Neural architectures for set regression problems aim at learning representations such that good predictions can be made based on the learned representations. This strategy, however, ignores the fact that meaningful intermediate results might be helpful to perform well. We study two new architectures that explicitly model latent intermediate utilities and use non-additive utility aggregation to estimate the set utility based on the latent utilities. We evaluate the new architectures with visual and textual datasets, which have non-additive set utilities due to redundancy and synergy effects. We find that the new architectures perform substantially better in this setup.
This paper studies non-additive utility aggregation for sets. The problem is very interesting. Choquet Integral is used to deal with set input. The authors propose two architectures. The two architectures, though not novel enough, are towards representing “non-additive utility”.
However, the experimental comparison is not fair, the description of the model (e.g. how Choquet is integrated into the model and help to learn “intermediate meaningful results”) is not clear, some claims are not true.
First, the authors claim that they are the first to combine Choquet integral with deep learning. However, there are a few, though not many, works in the literature trying to combine Choquet integral with deep learning. For example, “Fuzzy Choquet Integration of Deep Convolutional Neural Networks for Remote Sensing” by Derek T. Anderson et al. 
Second, the authors claim they are using/motivated by Choquet integral, but do not have any (appendix) sections to explain how this mathematical tool is really integrated into their models. How do you guarantee that the representation learned by the neural network still obeys the property of Choquet integral? What is your loss or your algorithm? These need to be further clarified.
Third, the comparison to baseline and “DeepSet” is not fair. According to the illustration, it seems that you first obtain “features/representations”. Then the representations are fed to the four architectures you listed in figure one. RNN-based approaches are with better “complexity” comparing to your sum baseline and “Deepset” approach. So, I have some doubts about the experimental results.