Information plane and compression-gnostic feedback in quantum machine learning

TL;DR

This paper extends the information plane concept to quantum machine learning, using it to develop compression-aware training methods that improve accuracy and convergence in quantum and classical models.

Contribution

It introduces a quantum information plane analysis and proposes compression-agnostic training strategies that enhance learning performance.

Findings

Improved test accuracy on quantum and classical tasks.

Faster convergence with compression-aware algorithms.

Effective regularization via information compression insights.

Abstract

The information plane (Tishby et al. arXiv:physics/0004057, Shwartz-Ziv et al. arXiv:1703.00810) has been proposed as an analytical tool for studying the learning dynamics of neural networks. It provides quantitative insight on how the model approaches the learned state by approximating a minimal sufficient statistics. In this paper we extend this tool to the domain of quantum learning models. In a second step, we study how the insight on how much the model compresses the input data (provided by the information plane) can be used to improve a learning algorithm. Specifically, we consider two ways to do so: via a multiplicative regularization of the loss function, or with a compression-gnostic scheduler of the learning rate (for algorithms based on gradient descent). Both ways turn out to be equivalent in our implementation. Finally, we benchmark the proposed learning algorithms on several classification and regression tasks using variational quantum circuits. The results demonstrate an improvement in test accuracy and convergence speed for both synthetic and real-world datasets. Additionally, with one example we analyzed the impact of the proposed modifications on the performances of neural networks in a classification task.