The Deep Equilibrium Algorithmic Reasoner

Abstract

Recent work on neural algorithmic reasoning has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. Doing so, however, has always used a recurrent architecture, where each iteration of the GNN aligns with an algorithm's iteration. Since an algorithm's solution is often an equilibrium, we conjecture and empirically validate that one can train a network to solve algorithmic problems by directly finding the equilibrium. Note that this does not require matching each GNN iteration with a step of the algorithm.