用平衡方程直接求解算法问题，无需知道迭代步数。
Deep Equilibrium Algorithmic Reasoning
- 将算法求解转化为求解平衡方程，跳过传统迭代过程。
- 在CLRS-30上性能优于传统GNN方法，且不依赖真实步数。
- 适合想加速算法推理模型的研究者和开发者。
神经算法推理（NAR）研究已证明图神经网络（GNN）可学习执行经典算法。然而，以往方法多采用递归架构，每轮GNN迭代对应算法一次迭代。本文从新视角出发：由于算法解常为平衡状态，可直接通过求解平衡方程获得解。该方法无需在训练和测试时知晓算法的真实迭代步数，同时提升了GNN在算法执行任务上的表现，并为加速现有NAR模型迈出一步。基于CLRS-30基准的实证表明，可通过直接寻找平衡点训练网络求解算法问题。本文还讨论了此类模型的实际实现，并提出正则化策略以提升平衡推理能力。
原文摘要 · Abstract (English)
Neural Algorithmic Reasoning (NAR) research has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. However, most previous approaches have always used a recurrent architecture, where each iteration of the GNN matches an iteration of the algorithm. In this paper we study neurally solving algorithms from a different perspective: since the algorithm's solution is often an equilibrium, it is possible to find the solution directly by solving an equilibrium equation. Our approach requires no information on the ground-truth number of steps of the algorithm, both during train and test time. Furthermore, the proposed method improves the performance of GNNs on executing algorithms and is a step towards speeding up existing NAR models. Our empirical evidence, leveraging algorithms from the CLRS-30 benchmark, validates that one can train a network to solve algorithmic problems by directly finding the equilibrium. We discuss the practical implementation of such models and propose regularisations to improve the performance of these equilibrium reasoners.
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