Understanding the Curse of Unrolling

Fuente: arXiv
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Autores principales: Mehmood, Sheheryar, Knoll, Florian, Ochs, Peter
Formato: Preprint
Publicado: 2026
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author Mehmood, Sheheryar
Knoll, Florian
Ochs, Peter
author_facet Mehmood, Sheheryar
Knoll, Florian
Ochs, Peter
contents Algorithm unrolling is ubiquitous in machine learning, particularly in hyperparameter optimization and meta-learning, where Jacobians of solution mappings are computed by differentiating through iterative algorithms. Although unrolling is known to yield asymptotically correct Jacobians under suitable conditions, recent work has shown that the derivative iterates may initially diverge from the true Jacobian, a phenomenon known as the curse of unrolling. In this work, we provide a non-asymptotic analysis that explains the origin of this behavior and identifies the algorithmic factors that govern it. We show that truncating early iterations of the derivative computation mitigates the curse while simultaneously reducing memory requirements. Finally, we demonstrate that warm-starting in bilevel optimization naturally induces an implicit form of truncation, providing a practical remedy. Our theoretical findings are supported by numerical experiments on representative examples.
format Preprint
id arxiv_https___arxiv_org_abs_2602_19733
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Understanding the Curse of Unrolling
Mehmood, Sheheryar
Knoll, Florian
Ochs, Peter
Machine Learning
Optimization and Control
Algorithm unrolling is ubiquitous in machine learning, particularly in hyperparameter optimization and meta-learning, where Jacobians of solution mappings are computed by differentiating through iterative algorithms. Although unrolling is known to yield asymptotically correct Jacobians under suitable conditions, recent work has shown that the derivative iterates may initially diverge from the true Jacobian, a phenomenon known as the curse of unrolling. In this work, we provide a non-asymptotic analysis that explains the origin of this behavior and identifies the algorithmic factors that govern it. We show that truncating early iterations of the derivative computation mitigates the curse while simultaneously reducing memory requirements. Finally, we demonstrate that warm-starting in bilevel optimization naturally induces an implicit form of truncation, providing a practical remedy. Our theoretical findings are supported by numerical experiments on representative examples.
title Understanding the Curse of Unrolling
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2602.19733