Theoretical Limitations of Ensembles in the Age of Overparameterization

ICLR 2025 Conference Submission12563 Authors

Keywords: Ensembles, Deep Ensembles, Uncertainty Quantification, Overparameterization, Random feature regression, Kernel regression

TL;DR: We theoretically characterize the generalization and uncertainty properties of overparameterized random feature regressors, proving a functional equivalence between ensembles and single (but larger) models under weak assumptions.

Abstract: Classic tree-based ensembles generalize better than any single decision tree. In contrast, recent empirical studies find that modern ensembles of (overparameterized) neural networks may not provide any inherent generalization advantage over single but larger neural networks. This paper clarifies how modern overparameterized ensembles differ from their classic underparameterized counterparts, using ensembles of random feature (RF) regressors as a basis for developing theory. In contrast to the underparameterized regime, where ensembling typically induces regularization and increases generalization, we prove that infinite ensembles of overparameterized RF regressors become pointwise equivalent to (single) infinite-width RF regressors. This equivalence, which is exact for ridgeless models and approximate for small ridge penalties, implies that overparameterized ensembles and single large models exhibit nearly identical generalization. As a consequence, we can characterize the predictive variance amongst ensemble members, and demonstrate that it quantifies the expected effects of increasing capacity rather than capturing any conventional notion of uncertainty. Our results challenge common assumptions about the advantages of ensembles in overparameterized settings, prompting a reconsideration of how well intuitions from underparameterized ensembles transfer to deep ensembles and the overparameterized regime.

Primary Area: learning theory

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 12563