On the Ability and Limitations of Transformers to Recognize Formal Languages
The transformative architecture known as Transformers, primarily introduced by Vaswani et al., has demonstrated impressive capabilities across numerous NLP tasks, replacing traditional RNN and LSTM models in many applications. Despite their empirical success, there remains an incomplete understanding of their abilities to model the syntactic properties of various formal languages. This paper systematically investigates the capacity of Transformers to learn and generalize formal languages, thereby offering insights into both the expressive power and limitations inherent in this model.
This paper focuses on analyzing Transformers' ability to model counter languages and regular languages. Counter languages, being a strict superset of regular languages, present an interesting avenue for exploration as they encapsulate languages that require counting operations, such as the Dyck-1 language or n-ary Boolean Expressions. The paper also explores regular languages, which consist of star-free and non-star-free subclasses, with a particular emphasis on evaluating simpler non-star-free languages and star-free languages with various complexities (dot-depths).
Key Methodological Contributions
The research begins by constructing theoretical foundations that illustrate the expressive strength of Transformers. It demonstrates that Transformers are indeed capable of recognizing a certain subclass of counter languages, such as Shuffle-Dyck and Boolean Expressions. It does so by using the self-attention mechanism to implement counter operations indirectly. Specifically, the self-attention allows for computing cumulative depth-to-length ratios of input sequences for languages like Shuffle-Dyck, closely mirroring the capabilities of a deterministic counter automaton (DCA).
Extensive experiments were conducted on 27 formal languages, with a focus on how Transformers and LSTM models learn and generalize these languages. The paper finds that, when no explicit positional encoding is used (relying solely on positional masking), Transformers can generalize well on generalized counter languages like Shuffle-Dyck and BoolExp-n. However, attempts to model more complex counter languages or those requiring specific reset operations were less successful, particularly when limited single-layer networks were employed.
Numerical and Comparative Insights
The experiments demonstrated that while Transformers can model some star-free languages with dot-depth 1, the results with more complex star-free regular languages and non-star-free regular languages are less promising. The tests underscore a key limitation: Transformers showed limited prowess in recognizing languages that involve intrinsic periodicity, modular counting, or maintaining more sophisticated counter states. For example, the language (aa)∗ posed a challenge, with performance heavily dependent on the design and training of positional encodings, underscoring the rigidity imposed by the self-attention mechanism’s reliance on its positional information.
Transformers fare well with Dyck-1 without explicit positional encodings, yet they struggle with the related language Dn for n>1, indicating that explicit encodings or tailored embeddings might be required to alleviate these issues. The scrutiny also exposed that potential solutions might involve enhancing the expressivity of positional encodings, which is critical for capturing and generalizing pattern periodicity beyond training data seen lengths.
Implications and Future Directions
These findings call for a reassessment of how Transformers are employed and adapted for tasks involving formal languages and algebraic computations. While the intrinsic architecture of Transformers exhibits a natural proclivity for learning hierarchical sentence structures in natural language tasks, adaptations or novelties in architecture, such as learnable positional encodings or augmented layers, might impart better modeling of formal language properties.
Future research could focus on extending this analysis to more complex language families like context-sensitive languages. Moreover, theoretical examination will be crucial to precisely mapping Transformers' potential with various formal language subclasses. Practical advancements could also involve designing neural models that integrate elements of recurrence or enhanced memory-augmentation to mirror the flexibility and comprehensive abilities observed in traditional models like LSTMs.
In conclusion, while Transformers have shown remarkable capacity in some formal language settings, they have decisive limitations that ought to shape their design, training strategies, and application scope in computational linguistics and beyond. This paper lays the groundwork for improved understanding and innovations targeted at these limitations, advancing both theoretical and practical fronts in sequential neural computation.