Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs
This addresses the challenge of handling variable-size inputs in machine learning, particularly for tasks like set or graph processing, with incremental improvements over existing approaches.
The paper tackles the problem of learning permutation-invariant functions for variable-size inputs by introducing Janossy pooling, which expresses such functions as averages over all input reorderings, and demonstrates improved performance over state-of-the-art methods in experiments.
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.