随机梯度下降,按照数据生成分布抽取m个样本,通过计算他们梯度的平均值来更新梯度。

VIP内容

题目: On the Generalization Benefit of Noise in Stochastic Gradient Descent

摘要:

长期以来一直有人认为,在深度神经网络中,小批量随机梯度下降比大批量梯度下降具有更好的泛化能力。但是,最近的论文对此主张提出了质疑,认为这种影响仅是批处理量较大时超优化超参数调整或计算预算不足的结果。在本文中,我们对一系列流行的模型进行了精心设计的实验并进行了严格的超参数扫描,这证明了小批量或中等批量都可以大大胜过测试集上的超大批量。即使两个模型都经过相同数量的迭代训练并且大批量实现较小的训练损失时,也会发生这种情况。我们的结果证实,随机梯度中的噪声可以增强泛化能力。我们研究最佳学习率时间表如何随着epoch budget的增长而变化,并基于SGD动力学的随机微分方程视角为我们的观察提供理论解释。

成为VIP会员查看完整内容
0
15

最新内容

The question of how and why the phenomenon of mode connectivity occurs in training deep neural networks has gained remarkable attention in the research community. From a theoretical perspective, two possible explanations have been proposed: (i) the loss function has connected sublevel sets, and (ii) the solutions found by stochastic gradient descent are dropout stable. While these explanations provide insights into the phenomenon, their assumptions are not always satisfied in practice. In particular, the first approach requires the network to have one layer with order of $N$ neurons ($N$ being the number of training samples), while the second one requires the loss to be almost invariant after removing half of the neurons at each layer (up to some rescaling of the remaining ones). In this work, we improve both conditions by exploiting the quality of the features at every intermediate layer together with a milder over-parameterization condition. More specifically, we show that: (i) under generic assumptions on the features of intermediate layers, it suffices that the last two hidden layers have order of $\sqrt{N}$ neurons, and (ii) if subsets of features at each layer are linearly separable, then no over-parameterization is needed to show the connectivity. Our experiments confirm that the proposed condition ensures the connectivity of solutions found by stochastic gradient descent, even in settings where the previous requirements do not hold.

0
0
下载
预览

最新论文

The question of how and why the phenomenon of mode connectivity occurs in training deep neural networks has gained remarkable attention in the research community. From a theoretical perspective, two possible explanations have been proposed: (i) the loss function has connected sublevel sets, and (ii) the solutions found by stochastic gradient descent are dropout stable. While these explanations provide insights into the phenomenon, their assumptions are not always satisfied in practice. In particular, the first approach requires the network to have one layer with order of $N$ neurons ($N$ being the number of training samples), while the second one requires the loss to be almost invariant after removing half of the neurons at each layer (up to some rescaling of the remaining ones). In this work, we improve both conditions by exploiting the quality of the features at every intermediate layer together with a milder over-parameterization condition. More specifically, we show that: (i) under generic assumptions on the features of intermediate layers, it suffices that the last two hidden layers have order of $\sqrt{N}$ neurons, and (ii) if subsets of features at each layer are linearly separable, then no over-parameterization is needed to show the connectivity. Our experiments confirm that the proposed condition ensures the connectivity of solutions found by stochastic gradient descent, even in settings where the previous requirements do not hold.

0
0
下载
预览
Top