arXiv Open Access 2022

Formal Language Recognition by Hard Attention Transformers: Perspectives from Circuit Complexity

Yiding Hao Dana Angluin Robert Frank

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Abstrak

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.

Topik & Kata Kunci

cs.CC cs.AI cs.CL cs.FL cs.LG

Penulis (3)

Yiding Hao

Dana Angluin

Robert Frank

Format Sitasi

APA MLA BibTeX

Hao, Y., Angluin, D., Frank, R. (2022). Formal Language Recognition by Hard Attention Transformers: Perspectives from Circuit Complexity. https://arxiv.org/abs/2204.06618

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓