Physics of Language Models: Part 1, Context-Free Grammar

We design experiments to study $\textit{how}$ generative language models, like GPT, learn context-free grammars (CFGs) -- diverse language systems with a tree-like structure capturing many aspects of natural languages, programs, and human logics. CFGs are as hard as pushdown automata, and can be ambiguous so that verifying if a string satisfies the rules requires dynamic programming. We construct synthetic data and demonstrate that even for very challenging CFGs, pre-trained transformers can learn to generate sentences with near-perfect accuracy and remarkable $\textit{diversity}$. More importantly, we delve into the $\textit{physical principles}$ behind how transformers learns CFGs. We discover that the hidden states within the transformer implicitly and $\textit{precisely}$ encode the CFG structure (such as putting tree node information exactly on the subtree boundary), and learn to form "boundary to boundary" attentions that resemble dynamic programming. We also cover some extension of CFGs as well as the robustness aspect of transformers against grammar mistakes. Overall, our research provides a comprehensive and empirical understanding of how transformers learn CFGs, and reveals the physical mechanisms utilized by transformers to capture the structure and rules of languages.