From hyperplanes to hyperellipsoids: characterizing the inherent interpretability of linear and single-qubit mixed-state binary classification models
Machine Learning
Summary
The authors compare how a basic linear model and a quantum-inspired single qubit mixed state model classify data into two groups. They find that while the linear model draws a flat dividing line (a hyperplane), the quantum model creates a curved boundary shaped like a stretched sphere (a hyperellipsoid). This difference changes how each model views and weighs features when making decisions. The authors aim to help beginners understand quantum machine learning by showing it as a slight extension of familiar linear models. They suggest teachers can use this insight to introduce quantum ideas in regular machine learning classes.
Authors
Kaitlin Gili
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.