arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节(Veterans Day),12 日无更新
arXiv 2203.15544cs.LGcs.AIcs.DSmath.CTstat.ML
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图神经网络是动态规划器

Graph Neural Networks are Dynamic Programmers

DeepMind(深度思维)

Andrew Dudzik, Petar Veličković

摘要:

最近的进展,神经算法推理与图神经网络(GNNs)的算法对齐的概念支撑。一般来说,如果神经网络的各个组件与目标算法很好地匹配,那么它将更善于学习执行推理任务(就样本复杂性而言)。具体来说,GNN被声称与动态规划(DP)保持一致,DP是一种通用的解决问题的策略,它表达了许多多项式时间算法。然而,这种一致性是否真的得到了证明和理论上的量化?在这里,我们使用范畴论和抽象代数的方法表明,GNN和DP之间存在着错综复杂的联系,远远超出了对Bellman-Ford等个别算法的最初观察。暴露这种联系,我们很容易验证文献中的几个先前的研究结果,为以边缘为中心的任务产生更好的接地GNN架构,并在CLRS算法推理基准上展示实证结果。我们希望我们的阐述将成为构建更强大的算法对齐GNN的基础。

英文摘要:

Recent advances in neural algorithmic reasoning with graph neural networks (GNNs) are propped up by the notion of algorithmic alignment. Broadly, a neural network will be better at learning to execute a reasoning task (in terms of sample complexity) if its individual components align well with the target algorithm. Specifically, GNNs are claimed to align with dynamic programming (DP), a general problem-solving strategy which expresses many polynomial-time algorithms. However, has this alignment truly been demonstrated and theoretically quantified? Here we show, using methods from category theory and abstract algebra, that there exists an intricate connection between GNNs and DP, going well beyond the initial observations over individual algorithms such as Bellman-Ford. Exposing this connection, we easily verify several prior findings in the literature, produce better-grounded GNN architectures for edge-centric tasks, and demonstrate empirical results on the CLRS algorithmic reasoning benchmark. We hope our exposition will serve as a foundation for building stronger algorithmically aligned GNNs.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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