Benchmarking Compositionality with Formal Languages

Proceedings of the 29th International Conference on Computational Linguistics, pages 6007–6018 October 12–17, 2022. Benchmarking Compositionality with Formal Languages Josef Valvoda Naomi Saphra Jonathan Rawski Adina Williams Ryan Cotterell University of Cambridge New York University San Jos´e State University FAIR ETH Z¨urich jv406@cam.ac.uk nsaphra@nyu.edu jon.rawski@sjsu.edu adinawilliams@fb.com ryan.cotterell@inf.ethz.ch Abstract Recombining known primitive concepts into larger novel combinations is a quintessentially human cognitive capability. Whether large neural models in NLP can acquire this abil- ity while learning from data is an open ques- tion. In this paper, we investigate this prob- lem from the perspective of formal languages. We use deterministic finite-state transducers to make an unbounded number of datasets with controllable properties governing composition- ality. By randomly sampling over many trans- ducers, we explore which of their properties contribute to learnability of a compositional re- lation by a neural network. We find that the models either learn the relations completely or not at all. The key is transition coverage, set- ting a soft learnability limit at 400 examples per transition. https://github.com/valvoda/ neuralTransducer 1 Introduction Compositionality is a hallmark of human language (Montague, 1970; Partee, 1995; Fodor, 1998). It is arguably a requirement for any model to count as a model of language, or to achieve human-like natural language understanding. Compositionality seems to be such a deep property of language that speakers draw conclusions about the overall meaning of sentences even when the meanings of individual words are not known. For instance, English speakers reading the Jabberwocky (Carroll, 1871) comprehend that the noun phrase slithy toves is built from the composition of the adjective slithy with the plural noun toves, despite lacking a clear understanding of what slithy or toves—let alone their composition—could mean. In cognitive science, whether neural networks can learn to combine a limited number of primitives (in the case of language, word or morphemes) to describe a complex environment has been debated for over 30 years (Fodor and Pylyshyn, 1988; Marcus, 1998). In recent work, researchers have explored the inherent limitations of neural models to exhibit compositionality by analyzing sequence-to- sequence model performance on small, controlled datasets (Lake and Baroni, 2018; Hewitt et al., 2020; Hupkes et al., 2020a; White and Cotterell, 2021; Dankers et al., 2022; White and Cotterell, 2022). However, the conclusions of these studies are often murky. For instance, Lake and Baroni (2018) cast doubt on neural models’ ability to do compositional generalization using their toy SCAN dataset, but shortly thereafter, Bastings et al. (2018) demonstrated that an out-of-the-box sequence-to- sequence model could indeed fully master the task. Instead of hand-crafting small challenge datasets, we propose to test for compositionality by randomly sampling from a whole class of string- to-string functions. In doing so, we draw on two linguistic traditions. On the one hand, we follow Montague’s assertion that no important theoretical difference exists between natural and artificial languages (Montague, 1970). Following this logic, the question of whether neural networks composi- tionally process human language is fundamentally equivalent to asking whether they compositionally process artificial languages. …

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