What makes Models Compositional? A Theoretical View: With Supplement
This work addresses the challenge of compositional generalization in language models for AI researchers, offering a theoretical framework to explain empirical failures, but it is incremental as it builds on existing benchmarks and models.
The paper tackles the problem of understanding why sequence processing models fail at compositional generalization by proposing a neuro-symbolic definition of compositional functions and analyzing models like recurrent, convolutional, and attention-based ones to show how their structure relates to expressivity and sample complexity, with theoretical guarantees provided for systematic generalization.
Compositionality is thought to be a key component of language, and various compositional benchmarks have been developed to empirically probe the compositional generalization of existing sequence processing models. These benchmarks often highlight failures of existing models, but it is not clear why these models fail in this way. In this paper, we seek to theoretically understand the role the compositional structure of the models plays in these failures and how this structure relates to their expressivity and sample complexity. We propose a general neuro-symbolic definition of compositional functions and their compositional complexity. We then show how various existing general and special purpose sequence processing models (such as recurrent, convolution and attention-based ones) fit this definition and use it to analyze their compositional complexity. Finally, we provide theoretical guarantees for the expressivity and systematic generalization of compositional models that explicitly depend on our proposed definition and highlighting factors which drive poor empirical performance.