Margin-Based Generalization for Quantum Machine Learning with Classical Data Encoding
Abstract
Understanding generalization is essential for assessing the practical viability of quantum machine learning. In many applications, quantum models operate on classical data that must first be encoded into quantum states, making the encoding part of the effective hypothesis class. We develop a margin-based generalization framework for this setting, covering both fixed and trainable quantum data encodings. For fixed encodings, the existing margin bound transfers unchanged. For trainable encodings, we derive a bound using a two-scale covering argument that combines the original margin-dependent term with an additive encoding-capacity term of order Õ(√(L/m)), where L is the number of trainable encoding parameters and m is the training-sample size. Across 19,440 simulated training runs spanning various image datasets, circuit architectures, and optimization settings, the inverse margin performs best among five baseline and two bound-derived complexity measures under conditional-independence and 90th-percentile sign-error criteria, within bootstrap uncertainty. These results provide a unified margin-based view of generalization in quantum machine learning with classical data.
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BibTeX
@misc{ryu2026marginbased,
title = {{Margin-Based Generalization for Quantum Machine Learning with Classical Data Encoding}},
author = {Ju-Young Ryu and Tak Hur and Daniel K. Park},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24426},
eprint = {2610.24426},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24426},
}
RIS
TY - UNPB
TI - Margin-Based Generalization for Quantum Machine Learning with Classical Data Encoding
AU - Ju-Young Ryu
AU - Tak Hur
AU - Daniel K. Park
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24426
UR - https://arxiv.org/abs/2610.24426
AB - Understanding generalization is essential for assessing the practical viability of quantum machine learning. In many applications, quantum models operate on classical data that must first be encoded into quantum states, making the encoding part of the effective hypothesis class. We develop a margin-based generalization framework for this setting, covering both fixed and trainable quantum data encodings. For fixed encodings, the existing margin bound transfers unchanged. For trainable encodings, we derive a bound using a two-scale covering argument that combines the original margin-dependent term with an additive encoding-capacity term of order Õ(√(L/m)), where L is the number of trainable encoding parameters and m is the training-sample size. Across 19,440 simulated training runs spanning various image datasets, circuit architectures, and optimization settings, the inverse margin performs best among five baseline and two bound-derived complexity measures under conditional-independence and 90th-percentile sign-error criteria, within bootstrap uncertainty. These results provide a unified margin-based view of generalization in quantum machine learning with classical data.
ER -