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arXiv 1905.09054cs.LGcs.CVmath.OCstat.ML
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深度神经网络的细粒度优化

Fine-grained Optimization of Deep Neural Networks

Mete Ozay

摘要:

在最近的研究中,理论上推导了深度神经网络(DNN)泛化误差的几个渐近上界。这些边界是DNN的权重的几个范数的函数,例如Frobenius范数和谱范数,并且它们是针对根据DNN的输入和输出通道分组的权重计算的。在这项工作中,我们推测,如果我们可以施加多重约束的权重DNN的上界的权重的范数,并训练的DNN与这些权重,那么我们可以获得经验的泛化误差更接近推导出的理论界,并提高DNN的准确性。为此,我们提出两个问题。首先,我们的目标是获得权重,其不同的范数都由一个常数(例如1.0)上界。为了实现这些界限,我们提出了一个两阶段的重正化过程;(i)根据界限中使用的不同规范对权重进行归一化,以及(ii)对归一化权重进行重新参数化,以设置其规范的恒定和有限的上限。在第二个问题中,我们考虑用这些重正化权重训练DNN。为此,我们首先提出了一种策略,根据DNN中的不同约束来构建权重的联合空间(流形)。接下来,我们提出了一种细粒度SGD算法(FG-SGD),用于优化权重流形,以训练DNN,并确保收敛到最小值。实验结果表明,使用FG-SGD可以提高基线DNN的图像分类精度。

英文摘要:

In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral norms, and they are computed for weights grouped according to either input and output channels of the DNNs. In this work, we conjecture that if we can impose multiple constraints on weights of DNNs to upper bound the norms of the weights, and train the DNNs with these weights, then we can attain empirical generalization errors closer to the derived theoretical bounds, and improve accuracy of the DNNs. To this end, we pose two problems. First, we aim to obtain weights whose different norms are all upper bounded by a constant number, e.g. 1.0. To achieve these bounds, we propose a two-stage renormalization procedure; (i) normalization of weights according to different norms used in the bounds, and (ii) reparameterization of the normalized weights to set a constant and finite upper bound of their norms. In the second problem, we consider training DNNs with these renormalized weights. To this end, we first propose a strategy to construct joint spaces (manifolds) of weights according to different constraints in DNNs. Next, we propose a fine-grained SGD algorithm (FG-SGD) for optimization on the weight manifolds to train DNNs with assurance of convergence to minima. Experimental results show that image classification accuracy of baseline DNNs can be boosted using FG-SGD on collections of manifolds identified by multiple constraints.

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