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Research on transformer expressivity shows whether a transformer is capable of solving a given task, but gives little indication of whether the solution, if learned, is generalizable to longer input lengths. We study this question through normalized exact-solution volume (NESV): the fraction of a bounded parameter regi...
This work studies softmax-attention, multi-layer transformers operating on real values, with very few additional assumptions, and proves limitations on how many bits of a real number a transformer can access.
A polynomial length generalization bound for transformers if the authors adopt compressed strings, via a novel connection to power words is shown, which yields a fine-grained analysis of the C-RASP conjecture that resolves contradicting experimental evidence against it.
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