Margin-based bounds help predict quantum model learning performance
Margin-Based Generalization for Quantum Machine Learning with Classical Data Encoding
Machine Learning
Summary
Quantum machine learning models need to turn normal data into quantum states before they can work, but how well they learn depends on this step. The authors studied how to measure the model's ability to generalize, or perform well on new data, using something called a margin bound. They found a way to include both fixed and adjustable data encoding in these bounds and tested many setups to see which measure predicted performance best. Their results offer a clearer way to understand and compare quantum learning models working with classical data.
What this means in practice
- •For quantum algorithm engineers: Estimate how well quantum machine learning models will generalize when designing algorithms with trainable data encodings.
- •For quantum hardware developers: Use margin-based complexity measures to guide the design of quantum circuits and data encoding strategies for machine learning tasks.
Authors
Ju-Young Ryu, Tak Hur, Daniel K. Park
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 $\tilde O(\sqrt{L/m})$, 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.