Do Deep Neural Networks Capture Compositionality in Arithmetic Reasoning?
This addresses a fundamental limitation in neural models for symbolic reasoning, which is incremental as it builds on existing methods to test compositionality.
The study investigated whether deep neural networks capture compositionality in arithmetic reasoning, finding that models struggled most with systematicity, performing poorly even on simple compositions, and this difficulty persisted despite training with intermediate steps.
Compositionality is a pivotal property of symbolic reasoning. However, how well recent neural models capture compositionality remains underexplored in the symbolic reasoning tasks. This study empirically addresses this question by systematically examining recently published pre-trained seq2seq models with a carefully controlled dataset of multi-hop arithmetic symbolic reasoning. We introduce a skill tree on compositionality in arithmetic symbolic reasoning that defines the hierarchical levels of complexity along with three compositionality dimensions: systematicity, productivity, and substitutivity. Our experiments revealed that among the three types of composition, the models struggled most with systematicity, performing poorly even with relatively simple compositions. That difficulty was not resolved even after training the models with intermediate reasoning steps.