We study a simple notion of structural invariance that readily suggests a parameter-sharing scheme in deep neural networks. In particular, we define structure as a collection of relations, and derive graph convolution and recurrent neural networks as special cases. We study composition of basic structures in defining models that are invariant to more complex "product" structures such as graph of graphs, sets of images or sequence of sets. For demonstration, our experimental results are focused on the setting where the discrete structure of interest is a set. We present results on several novel and non-trivial problems on sets, including semi-supervised learning using clustering information, point-cloud classification and set outlier detection.
['Siamak Ravanbakhsh', 'Jeff G. Schneider', 'Barnabás Póczos']
Deep Learning with Sets and Point Clouds