For humans, language production and comprehension is sensitive to the
hierarchical structure of sentences. In natural language processing, past work
has questioned how effectively neural sequence models like transformers capture
this hierarchical structure when generalizing to structurally novel inputs. We
show that transformer language models can learn to generalize hierarchically
after training for extremely long periods -- far beyond the point when
in-domain accuracy has saturated. We call this phenomenon \emph{structural
grokking}. On multiple datasets, structural grokking exhibits inverted U-shaped
scaling in model depth: intermediate-depth models generalize better than both
very deep and very shallow transformers. When analyzing the relationship
between model-internal properties and grokking, we find that optimal depth for
grokking can be identified using the tree-structuredness metric of
\citet{murty2023projections}. Overall, our work provides strong evidence that,
with extended training, vanilla transformers discover and use hierarchical
structure.

本文研究了神经序列和转换语言模型的层次结构泛化能力，发现通过长时间训练，模型能够学习到层次结构的一般性，对模型深度的分析证明浅层和深层不如中等深度的模型性能优秀。此发现证实了香草珂朵莉模型能够发现和使用自然语言中的层次结构。