Neural Algorithmic Reasoning (NAR) is a research area focused on designing
neural architectures that can reliably capture classical computation, usually
by learning to execute algorithms. A typical approach is to rely on Graph
Neural Network (GNN) architectures, which encode inputs in high-dimensional
latent spaces that are repeatedly transformed during the execution of the
algorithm. In this work we perform a detailed analysis of the structure of the
latent space induced by the GNN when executing algorithms. We identify two
possible failure modes: (i) loss of resolution, making it hard to distinguish
similar values; (ii) inability to deal with values outside the range observed
during training. We propose to solve the first issue by relying on a softmax
aggregator, and propose to decay the latent space in order to deal with
out-of-range values. We show that these changes lead to improvements on the
majority of algorithms in the standard CLRS-30 benchmark when using the
state-of-the-art Triplet-GMPNN processor. Our code is available at
\href{https://github.com/mirjanic/nar-latent-spaces}{this https URL}.

神经算法推理 (NAR) 是一个研究领域，旨在设计神经网络结构，能够可靠地捕捉经典计算，通常通过学习执行算法。该研究分析了图神经网络 (GNN) 在执行算法时所产生的潜在空间结构，并提出了解决失去分辨率和处理训练范围之外值的方法。通过在基准测试中使用最先进的 Triplet-GMPNN 处理器，我们表明这些改变可以改善大多数算法的性能。