## 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 language | American English |
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State | Published - 2018 |

Event | 6th International Conference on Learning Representations, ICLR 2018 - Vancouver, Canada Duration: 30 Apr 2018 → 3 May 2018 |

### Conference

Conference | 6th International Conference on Learning Representations, ICLR 2018 |
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Country/Territory | Canada |

City | Vancouver |

Period | 30/04/18 → 3/05/18 |

### Bibliographical note

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