Formal Language Recognition by Hard Attention Transformers: Perspectives from Circuit Complexity
It provides theoretical insights into the computational limits of hard attention Transformers, relevant for researchers in formal language theory and neural network expressivity.
This paper analyzes three Transformer encoder models with different self-attention mechanisms (UHAT, GUHAT, AHAT) to determine their formal language recognition capabilities, showing that UHAT and GUHAT are limited to AC$^0$ languages while AHAT can recognize non-AC$^0$ languages like MAJORITY and DYCK-1.
This paper analyzes three formal models of Transformer encoders that differ in the form of their self-attention mechanism: unique hard attention (UHAT); generalized unique hard attention (GUHAT), which generalizes UHAT; and averaging hard attention (AHAT). We show that UHAT and GUHAT Transformers, viewed as string acceptors, can only recognize formal languages in the complexity class AC$^0$, the class of languages recognizable by families of Boolean circuits of constant depth and polynomial size. This upper bound subsumes Hahn's (2020) results that GUHAT cannot recognize the DYCK languages or the PARITY language, since those languages are outside AC$^0$ (Furst et al., 1984). In contrast, the non-AC$^0$ languages MAJORITY and DYCK-1 are recognizable by AHAT networks, implying that AHAT can recognize languages that UHAT and GUHAT cannot.