  Deep ensembles have recently gained popularity in the deep learning community
for their conceptual simplicity and efficiency. However, maintaining functional
diversity between ensemble members that are independently trained with gradient
descent is challenging. This can lead to pathologies when adding more ensemble
members, such as a saturation of the ensemble performance, which converges to
the performance of a single model. Moreover, this does not only affect the
quality of its predictions, but even more so the uncertainty estimates of the
ensemble, and thus its performance on out-of-distribution data. We hypothesize
that this limitation can be overcome by discouraging different ensemble members
from collapsing to the same function. To this end, we introduce a kernelized
repulsive term in the update rule of the deep ensembles. We show that this
simple modification not only enforces and maintains diversity among the members
but, even more importantly, transforms the maximum a posteriori inference into
proper Bayesian inference. Namely, we show that the training dynamics of our
proposed repulsive ensembles follow a Wasserstein gradient flow of the KL
divergence with the true posterior. We study repulsive terms in weight and
function space and empirically compare their performance to standard ensembles
and Bayesian baselines on synthetic and real-world prediction tasks.
