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Computer Science > Machine Learning

arXiv:2301.10743 (cs)
[Submitted on 25 Jan 2023]

Title:Tighter Bounds on the Expressivity of Transformer Encoders

Authors:David Chiang, Peter Cholak, Anand Pillay
Download a PDF of the paper titled Tighter Bounds on the Expressivity
of Transformer Encoders, by David Chiang and Peter Cholak and Anand
Pillay
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    Abstract: Characterizing neural networks in terms of
    better-understood formal systems has the potential to yield new
    insights into the power and limitations of these networks. Doing
    so for transformers remains an active area of research.
    Bhattamishra and others have shown that transformer encoders are
    at least as expressive as a certain kind of counter machine,
    while Merrill and Sabharwal have shown that fixed-precision
    transformer encoders recognize only languages in uniform $TC^0$.
    We connect and strengthen these results by identifying a variant
    of first-order logic with counting quantifiers that is
    simultaneously an upper bound for fixed-precision transformer
    encoders and a lower bound for transformer encoders. This brings
    us much closer than before to an exact characterization of the
    languages that transformer encoders recognize.

Subjects: Machine Learning (cs.LG); Formal Languages and Automata
          Theory (cs.FL); Logic in Computer Science (cs.LO)
Cite as:  arXiv:2301.10743 [cs.LG]
          (or arXiv:2301.10743v1 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2301.10743
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: David Chiang [view email]
[v1] Wed, 25 Jan 2023 18:05:55 UTC (48 KB)
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