Estimating information flow in deep neural networks

Ziv Goldfeld, Ewout Van Den Berg, Kristjan Greenewald, Igor Melnyk, Nam Nguyen, Brian Kingsbury, Yury Polyanskiy

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

20 Scopus citations


We study the estimation of the mutual information I(X;T) between the input X to a deep neural network (DNN) and the output vector T of its th hidden layer (an "internal representation"). Focusing on feedforward networks with fixed weights and noisy internal representations, we develop a rigorous framework for accurate estimation of I(X; T). By relating I(X; T) to information transmission over additive white Gaussian noise channels, we reveal that compression, i.e. reduction in I(X;T) over the course of training, is driven by progressive geometric clustering of the representations of samples from the same class. Experimental results verify this connection. Finally, we shift focus to purely deterministic DNNs, where I(X; T) is provably vacuous, and show that nevertheless, these models also cluster inputs belonging to the same class. The binning-based approximation of I(X; T) employed in past works to measure compression is identified as a measure of clustering, thus clarifying that these experiments were in fact tracking the same clustering phenomenon. Leveraging the clustering perspective, we provide new evidence that compression and generalization may not be causally related and discuss potential future research ideas.

Original languageEnglish
Title of host publication36th International Conference on Machine Learning, ICML 2019
PublisherInternational Machine Learning Society (IMLS)
Number of pages10
ISBN (Electronic)9781510886988
StatePublished - 1 Jan 2019
Externally publishedYes
Event36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States
Duration: 9 Jun 201915 Jun 2019

Publication series

Name36th International Conference on Machine Learning, ICML 2019


Conference36th International Conference on Machine Learning, ICML 2019
Country/TerritoryUnited States
CityLong Beach

ASJC Scopus subject areas

  • Education
  • Computer Science Applications
  • Human-Computer Interaction


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