Reviews: Powerset Convolutional Neural Networks

The authors built their work on top of "A discrete signal processing framework for set functions" where powerset convolutions were defined, adding powerset pooling operations and defining powerset convolutional neural networks that can be used to classify set functions. The authors provided a detailed analysis of the kind of patterns that powerset convolutions are sensitive to from a pattern matching perspective, and defined their implementation. The authors recognize the exponential growth of complexity O(n2 n) and that to scale their approach to larger ground sets, which limits the applicability of the current method. The empirical results show that the powerset CNNs perform similarly to the baselines on both the synthetic and real datasets, maybe the tasks chosen are too small or well suited to showcase the proposed powerset CNNs. The authors recognizes the lack of datasets containing set functions well suited for their method, however the current set of experiments weakens the argument than powerset CNNs can handle set functions better than graph-convolutional baselines.