Paper:
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 diversityaccuracy plane, we show that the decorrelation power of random initializations is unmatched by popular subspace sampling methods.

Review:
This paper analyzes ensembling methods in deep learning from the perspective of the loss landscapes. The authors empirically show that popular methods for learning Bayesian neural networks produce samples with limited diversity in the function space compared to modes of the loss found using different random initializations. The paper also considers the low-loss paths connecting independent local optima in the weight-space. The analysis shows that while the values of the loss and accuracy are nearly constant along the paths, the models corresponding to different points on a path define different functions with diverse predictions. The paper also demonstrates the complementary benefits of using subspace sampling/weight averaging in combination with deep ensembles and shows that relative benefits of deep ensembles are higher. 
The paper is well-written. The experiments are described well and the results are presented clearly in highly-detailed and visually-appealing figures. There are occasional statements which are not formulated rigorously enough (see comments below).
The paper presents a thorough experimental study of different ensemble types, their performance, and function space diversity of individual members of an ensemble. In my view, the strongest contribution of the paper is the analysis of the diversity of the predictions for different sampling procedures in comparison to deep ensembles. However, the novelty and the significance of the other contributions are limited (see comments below). Therefore, I consider the paper to be below the acceptance threshold.   
Comments and questions to authors:
1) The practical aspects of different ensembling techniques are not discussed in the paper. While it is known that deep ensembles generally demonstrate stronger performance [1], there is a trade-off between the ensemble performance and training time/memory consumption. The considered alternative ensembling procedures can be favorable in specialized settings (e.g. limited training time and/or memory).
2) It remains unclear to me what new insights does the analysis of the low-loss connectors provide? It is expected (and in fact can be shown analytically) that if the two modes define different functions then intermediate points on a continuous path define functions which are different from those defined by the end-points of the path. This result was also analyzed before from the perspective of the performance of ensembles formed by the intermediate points on the connecting paths (see Fig. 2 right in [2]).
Moreover, I would encourage authors to reformulate the statements on the connectivity in the function space such as: 
-- “We demonstrate that while low-loss connectors between modes exist, they are not connected in the space of predictions.”  (Abstract)
-- “the connectivity in the loss landscape does not imply connectivity in the space of functions” (Discussion)
In my opinion, these claims are somewhat misleading. What does it mean that the modes are disconnected in the function space? Neural networks define continuous functions (w.r.t to both the inputs and the weights), and a connector is continuous path in the weight space which continuously connects the modes in the function space (i.e. a path defines a homotopy between two functions). It is true that two modes correspond to two different functions. However, it is unclear in which sense these functions can be considered to be disconnected. 
[1] Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. In NeurIPS, 2017.
[2] Timur Garipov, Pavel Izmailov, Dmitrii Podoprikhin, Dmitry P Vetrov, and Andrew G Wilson. Loss surfaces, mode connectivity, and fast ensembling of DNNs. In NeurIPS, 2018.