The paper "Deep Sets" by Manzil Zaheer et al. addresses the problem of designing models for machine learning tasks defined on sets, rather than fixed-dimensional vectors. The authors focus on objective functions that are invariant to permutations of set elements, which are common in various applications such as population statistics estimation, anomaly detection, and cosmology. They provide a characterization of permutation-invariant functions and introduce DeepSets, a deep network architecture that can handle sets and is applicable to both supervised and unsupervised learning tasks. The architecture is designed to be permutation-invariant, and the authors also extend it to be permutation-equivariant, which is useful for tasks like set expansion and outlier detection. The paper includes theoretical results, experimental demonstrations, and comparisons with state-of-the-art methods, showing that DeepSets outperforms other models in several applications, including population statistic estimation, point cloud classification, set expansion, and outlier detection.The paper "Deep Sets" by Manzil Zaheer et al. addresses the problem of designing models for machine learning tasks defined on sets, rather than fixed-dimensional vectors. The authors focus on objective functions that are invariant to permutations of set elements, which are common in various applications such as population statistics estimation, anomaly detection, and cosmology. They provide a characterization of permutation-invariant functions and introduce DeepSets, a deep network architecture that can handle sets and is applicable to both supervised and unsupervised learning tasks. The architecture is designed to be permutation-invariant, and the authors also extend it to be permutation-equivariant, which is useful for tasks like set expansion and outlier detection. The paper includes theoretical results, experimental demonstrations, and comparisons with state-of-the-art methods, showing that DeepSets outperforms other models in several applications, including population statistic estimation, point cloud classification, set expansion, and outlier detection.