Deep Ensembles: A Loss Landscape Perspective

Stanislav Fort, Clara Huiyi Hu, Balaji Lakshminarayanan

TL;DR: We study deep ensembles through the lens of loss landscape and the space of predictions, demonstrating that the decorrelation power of random initializations is unmatched by subspace sampling that only explores a single mode.

Abstract: Deep ensembles have been empirically shown to be a promising approach for improving accuracy, uncertainty and out-of-distribution robustness of deep learning models. While deep ensembles were theoretically motivated by the bootstrap, non-bootstrap ensembles trained with just random initialization also perform well in practice, which suggests that there could be other explanations for why deep ensembles work well. Bayesian neural networks, which learn distributions over the parameters of the network, are theoretically well-motivated by Bayesian principles, but do not perform as well as deep ensembles in practice, particularly under dataset shift. One possible explanation for this gap between theory and practice is that popular scalable approximate Bayesian methods tend to focus on a single mode, whereas deep ensembles tend to explore diverse modes in function space. We investigate this hypothesis by building on recent work on understanding the loss landscape of neural networks and adding our own exploration to measure the similarity of functions in the space of predictions. Our results show that random initializations explore entirely different modes, while functions along an optimization trajectory or sampled from the subspace thereof cluster within a single mode predictions-wise, while often deviating significantly in the weight space. We demonstrate that while low-loss connectors between modes exist, they are not connected in the space of predictions. Developing the concept of the diversity--accuracy plane, we show that the decorrelation power of random initializations is unmatched by popular subspace sampling methods.

Keywords: loss landscape, deep ensemble, subspace, tunnel, low loss, connector, weight averaging, dropout, gaussian, connectivity, diversity, function space

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:1912.02757/code)