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arXiv · 2605.13203

Double Descent, Ensemble Emergence, and Large Model Averaging in High-Dimensional Multimodel Prediction

Ke Chen·Dandan Jiang·Xinyu Zhang
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Abstract

This paper investigates the predictive performance of high-dimensional multimodel prediction, where the number of regressors is comparable to the sample size. Leveraging tools from random matrix theory, we derive the exact limiting out-of-sample risk under a nested model setting and comprehensively characterize the risk landscape. This limiting risk helps to reveal two phenomena: simple weighting inherits the double descent trajectory and its associated variance explosion near the interpolation boundary; strategic weighting triggers an ensemble emergence that suppresses the localized risk surge and yields a globally flat risk surface. Building on this limiting risk, we also propose the Large Model Averaging (LaMA) method, in which we consider the discrepancy between in-sample and out-of-sample risks in the high-dimensional regime. Numerical studies and real data applications confirm that LaMA achieves superior predictive accuracy in high-dimensional environments.

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Ke Chen, Dandan Jiang, Xinyu Zhang. 2026-05-13. Double Descent, Ensemble Emergence, and Large Model Averaging in High-Dimensional Multimodel Prediction. https://arxiv.org/abs/2605.13203

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