The Coverage Principle: A Framework for Understanding Compositional
  Generalization
Authors: name: Hoyeon Chang, name: Jinho Park, name: Hanseul Cho, name: Sohee Yang, name: Miyoung Ko, name: Hyeonbin Hwang, name: Seungpil Won, name: Dohaeng Lee, name: Youbin Ahn, name: Minjoon Seo

Large language models excel at pattern matching, yet often fall short in
systematic compositional generalization. We propose the coverage principle: a
data-centric framework showing that models relying primarily on pattern
matching for compositional tasks cannot reliably generalize beyond substituting
fragments that yield identical results when used in the same contexts. We
demonstrate that this framework has a strong predictive power for the
generalization capabilities of Transformers. First, we derive and empirically
confirm that the training data required for two-hop generalization grows at
least quadratically with the token set size, and the training data efficiency
does not improve with 20x parameter scaling. Second, for compositional tasks
with path ambiguity where one variable affects the output through multiple
computational paths, we show that Transformers learn context-dependent state
representations that undermine both performance and interoperability. Third,
Chain-of-Thought supervision improves training data efficiency for multi-hop
tasks but still struggles with path ambiguity. Finally, we outline a
mechanism-based taxonomy that distinguishes three ways neural networks
can generalize: structure-based (bounded by coverage), property-based
(leveraging algebraic invariances), and shared-operator (through function
reuse). This conceptual lens contextualizes our results and highlights where
new architectural ideas are needed to achieve systematic compositionally.
Overall, the coverage principle provides a unified lens for understanding
compositional reasoning, and underscores the need for fundamental architectural
or training innovations to achieve truly systematic compositionality.