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arXiv 2209.07587stat.MLcs.LG
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批量归一化的理论研究:基于数据的正则化率自动调整

Theoretical Insight into Batch Normalization: Data Dependant Auto-Tuning of Regularization Rate

Lakshmi Annamalai, Chetan Singh Thakur

摘要:

批量归一化广泛用于深度学习中,以规范化中间激活。众所周知,深度网络的训练复杂性增加,需要仔细初始化权重,需要较低的学习率等。这些问题已经通过批量归一化(\textbf{BN})解决,通过将激活的输入归一化为零均值和单位标准差。将这种批量归一化作为训练过程的一部分,可以大大加快深度网络的训练过程。一个新的研究领域已经开始研究\textbf{BN}成功背后的确切理论解释。大多数这些理论见解试图解释\textbf{BN}的好处,将它们放在优化,权重标度不变性和正则化的影响上。尽管\textbf{BN}在加速泛化方面取得了不可否认的成功,但在分析上将\textbf{BN}的效果与正则化参数联系起来的差距仍然缺失。本文的目的是提出的数据依赖的正则化参数的\textbf{BN}的分析证明。我们提出了\textbf{BN}作为一个约束优化施加在非\textbf{BN}的权重,通过它,我们证明了它的数据统计依赖的正则化参数的自动调整。我们还给出了分析证明其行为下的噪声输入的情况下,这揭示了信号与噪声调整的正则化参数。我们还通过MNIST数据集实验的经验结果证实了我们的主张。

英文摘要:

Batch normalization is widely used in deep learning to normalize intermediate activations. Deep networks suffer from notoriously increased training complexity, mandating careful initialization of weights, requiring lower learning rates, etc. These issues have been addressed by Batch Normalization (\textbf{BN}), by normalizing the inputs of activations to zero mean and unit standard deviation. Making this batch normalization part of the training process dramatically accelerates the training process of very deep networks. A new field of research has been going on to examine the exact theoretical explanation behind the success of \textbf{BN}. Most of these theoretical insights attempt to explain the benefits of \textbf{BN} by placing them on its influence on optimization, weight scale invariance, and regularization. Despite \textbf{BN} undeniable success in accelerating generalization, the gap of analytically relating the effect of \textbf{BN} to the regularization parameter is still missing. This paper aims to bring out the data-dependent auto-tuning of the regularization parameter by \textbf{BN} with analytical proofs. We have posed \textbf{BN} as a constrained optimization imposed on non-\textbf{BN} weights through which we demonstrate its data statistics dependant auto-tuning of regularization parameter. We have also given analytical proof for its behavior under a noisy input scenario, which reveals the signal vs. noise tuning of the regularization parameter. We have also substantiated our claim with empirical results from the MNIST dataset experiments.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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