We consider a simple and overarching representation for permutation-invariant
functions of sequences (or multiset functions). Our approach, which we call
Janossy pooling, expresses a permutation-invariant function as the average of a
permutation-sensitive function applied to all reorderings of the input
sequence. This allows us to leverage the rich and mature literature on
permutation-sensitive functions to construct novel and flexible
permutation-invariant functions. If carried out naively, Janossy pooling can be
computationally prohibitive. To allow computational tractability, we consider
three kinds of approximations: canonical orderings of sequences, functions with
$k$-order interactions, and stochastic optimization algorithms with random
permutations. Our framework unifies a variety of existing work in the
literature, and suggests possible modeling and algorithmic extensions. We
explore a few in our experiments, which demonstrate improved performance over
current state-of-the-art methods.

本文提出了 Janossy pooling 方法，可以将置换不变函数表示为输入序列的所有重新排序应用置换敏感函数的平均值，并且通过三种近似方法实现了可计算性可控，实验结果表明该方法在置换不变函数的构建上表现出了比当前最先进的方法更好的性能。