Exact-Solution Volume and Length Generalization in Transformers
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 region that achieves an exact solution on every input of length $n$. For fixed-width, single-layer transformers with $\log n$-scaled attention, we establish asymptotic bounds on NESV for four tasks: FIRST ($Θ(1)$), MAJORITY ($Θ(1/(n\log n))$), INDEX ($Θ(1/n^3)$), and PARITY ($0$). These results are consistent with previous empirical results: the faster the exact-solution volume ...
| Authors | Yijia Jessica Zhu, David Chiang |
|---|---|
| Primary category | cs.LG |
| Published | 6 October 2026 |
| Last updated at source | 6 October 2026 |
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