能任意接近经验最优得分,从而减轻记忆化。为了使分析易于处理,我们考虑一维数据和两层神经网络。实验验证了学习率在防止记忆化中的关键作用,即使在一维设置之外也是如此。
英文摘要:
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.
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