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Compositionality is a pivotal property of symbolic reasoning. However, howwell recent neural models capture compositionality remains underexplored in thesymbolic reasoning tasks. This study empirically addresses this question bysystematically examining recently published pre-trained seq2seq models with acarefully controlled dataset of multi-hop arithmetic symbolic reasoning. Weintroduce a skill tree on compositionality in arithmetic symbolic reasoningthat defines the hierarchical levels of complexity along with threecompositionality dimensions: systematicity, productivity, and substitutivity.Our experiments revealed that among the three types of composition, the modelsstruggled most with systematicity, performing poorly even with relativelysimple compositions. That difficulty was not resolved even after training themodels with intermediate reasoning steps.

Do Deep Neural Networks Capture Compositionality in Arithmetic Reasoning?