Generalization despite overfitting in quantum machine learning models

TL;DR

This paper explores how quantum machine learning models can exhibit benign overfitting, similar to classical models, by analyzing their structure and behavior in noisy data scenarios, enhancing understanding of quantum generalization.

Contribution

It characterizes benign overfitting in quantum models by linking quantum circuit structures to overparameterization and generalization phenomena.

Findings

Quantum models can interpolate noisy data with 'spiky' behavior.

Classical Fourier features models relate to quantum model behavior.

Demonstrates benign overfitting in a quantum example.

Abstract

The widespread success of deep neural networks has revealed a surprise in classical machine learning: very complex models often generalize well while simultaneously overfitting training data. This phenomenon of benign overfitting has been studied for a variety of classical models with the goal of better understanding the mechanisms behind deep learning. Characterizing the phenomenon in the context of quantum machine learning might similarly improve our understanding of the relationship between overfitting, overparameterization, and generalization. In this work, we provide a characterization of benign overfitting in quantum models. To do this, we derive the behavior of a classical interpolating Fourier features models for regression on noisy signals, and show how a class of quantum models exhibits analogous features, thereby linking the structure of quantum circuits (such as data-encoding and state preparation operations) to overparameterization and overfitting in quantum models. We intuitively explain these features according to the ability of the quantum model to interpolate noisy data with locally "spiky" behavior and provide a concrete demonstration example of benign overfitting.