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Set-input deep networks have recently drawn much interest in computer visionand machine learning. This is in part due to the increasing number of importanttasks such as meta-learning, clustering, and anomaly detection that are definedon set inputs. These networks must take an arbitrary number of input samplesand produce the output invariant to the input set permutation. Severalalgorithms have been recently developed to address this urgent need. Our paperanalyzes these algorithms using both synthetic and real-world datasets, andshows that they are not effective in dealing with common data variations suchas image translation or viewpoint change. To address this limitation, wepropose a permutation-invariant cascaded attentional set operator (PICASO). Thegist of PICASO is a cascade of multihead attention blocks with dynamictemplates. The proposed operator is a stand-alone module that can be adaptedand extended to serve different machine learning tasks. We demonstrate theutilities of PICASO in four diverse scenarios: (i) clustering, (ii) imageclassification under novel viewpoints, (iii) image anomaly detection, and (iv)state prediction. PICASO increases the SmallNORB image classification accuracywith novel viewpoints by about 10% points. For set anomaly detection on CelebAdataset, our model improves the areas under ROC and PR curves dataset by about22% and 10%, respectively. For the state prediction on CLEVR dataset, itimproves the AP by about 40%.

PICASO: Permutation-Invariant Cascaded Attentional Set Operator