Deep learning and quantum entanglement: Fundamental connections with implications to network design

Yoav Levine, David Yakira, Nadav Cohen, Amnon Shashua

Research output: Contribution to conferencePaperpeer-review

27 Scopus citations

Abstract

Formal understanding of the inductive bias behind deep convolutional networks, i.e. the relation between the network’s architectural features and the functions it is able to model, is limited. In this work, we establish a fundamental connection between the fields of quantum physics and deep learning, and use it for obtaining novel theoretical observations regarding the inductive bias of convolutional networks. Specifically, we show a structural equivalence between the function realized by a convolutional arithmetic circuit (ConvAC) and a quantum many-body wave function, which facilitates the use of quantum entanglement measures as quantifiers of a deep network’s expressive ability to model correlations. Furthermore, the construction of a deep ConvAC in terms of a quantum Tensor Network is enabled. This allows us to perform a graph-theoretic analysis of a convolutional network, tying its expressiveness to a min-cut in its underlying graph. We demonstrate a practical outcome in the form of a direct control over the inductive bias via the number of channels (width) of each layer. We empirically validate our findings on standard convolutional networks which involve ReLU activations and max pooling. The description of a deep convolutional network in well-defined graph-theoretic tools and the structural connection to quantum entanglement, are two interdisciplinary bridges that are brought forth by this work.

Original languageAmerican English
StatePublished - 2018
Event6th International Conference on Learning Representations, ICLR 2018 - Vancouver, Canada
Duration: 30 Apr 20183 May 2018

Conference

Conference6th International Conference on Learning Representations, ICLR 2018
Country/TerritoryCanada
CityVancouver
Period30/04/183/05/18

Bibliographical note

Publisher Copyright:
© Learning Representations, ICLR 2018 - Conference Track Proceedings.All right reserved.

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