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About this paper
David Chiang, Peter Cholak
This paper by Chiang and Cholak investigates the theoretical limitations of transformer encoders, demonstrating they can perfectly recognize formal languages like PARITY and FIRST through explicit constructions. The work shows how layer normalization's epsilon parameter impacts classification confidence and proposes log-length scaled attention to improve length generalization, yielding performance gains on both synthetic and real-world machine translation tasks.
Key insights
- A crucial distinction exists between a transformer's recognition capability (theoretical classification), prediction confidence (low cross-entropy), and practical learnability (trainability via optimization).
- The epsilon parameter in layer normalization significantly influences classification confidence, where setting it to zero can theoretically overcome confidence limitations by breaking Lipschitz continuity assumptions.
- Practical learning difficulties for formal languages arise from 'spiky' loss landscapes for PARITY and attention weight 'dilution' on critical tokens for FIRST as sequence length increases.
Summary by alphaXiv.
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