Black hole/quantum machine learning correspondence

TL;DR

This paper draws a conceptual parallel between black hole information retrieval and quantum machine learning, suggesting that the Page time corresponds to an interpolation threshold where test error decreases despite overparameterization.

Contribution

It introduces a novel analogy linking black hole physics with quantum machine learning, using the Marchenko-Pastur law to analyze error variance and subsystem rank changes.

Findings

Test error decreases after Page time despite overparameterization

Transition in subsystem rank structure correlates with error behavior

Black hole information paradox and double descent phenomenon are conceptually connected

Abstract

We explore a potential connection between the black hole information paradox and the double descent phenomenon in quantum machine learning. Information retrieval from Hawking radiation can be viewed through the lens of quantum linear regression over black hole microstates, with the Page time corresponding to the interpolation threshold, beyond which test error decreases despite overparameterization. Using the Marchenko-Pastur law, we derive the variance in test error for the quantum linear regression problem and show that the transition across the Page time is associated with a change in the rank structure of subsystems. This observation suggests a conceptual parallel between black hole physics and machine learning that may provide new perspectives for both fields.