Abstract
Weak-to-strong generalization is the phenomenon where a strong student model trained with labels produced by a weak teacher model is able to generalize better than the teacher. In this paper, we study this phenomenon in two-layer random feature networks where the model strength is determined by its width. Using tools from random matrix theory, we derive deterministic equivalents for the population errors of an optimally trained teacher and a student trained with gradient flow. For ReLU activation and a pure spherical harmonic target, we obtain sharp asymptotics under a Gaussian universality assumption, showing a quadratic improvement: the student error scales as the square of the teacher error. These results attain the general lower bound of Medvedev at al (2025). We also analyze how the student behaves under more general stopping times and targets supported on multiple harmonic degrees, characterizing the regimes in which weak-to-strong generalization occurs and identifying the transition between quadratic, non-quadratic, and no improvement.
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Publication details
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Cite this article
APA 7
Oliveira, D., & Paquette, E. (2026). Quadratic Weak-to-Strong Generalization in Random Feature Networks via Random Matrix Theory. https://omanscience.com/en/articles/quadratic-weak-to-strong-generalization-in-random-feature-networks-via-random-matrix-theory
MLA 9
Oliveira, Deborah, and Elliot Paquette. "Quadratic Weak-to-Strong Generalization in Random Feature Networks via Random Matrix Theory." https://omanscience.com/en/articles/quadratic-weak-to-strong-generalization-in-random-feature-networks-via-random-matrix-theory.
Chicago (author–date)
Oliveira, Deborah, and Elliot Paquette. 2026. "Quadratic Weak-to-Strong Generalization in Random Feature Networks via Random Matrix Theory." https://omanscience.com/en/articles/quadratic-weak-to-strong-generalization-in-random-feature-networks-via-random-matrix-theory.
Harvard
Oliveira, D. and Paquette, E. (2026) 'Quadratic Weak-to-Strong Generalization in Random Feature Networks via Random Matrix Theory', Available at: https://omanscience.com/en/articles/quadratic-weak-to-strong-generalization-in-random-feature-networks-via-random-matrix-theory.
Vancouver
Oliveira D, Paquette E. Quadratic Weak-to-Strong Generalization in Random Feature Networks via Random Matrix Theory. https://omanscience.com/en/articles/quadratic-weak-to-strong-generalization-in-random-feature-networks-via-random-matrix-theory
IEEE
D. Oliveira, and E. Paquette, "Quadratic Weak-to-Strong Generalization in Random Feature Networks via Random Matrix Theory," https://omanscience.com/en/articles/quadratic-weak-to-strong-generalization-in-random-feature-networks-via-random-matrix-theory.