Do Deep Neural Networks Capture Compositionality in Arithmetic Reasoning?

TL;DR

This paper investigates how well pre-trained sequence-to-sequence neural models understand compositionality in arithmetic reasoning, revealing significant struggles with systematicity even after training on intermediate steps.

Contribution

It introduces a hierarchical skill tree and three compositionality dimensions to systematically evaluate neural models' reasoning capabilities.

Findings

Models perform poorly on systematicity in arithmetic reasoning.

Training with intermediate steps does not significantly improve systematicity.

The study highlights limitations of current neural models in capturing compositional reasoning.

Abstract

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.