Deep learning and the information bottleneck principle
Naftali Tishby,Noga Zaslavsky +1 more
- pp 1-5
TLDR
It is argued 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.Abstract:
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.read more
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Nonlinear Information Bottleneck.
TL;DR: This work proposes a method for performing IB on arbitrarily-distributed discrete and/or continuous X and Y, while allowing for nonlinear encoding and decoding maps, that achieves better performance than the recently-proposed “variational IB” method on several real-world datasets.
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Deep Learning Theory Review: An Optimal Control and Dynamical Systems Perspective.
TL;DR: This article provides one possible way to align existing branches of deep learning theory through the lens of dynamical system and optimal control and provides a principled way for hyper-parameter tuning when optimal control theory is introduced.
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Explaining a black-box using Deep Variational Information Bottleneck Approach
TL;DR: The variational information bottleneck for interpretation, VIBI, is proposed, a system-agnostic interpretable method that provides a brief but comprehensive explanation that is both interpretability and fidelity evaluated by human and quantitative metrics.
Proceedings ArticleDOI
Global Model Interpretation Via Recursive Partitioning
TL;DR: In this article, a binary tree is learned from the contribution matrix, which consists of the contributions of input variables to predicted scores for each single prediction, and a unified process recursively partitions the input variable space by maximizing the difference in the average contribution of the split variable between the divided spaces.
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The Description Length of Deep Learning Models
Léonard Blier,Yann Ollivier +1 more
TL;DR: This work shows experimentally that despite their huge number of parameters, deep neural networks can compress the data losslessly even when taking the cost of encoding the parameters into account.
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