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
Citations
More filters
Journal ArticleDOI
Local Intrinsic Dimensional Entropy
Rohan Ghosh,Mehul Motani +1 more
TL;DR: This paper showed that the average value of the local intrinsic dimension of a distribution, denoted as ID-entropy, can serve as a robust entropy measure for continuous spaces, while capturing the data dimensionality.
Posted Content
Locally Sparse Networks for Interpretable Predictions.
TL;DR: In this article, a sample-specific gating mechanism is proposed to identify the subset of most relevant features for each measurement, which is then used to predict the sparsity of local features.
Journal ArticleDOI
Information Bottleneck Analysis of Deep Neural Networks via Lossy Compression
TL;DR: In this article , the authors proposed a framework for conducting information bottleneck analysis of general neural networks, which leverages the stochastic NN method proposed by Goldfeld et al. and incorporates a compression step to overcome the obstacles associated with high dimensionality.
Proceedings ArticleDOI
Distributed Information Bottleneck for a Primitive Gaussian Diamond Channel with Rayleigh Fading
TL;DR: In this article , the authors considered the distributed information bottleneck (D-IB) problem for a primitive Gaussian diamond channel with two relays and Rayleigh fading, and provided an upper bound by assuming that the destination node knows the CSI and the relays can cooperate with each other.
References
More filters
Proceedings Article
ImageNet Classification with Deep Convolutional Neural Networks
TL;DR: The state-of-the-art performance of CNNs was achieved by Deep Convolutional Neural Networks (DCNNs) as discussed by the authors, which consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax.
Book
Elements of information theory
Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Journal ArticleDOI
Reducing the Dimensionality of Data with Neural Networks
TL;DR: In this article, an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data is described.
Journal ArticleDOI
Representation Learning: A Review and New Perspectives
TL;DR: Recent work in the area of unsupervised feature learning and deep learning is reviewed, covering advances in probabilistic models, autoencoders, manifold learning, and deep networks.
Book
Learning Deep Architectures for AI
TL;DR: The motivations and principles regarding learning algorithms for deep architectures, in particular those exploiting as building blocks unsupervised learning of single-layer modelssuch as Restricted Boltzmann Machines, used to construct deeper models such as Deep Belief Networks are discussed.