AI BriefingTransformers Are Inherently Succinct
Key point
It has been theoretically proven that Transformers can represent language far more succinctly than RNNs or finite automata.
Details
This presents Succinctness as a new perspective for evaluating the expressive power of Transformers. Succinctness is a measure of how compactly a given model can describe a language.
The research findings show that fixed-precision Transformers exhibit overwhelming compression efficiency compared to existing models. The specific comparison results are as follows:
- Exponentially more succinct than LTL (Linear Temporal Logic) and RNNs (Recurrent Neural Networks).
- Doubly exponentially more succinct than Finite Automata.
This means that for describing certain languages, a Transformer needs only polynomial-size, whereas representing the same language with LTL or RNNs requires exponential size, and with automata requires doubly exponential size.
This high degree of succinctness is a cause of difficulty for the Verification problem of these models. The problems of checking a Transformer's emptiness or equivalence have been shown to be EXPSPACE-complete, proving them to be computationally intractable.
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