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.

The authors present a neural network architecture for set functions, i.e. to identify a subset within a larger set. The authors provide a clear introduction to the problem in terms of convolutional operators and design CNN architectures on top of [1] through the addition of pooling operations for addressing the set function problem. The resulting networks performed competitively with baseline graph convolutional networks although they were outperformed slightly on subsets of tasks. The reviewers greatly appreciated the presentation of the work as the ideas were well motivated, the explanations were clear and the overall presentation were organized. Reviewers commented on the fact that the experiments were conducted on relatively small datasets.

We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions based on the Laplacian, as it provides not one but several basic shifts, one for each element in the ground set. Prototypical experiments with several set function classification tasks on synthetic datasets and on datasets derived from real-world hypergraphs demonstrate the potential of our new powerset CNNs.

We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions based on the Laplacian, as it provides not one but several basic shifts, one for each element in the ground set. Prototypical experiments with several set function classification tasks on synthetic datasets and on datasets derived from real-world hypergraphs demonstrate the potential of our new powerset CNNs. Papers published at the Neural Information Processing Systems Conference.