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Hyperparameter Importance of Quantum Neural Networks Across Small Datasets

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Discovery Science (DS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13601))

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Abstract

As restricted quantum computers are slowly becoming a reality, the search for meaningful first applications intensifies. In this domain, one of the more investigated approaches is the use of a special type of quantum circuit – a so-called quantum neural network – to serve as a basis for a machine learning model. Roughly speaking, as the name suggests, a quantum neural network can play a similar role to a neural network. However, specifically for applications in machine learning contexts, very little is known about suitable circuit architectures, or model hyperparameters one should use to achieve good learning performance. In this work, we apply the functional ANOVA framework to quantum neural networks to analyze which of the hyperparameters were most influential for their predictive performance. We analyze one of the most typically used quantum neural network architectures. We then apply this to 7 open-source datasets from the OpenML-CC18 classification benchmark whose number of features is small enough to fit on quantum hardware with less than 20 qubits. Three main levels of importance were detected from the ranking of hyperparameters obtained with functional ANOVA. Our experiment both confirmed expected patterns and revealed new insights. For instance, setting well the learning rate is deemed the most critical hyperparameter in terms of marginal contribution on all datasets, whereas the particular choice of entangling gates used is considered the least important except on one dataset. This work introduces new methodologies to study quantum machine learning models and provides new insights toward quantum model selection.

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Notes

  1. 1.

    A 10-fold cross-validation run in our experiment takes on average 262 minutes for 100 epochs with Tensorflow Quantum [7].

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Acknowledgements

CM and VD acknowledge support from TotalEnergies. This work was supported by the Dutch Research Council (NWO/OCW), as part of the Quantum Software Consortium programme (project number 024.003.037). This research is also supported by the project NEASQC funded from the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 951821).

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Authors and Affiliations

  1. LIACS, Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, Netherlands

    Charles Moussa, Jan N. van Rijn, Thomas Bäck & Vedran Dunjko

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  1. Charles Moussa
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  2. Jan N. van Rijn
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  3. Thomas Bäck
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  4. Vedran Dunjko
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Correspondence to Charles Moussa .

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Editors and Affiliations

  1. University of Montpellier, Montpellier, France

    Poncelet Pascal

  2. INRAE, Montpellier, France

    Dino Ienco

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Moussa, C., van Rijn, J.N., Bäck, T., Dunjko, V. (2022). Hyperparameter Importance of Quantum Neural Networks Across Small Datasets. In: Pascal, P., Ienco, D. (eds) Discovery Science. DS 2022. Lecture Notes in Computer Science(), vol 13601. Springer, Cham. https://doi.org/10.1007/978-3-031-18840-4_3

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  • DOI: https://doi.org/10.1007/978-3-031-18840-4_3

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