The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning

Roberto Bondesan, Max Welling
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:1038-1048, 2021.

Abstract

In this work we develop a quantum field theory formalism for deep learning, where input signals are encoded in Gaussian states, a generalization of Gaussian processes which encode the agent’s uncertainty about the input signal. We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles, dubbed “Hintons”. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing, and provides quantum deformations of neural networks that can be run efficiently on those devices. Finally, we discuss a semi-classical limit of the quantum deformed models which is amenable to classical simulation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-bondesan21a, title = {The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning}, author = {Bondesan, Roberto and Welling, Max}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {1038--1048}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/bondesan21a/bondesan21a.pdf}, url = {https://proceedings.mlr.press/v139/bondesan21a.html}, abstract = {In this work we develop a quantum field theory formalism for deep learning, where input signals are encoded in Gaussian states, a generalization of Gaussian processes which encode the agent’s uncertainty about the input signal. We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles, dubbed “Hintons”. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing, and provides quantum deformations of neural networks that can be run efficiently on those devices. Finally, we discuss a semi-classical limit of the quantum deformed models which is amenable to classical simulation.} }
Endnote
%0 Conference Paper %T The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning %A Roberto Bondesan %A Max Welling %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-bondesan21a %I PMLR %P 1038--1048 %U https://proceedings.mlr.press/v139/bondesan21a.html %V 139 %X In this work we develop a quantum field theory formalism for deep learning, where input signals are encoded in Gaussian states, a generalization of Gaussian processes which encode the agent’s uncertainty about the input signal. We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles, dubbed “Hintons”. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing, and provides quantum deformations of neural networks that can be run efficiently on those devices. Finally, we discuss a semi-classical limit of the quantum deformed models which is amenable to classical simulation.
APA
Bondesan, R. & Welling, M.. (2021). The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:1038-1048 Available from https://proceedings.mlr.press/v139/bondesan21a.html.

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