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arXiv 2012.10424cs.LGcs.CV
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深度网络中的分离和集中

Separation and Concentration in Deep Networks

ENS, CNRS, PSL University(巴黎高等师范学院、法国国家科学研究中心、PSL大学);Collège de France(法兰西学院);Flatiron Institute(弗拉蒂伦研究所)

John Zarka, Florentin Guth, Stéphane Mallat

摘要:

数值实验表明,深度神经网络分类器逐渐分离其平均值周围的类分布,在训练集上实现线性可分性,并提高Fisher判别比。我们使用两种类型的运算符来解释这种机制。我们证明了一个没有偏见的整流器应用于符号不变的紧框架可以分离类的手段,并增加费舍尔比。相反,对紧框架进行软阈值处理可以减少类内变异,同时保持类均值。证明了高斯混合模型的方差缩减界。对于图像分类,我们表明,类的手段,可以实现与整流小波紧框架,没有学习的分离。它定义了散射变换。沿散射通道学习$1 \times 1$卷积紧帧并应用软阈值降低类内变异性。由此产生的散射网络在CIFAR-10和ImageNet上达到了ResNet-18的分类精度,层数更少,没有学习偏差。

英文摘要:

Numerical experiments demonstrate that deep neural network classifiers progressively separate class distributions around their mean, achieving linear separability on the training set, and increasing the Fisher discriminant ratio. We explain this mechanism with two types of operators. We prove that a rectifier without biases applied to sign-invariant tight frames can separate class means and increase Fisher ratios. On the opposite, a soft-thresholding on tight frames can reduce within-class variabilities while preserving class means. Variance reduction bounds are proved for Gaussian mixture models. For image classification, we show that separation of class means can be achieved with rectified wavelet tight frames that are not learned. It defines a scattering transform. Learning $1 \times 1$ convolutional tight frames along scattering channels and applying a soft-thresholding reduces within-class variabilities. The resulting scattering network reaches the classification accuracy of ResNet-18 on CIFAR-10 and ImageNet, with fewer layers and no learned biases.

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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