DeepSets is a deep learning framework designed for tasks involving sets of data. Unlike traditional models that operate on fixed-dimensional vectors, DeepSets handles inputs that are sets, and is invariant to the order of elements within the set. The framework is based on permutation-invariant functions, which remain unchanged under any permutation of the set elements. The key idea is to transform each element of the set into a representation, sum these representations, and then apply a non-linear transformation to produce the final output. This approach allows DeepSets to be applied to a wide range of tasks, including supervised and unsupervised learning, as well as set expansion and anomaly detection. The paper presents a theoretical foundation for permutation-invariant functions, showing that any such function can be expressed as a transformation of the sum of individual transformations of the set elements. This result is extended to permutation-equivariant functions, which change in a predictable way when the input set is permuted. The paper also introduces a deep network architecture that can handle sets of varying sizes and is applicable to both supervised and unsupervised learning tasks. The framework is demonstrated on several applications, including population statistic estimation, point cloud classification, set expansion, and outlier detection. The results show that DeepSets outperforms other methods in many cases, particularly in high-dimensional problems where it can scale efficiently. The paper also discusses related works in the field of deep learning and permutation invariance, highlighting the novelty and significance of the proposed framework. Overall, DeepSets provides a powerful and flexible approach to handling data that is naturally represented as sets.DeepSets is a deep learning framework designed for tasks involving sets of data. Unlike traditional models that operate on fixed-dimensional vectors, DeepSets handles inputs that are sets, and is invariant to the order of elements within the set. The framework is based on permutation-invariant functions, which remain unchanged under any permutation of the set elements. The key idea is to transform each element of the set into a representation, sum these representations, and then apply a non-linear transformation to produce the final output. This approach allows DeepSets to be applied to a wide range of tasks, including supervised and unsupervised learning, as well as set expansion and anomaly detection. The paper presents a theoretical foundation for permutation-invariant functions, showing that any such function can be expressed as a transformation of the sum of individual transformations of the set elements. This result is extended to permutation-equivariant functions, which change in a predictable way when the input set is permuted. The paper also introduces a deep network architecture that can handle sets of varying sizes and is applicable to both supervised and unsupervised learning tasks. The framework is demonstrated on several applications, including population statistic estimation, point cloud classification, set expansion, and outlier detection. The results show that DeepSets outperforms other methods in many cases, particularly in high-dimensional problems where it can scale efficiently. The paper also discusses related works in the field of deep learning and permutation invariance, highlighting the novelty and significance of the proposed framework. Overall, DeepSets provides a powerful and flexible approach to handling data that is naturally represented as sets.