arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2502.06751cs.LGcs.AIcs.SIstat.ML
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什么构成了一个好的前馈计算图?

What makes a good feedforward computational graph?

Google DeepMind(谷歌DeepMind);University of Oxford(牛津大学)

Alex Vitvitskyi, João G. M. Araújo, Marc Lackenby, Petar Veličković

AI总结:

本文研究前馈计算图的理想特性,提出保真度和混合时间两个互补度量,通过理论分析与模型性能关联验证了其在评估图选择上的有效性。

摘要:

正如大量关于图重连的文献所暗示的那样,神经网络所采用计算图的选择会对其下游性能产生显著影响。与计算图相关的某些效应,例如欠达和过挤压,甚至可能使模型无法学习某些函数。这些效应中的大多数仅在无向图领域得到了深入研究;然而,近年来人们对前馈计算图(没有任何反向边的有向图)的兴趣显著上升。在本文中,我们研究了前馈计算图的理想特性,发现了两个重要的互补度量:保真度和混合时间,并通过这些度量的视角评估了几种流行的图选择。我们的研究得到了对各种图度量渐近行为的理论分析支持,以及将这些度量与使用相应图的训练神经网络模型的性能相关联的支持。

英文摘要:

As implied by the plethora of literature on graph rewiring, the choice of computational graph employed by a neural network can make a significant impact on its downstream performance. Certain effects related to the computational graph, such as under-reaching and over-squashing, may even render the model incapable of learning certain functions. Most of these effects have only been thoroughly studied in the domain of undirected graphs; however, recent years have seen a significant rise in interest in feedforward computational graphs: directed graphs without any back edges. In this paper, we study the desirable properties of a feedforward computational graph, discovering two important complementary measures: fidelity and mixing time, and evaluating a few popular choices of graphs through the lens of these measures. Our study is backed by both theoretical analyses of the metrics' asymptotic behaviour for various graphs, as well as correlating these metrics to the performance of trained neural network models using the corresponding graphs.

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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