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arXiv 1503.02406cs.LG
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深度学习与信息瓶颈原理

Deep Learning and the Information Bottleneck Principle

The Edmond and Lilly Safra Center for Brain Sciences, Hebrew University of Jerusalem(耶路撒冷希伯来大学埃德蒙与莉莉·萨夫拉脑科学中心);School of Engineering and Computer Science, Hebrew University of Jerusalem(耶路撒冷希伯来大学工程与计算机科学学院)

Naftali Tishby, Noga Zaslavsky

摘要:

深度神经网络(DNN)是通过信息瓶颈(IB)原理的理论框架进行分析的。我们首先证明了任何DNN都可以通过层与输入和输出变量之间的互信息来量化。使用这种表示,我们可以计算DNN的最佳信息论极限,并获得有限样本泛化界。接近理论极限的优点可以通过泛化界和网络的简单性来量化。我们认为,这两个最佳的架构,层数和功能/连接在每一层,有关的信息瓶颈权衡的分叉点,即,相对于输出层的输入层的相关压缩。分层网络中的分层表示自然对应于沿着信息曲线的结构相变。我们相信,这种新的见解可以带来新的最优性界限和深度学习算法。

英文摘要:

Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output variables. Using this representation we can calculate the optimal information theoretic limits of the DNN and obtain finite sample generalization bounds. The advantage of getting closer to the theoretical limit is quantifiable both by the generalization bound and by the network's simplicity. We argue that both the optimal architecture, number of layers and features/connections at each layer, are related to the bifurcation points of the information bottleneck tradeoff, namely, relevant compression of the input layer with respect to the output layer. The hierarchical representations at the layered network naturally correspond to the structural phase transitions along the information curve. We believe that this new insight can lead to new optimality bounds and deep learning algorithms.

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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