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arXiv 2005.07783cs.LGcs.ITmath.ITstat.ML
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自动编码器的信息平面

On the Information Plane of Autoencoders

Department of Electrical Engineering Universidad de Chile(智利大学电气工程系)

Nicolás I. Tapia, Pablo A. Estévez

摘要:

深度学习中隐藏层的训练动态在理论上知之甚少。近年来,基于信息论中的互信息(互信息)概念,提出了信息平面(IP)来分析它们。信息瓶颈(IB)理论预测层最大化相关信息并压缩不相关信息。由于样本MI估计的局限性,监督学习情况下IP的属性一直存在争议。在这项工作中,我们推导出一个理论收敛的IP自动编码器。该理论预测,具有大瓶颈层大小的理想自动编码器不会压缩输入信息,而小尺寸仅在编码器层中引起压缩。对于实验,我们使用一个基于克矩阵的MI估计最近提出的文献。我们提出了一个新的规则来调整其参数,补偿规模和维度的影响。使用我们提出的规则,我们得到的实验IP更接近理论。我们的自动编码器的理论IP可以作为一个基准,以验证新的方法来估计MI的神经网络。通过这种方式,实验的局限性可以被认识和纠正,有助于正在进行的关于监督学习案例的辩论。

英文摘要:

The training dynamics of hidden layers in deep learning are poorly understood in theory. Recently, the Information Plane (IP) was proposed to analyze them, which is based on the information-theoretic concept of mutual information (MI). The Information Bottleneck (IB) theory predicts that layers maximize relevant information and compress irrelevant information. Due to the limitations in MI estimation from samples, there is an ongoing debate about the properties of the IP for the supervised learning case. In this work, we derive a theoretical convergence for the IP of autoencoders. The theory predicts that ideal autoencoders with a large bottleneck layer size do not compress input information, whereas a small size causes compression only in the encoder layers. For the experiments, we use a Gram-matrix based MI estimator recently proposed in the literature. We propose a new rule to adjust its parameters that compensates scale and dimensionality effects. Using our proposed rule, we obtain experimental IPs closer to the theory. Our theoretical IP for autoencoders could be used as a benchmark to validate new methods to estimate MI in neural networks. In this way, experimental limitations could be recognized and corrected, helping with the ongoing debate on the supervised learning case.

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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