Theoretical Analysis of Hierarchical Language Recognition and Generation by Transformers without Positional Encoding
This addresses the problem of understanding Transformer capabilities for hierarchical structures in language processing, with potential implications for model design and efficiency.
The study proves that Transformers can efficiently recognize and generate hierarchical languages without positional encoding, using causal masking and a starting token to compute positional information and depth, and suggests that explicit positional encoding may harm generalization across sequence lengths.
In this study, we provide constructive proof that Transformers can recognize and generate hierarchical language efficiently with respect to model size, even without the need for a specific positional encoding. Specifically, we show that causal masking and a starting token enable Transformers to compute positional information and depth within hierarchical structures. We demonstrate that Transformers without positional encoding can generate hierarchical languages. Furthermore, we suggest that explicit positional encoding might have a detrimental effect on generalization with respect to sequence length.