Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs

TL;DR

Janossy pooling introduces a flexible framework for learning permutation-invariant functions on variable-size inputs by averaging permutation-sensitive functions over all reorderings, with practical approximations for computational efficiency.

Contribution

The paper proposes Janossy pooling, a novel method for constructing permutation-invariant functions by leveraging permutation-sensitive functions, and introduces approximations for computational tractability.

Findings

Demonstrates improved performance over state-of-the-art methods

Unifies existing permutation-invariant approaches within a single framework

Provides practical approximations for efficient computation

Abstract

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.