Theoretical Limitations of Ensembles in the Age of Overparameterization

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.
Comment: 26 pages, 12 figures