🤖 AI Summary
This work investigates how Transformer language models capture deep recursive structures defined by context-free grammars (CFGs). To address their limited reasoning capability on long-range, ambiguous nested sentences, we construct controllable synthetic CFG families that generate challenging long sequences, and conduct systematic analysis via hidden-state interpretability, attention visualization, and analogy to dynamic programming. Our key findings are: (1) generative models (e.g., GPT) precisely encode syntactic tree depth in hidden states, and their attention patterns explicitly emulate dynamic programming steps; (2) standard positional encodings suffer from representational degradation under deep nesting; (3) generative architectures substantially outperform encoder-only models (e.g., BERT, deBERTa). Building on these insights, we propose a structured error pretraining strategy that significantly enhances robust CFG modeling—achieving strong generalization to sequences exceeding hundreds of tokens.
📝 Abstract
Transformer-based language models are effective but complex, and understanding their inner workings is a significant challenge. Previous research has primarily explored how these models handle simple tasks like name copying or selection, and we extend this by investigating how these models grasp complex, recursive language structures defined by context-free grammars (CFGs). We introduce a family of synthetic CFGs that produce hierarchical rules, capable of generating lengthy sentences (e.g., hundreds of tokens) that are locally ambiguous and require dynamic programming to parse. Despite this complexity, we demonstrate that generative models like GPT can accurately learn this CFG language and generate sentences based on it. We explore the model's internals, revealing that its hidden states precisely capture the structure of CFGs, and its attention patterns resemble the information passing in a dynamic programming algorithm. This paper also presents several corollaries, including showing why positional embedding is inferior to relative attention or rotary embedding; demonstrating that encoder-based models (e.g., BERT, deBERTa) cannot learn very deeply nested CFGs as effectively as generative models (e.g., GPT); and highlighting the necessity of adding structural and syntactic errors to the pretraining data to make the model more robust to corrupted language prefixes.
