Do Deep Neural Networks Capture Compositionality in Arithmetic Reasoning?

Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics, pages 1351–1362 May 2-6, 2023 ©2023 Association for Computational Linguistics Do Deep Neural Networks Capture Compositionality in Arithmetic Reasoning? Keito Kudo1 Yoichi Aoki1 Tatsuki Kuribayashi1,2 Ana Brassard3,1 Masashi Yoshikawa1 Keisuke Sakaguchi1,3 Kentaro Inui1,3 1Tohoku University 2Langsmith, Inc. 3RIKEN {keito.kudo.q4, youichi.aoki.p2}@dc.tohoku.ac.jp, kuribayashi@tohoku.ac.jp, ana.brassard@riken.jp, {yoshikawa,keisuke.sakaguchi,inui}@tohoku.ac.jp Abstract Compositionality is a pivotal property of sym- bolic reasoning. However, how well recent neu- ral 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 sym- bolic reasoning. We introduce a skill tree on compositionality in arithmetic symbolic rea- soning 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 mod- els struggled most with systematicity, perform- ing poorly even with relatively simple compo- sitions. That difficulty was not resolved even after training the models with intermediate rea- soning steps.1 1 Introduction Integrating symbolic reasoning capabilities into neural models has been a crucial goal of artifi- cial intelligence (Marcus, 2003; d’Avila Garcez and Lamb, 2020). With this in mind, many re- searchers investigated how well modern neural models achieve symbolic reasoning (Lake and Ba- roni, 2018). However, recent studies have reported conflicting results on this; some suggest that neu- ral models can solve complex multi-hop reason- ing (Clark et al., 2020), while others claim that models struggle even with performing simple sym- bolic operations (Qian et al., 2022). As a step toward further understanding neu- ral models’ symbolic reasoning ability, this study systematically analyzes recently published pre- trained seq2seq models using a carefully controlled dataset of multi-hop arithmetic symbolic reasoning. 1Our code and data are available at https://github. com/keitokudo/dentaku_skill_tree. A=1+2, A=? Systematicity A=1, B=2, B=? A=1, B=2, C=3, C=? Productivity Substitutivity A=1+2, B=2+3, B=? A=1, B=2, B=? A=1, B=2, B=? (train data) (test data) α=1, β=2, γ=? Figure 1: Three dimensionalities of compositionality in arithmetic symbolic reasoning Specifically, our study empirically evaluates the models’ ability to generalize the compositionality underlying arithmetic reasoning, where we explore three dimensions of compositionality: (i) system- aticity, (ii) productivity, and (iii) substitutivity, as illustrated in Figure 1. Capturing compositionality is crucial in performing symbolic reasoning since compositionality is a pivotal property of generaliz- ability over training instances. To systematically explore the models’ compo- sition ability, we introduce a skill tree on compo- sitionality that defined the hierarchical levels of complexity in arithmetic symbolic reasoning, as il- lustrated in Figure 2. Using this hierarchy as a lens, we identify the limitations of the neural seq2seq models in capturing the compositionality in arith- metic symbolic reasoning. Our major findings can be summarized as follows: • Among the three types of composition, the models struggled most with systematicity, performing poorly even with relatively simple compositions. • The major difficulty in systematicity was in the access to intermediate information that is …

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