On the Ability and Limitations of Transformers to Recognize Formal Languages

Abstract

Transformers have supplanted recurrent models in a large number of NLP tasks. However, the differences in their abilities to model different syntactic properties remain largely unknown. Past works suggest that LSTMs generalize very well on regular languages and have close connections with counter languages. In this work, we systematically study the ability of Transformers to model such languages as well as the role of its individual components in doing so. We first provide a construction of Transformers for a subclass of counter languages, including well-studied languages such as n-ary Boolean Expressions, Dyck-1, and its generalizations. In experiments, we find that Transformers do well on this subclass, and their learned mechanism strongly correlates with our construction. Perhaps surprisingly, in contrast to LSTMs, Transformers do well only on a subset of regular languages with degrading performance as we make languages more complex according to a well-known measure of complexity. Our analysis also provides insights on the role of self-attention mechanism in modeling certain behaviors and the influence of positional encoding schemes on the learning and generalization abilities of the model.

Can the Transformer Learn Nested Recursion with Symbol Masking?

“…In contrast to us, they studied models trained autoregressively only. Bhattamishra et al (2020) studies how autoregressive Transformer architecture learns a subset of formal languages, including Dyck language and its generalisations. In contrast to our study, they examine Shuffle-Dyck languages, which allows constructions like "([)]" and provide theoretical and experimental evidence that the Transformer is capable of learning such a language.…”

On the Practical Ability of Recurrent Neural Networks to Recognize Hierarchical Languages

“…Note that, this is a relatively stringent metric as a correct prediction is obtained only when the model's output is correct at every step as opposed to standard classification tasks. Refer to Bhattamishra et al (2020) for a discussion on the choice of character prediction task and its relation with other tasks such as standard classification and language modeling. Details of the dataset and parameters relevant for reproducibility can be found in section C in Appendix.…”

Self-Attention Networks Can Process Bounded Hierarchical Languages

“…Hahn (2020) proves that (even with positional encodings) hard-attention Transformers cannot model Dyck k , and soft-attention Transformers with bounded Lipschitz continuity cannot model Dyck k with perfect cross entropy. Bhattamishra et al (2020a) prove a soft-attention network with positional masking (but no positional encodings) can solve Dyck 1 but not Dyck 2 . Despite the expressivity issues theoretically posed by the above work, empirical findings have shown Transformers can learn Dyck k from finite samples and outperform LSTM (Ebrahimi et al, 2020).…”

“…In particular, it was recently shown that selfattention networks cannot process various kinds of formal languages (Hahn, 2020;Bhattamishra et al, 2020a), among which particularly notable is Dyck k , the language of well-balanced brackets of k types. By the Chomsky-Schützenberger Theorem (Chomsky and Schützenberger, 1959), any context-free language can be obtained from a Dyck k language through intersections with regular languages and homomorphisms.…”