Black hole/quantum machine learning correspondence

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.