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This paper establishes a geometric bridge between classical linear models and quantum single-qubit mixed-state classifiers by demonstrating that the latter effectively learns hyperellipsoids rather than standard hyperplanes. The analysis highlights distinct feature importance inductive biases inherent to each approach, offering pedagogical tools for integrating these concepts into machine learning curricula without requiring deep prior knowledge of quantum physics.
From hyperplanes to hyperellipsoids: characterizing the inherent interpretability of linear and single-qubit mixed-state binary classification models
arXiv:2607.15433v1 Announce Type: cross Abstract: We characterize and compare the inherent interpretability offerings of a standard linear model with a single qubit mixed state model for the task of supervised binary classification. A side by side comparison reveals that a single qubit mixed state model for binary classification is just the ``ellipsoid version" of standard linear model classification. More precisely, rather than learning a hyperplane to classify data, we learn a hyperellipsoid. We discuss the consequences of the geometric inductive biases of both models, as well as how each model contains a different feature importance inductive bias. This short characterization offers an accessible route to quantum machine learning (ML) ideas for readers who have zero background in quantum and are only familiar with linear classification in ML. In support of ML pedagogy, we encourage instructors to utilize this piece to smoothly introduce quantum ML ideas into the undergraduate ML classroom.
Abstract:We characterize and compare the inherent interpretability offerings of a standard linear model with a single qubit mixed state model for the task of supervised binary classification. A side by side comparison reveals that a single qubit mixed state model for binary classification is just the ``ellipsoid version" of standard linear model classification. More precisely, rather than learning a hyperplane to classify data, we learn a hyperellipsoid. We discuss the consequences of the geometric inductive biases of both models, as well as how each model contains a different feature importance inductive bias. This short characterization offers an accessible route to quantum machine learning (ML) ideas for readers who have zero background in quantum and are only familiar with linear classification in ML. In support of ML pedagogy, we encourage instructors to utilize this piece to smoothly introduce quantum ML ideas into the undergraduate ML classroom.
Machine Learning (cs.LG); Quantum Physics (quant-ph)
arXiv:2607.15433 [cs.LG]
(or arXiv:2607.15433v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.15433 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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