Shaping double descent in quantum extreme learning through model design
Abstract
Increasing capacity can induce a machine learning model to generalize worse until it perfectly interpolates the training data, and better once it moves beyond interpolation. This inversion, known as \emph{double descent}, is well understood for independent features. For correlated features, its shape is governed by the spectrum of the feature covariance, but existing analyses typically yield only implicit equations. We first close this gap for classical linear regression, analytically characterizing the entire risk curve through two quantities, namely the condition number of the feature population covariance and a spectral measure of correlation strength. Then, we apply this theory on quantum models, focusing on quantum extreme learning machines (QELMs). We show that three tunable design knobs, \textit{i.e.,} encoding strength, input reuploads, and measurement shots, each regularize the QELM output covariance, and derive conditions under which the interpolation threshold remains stable. Finite measurement shot noise can be leveraged to guarantee this stability. Numerical experiments confirm each prediction, yielding concrete design principles for QELMs that generalize well beyond interpolation.
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BibTeX
@misc{meyer2026shaping,
title = {{Shaping double descent in quantum extreme learning through model design}},
author = {Sabri Meyer and Ege Yilmaz and Aurelien Lucchi and Francesco Tacchino and Francesco Scala},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06581},
eprint = {2610.06581},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06581},
}
RIS
TY - UNPB
TI - Shaping double descent in quantum extreme learning through model design
AU - Sabri Meyer
AU - Ege Yilmaz
AU - Aurelien Lucchi
AU - Francesco Tacchino
AU - Francesco Scala
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06581
UR - https://arxiv.org/abs/2610.06581
AB - Increasing capacity can induce a machine learning model to generalize worse until it perfectly interpolates the training data, and better once it moves beyond interpolation. This inversion, known as \emph{double descent}, is well understood for independent features. For correlated features, its shape is governed by the spectrum of the feature covariance, but existing analyses typically yield only implicit equations. We first close this gap for classical linear regression, analytically characterizing the entire risk curve through two quantities, namely the condition number of the feature population covariance and a spectral measure of correlation strength. Then, we apply this theory on quantum models, focusing on quantum extreme learning machines (QELMs). We show that three tunable design knobs, \textit{i.e.,} encoding strength, input reuploads, and measurement shots, each regularize the QELM output covariance, and derive conditions under which the interpolation threshold remains stable. Finite measurement shot noise can be leveraged to guarantee this stability. Numerical experiments confirm each prediction, yielding concrete design principles for QELMs that generalize well beyond interpolation.
ER -